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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | none | [
"none"
] | null | null | For an array $b$ of length $m$ we define the function $f$ as
where $\oplus$ is [bitwise exclusive OR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
For example, $f(1,2,4,8)=f(1\oplus2,2\oplus4,4\oplus8)=f(3,6,12)=f(3\oplus6,6\oplus12)=f(5,10)=f(5\oplus10)=f(15)=15$
You are given an array $a$ and a few queries. Each query is represented as two integers $l$ and $r$. The answer is the maximum value of $f$ on all continuous subsegments of the array $a_l, a_{l+1}, \ldots, a_r$. | The first line contains a single integer $n$ ($1 \le n \le 5000$)Β β the length of $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2^{30}-1$)Β β the elements of the array.
The third line contains a single integer $q$ ($1 \le q \le 100\,000$)Β β the number of queries.
Each of the next $q$ lines contains a query represented as two integers $l$, $r$ ($1 \le l \le r \le n$). | Print $q$ linesΒ β the answers for the queries. | [
"3\n8 4 1\n2\n2 3\n1 2\n",
"6\n1 2 4 8 16 32\n4\n1 6\n2 5\n3 4\n1 2\n"
] | [
"5\n12\n",
"60\n30\n12\n3\n"
] | In first sample in both queries the maximum value of the function is reached on the subsegment that is equal to the whole segment.
In second sample, optimal segment for first query are $[3,6]$, for second query β $[2,5]$, for third β $[3,4]$, for fourth β $[1,2]$. | [
{
"input": "3\n8 4 1\n2\n2 3\n1 2",
"output": "5\n12"
},
{
"input": "6\n1 2 4 8 16 32\n4\n1 6\n2 5\n3 4\n1 2",
"output": "60\n30\n12\n3"
}
] | 2,000 | 94,617,600 | 0 | 4,573 |
|
792 | Counting-out Rhyme | [
"implementation"
] | null | null | *n* children are standing in a circle and playing the counting-out game. Children are numbered clockwise from 1 to *n*. In the beginning, the first child is considered the leader. The game is played in *k* steps. In the *i*-th step the leader counts out *a**i* people in clockwise order, starting from the next person. The last one to be pointed at by the leader is eliminated, and the next player after him becomes the new leader.
For example, if there are children with numbers [8,<=10,<=13,<=14,<=16] currently in the circle, the leader is child 13 and *a**i*<==<=12, then counting-out rhyme ends on child 16, who is eliminated. Child 8 becomes the leader.
You have to write a program which prints the number of the child to be eliminated on every step. | The first line contains two integer numbers *n* and *k* (2<=β€<=*n*<=β€<=100, 1<=β€<=*k*<=β€<=*n*<=-<=1).
The next line contains *k* integer numbers *a*1,<=*a*2,<=...,<=*a**k* (1<=β€<=*a**i*<=β€<=109). | Print *k* numbers, the *i*-th one corresponds to the number of child to be eliminated at the *i*-th step. | [
"7 5\n10 4 11 4 1\n",
"3 2\n2 5\n"
] | [
"4 2 5 6 1 \n",
"3 2 \n"
] | Let's consider first example:
- In the first step child 4 is eliminated, child 5 becomes the leader. - In the second step child 2 is eliminated, child 3 becomes the leader. - In the third step child 5 is eliminated, child 6 becomes the leader. - In the fourth step child 6 is eliminated, child 7 becomes the leader. - In the final step child 1 is eliminated, child 3 becomes the leader. | [
{
"input": "7 5\n10 4 11 4 1",
"output": "4 2 5 6 1 "
},
{
"input": "3 2\n2 5",
"output": "3 2 "
},
{
"input": "2 1\n1",
"output": "2 "
},
{
"input": "2 1\n2",
"output": "1 "
},
{
"input": "2 1\n3",
"output": "2 "
},
{
"input": "10 7\n5 10 4 3 8 10 6",
"output": "6 8 3 9 2 4 10 "
},
{
"input": "10 8\n12 6 12 15 20 8 17 12",
"output": "3 10 6 8 2 9 4 5 "
},
{
"input": "12 10\n76 58 82 54 97 46 17 40 36 15",
"output": "5 9 12 1 3 10 8 11 2 4 "
},
{
"input": "12 6\n76 61 94 15 66 26",
"output": "5 12 6 2 7 3 "
},
{
"input": "90 10\n1045 8705 6077 3282 1459 9809 383 6206 2674 7274",
"output": "56 39 45 20 17 55 14 85 51 33 "
},
{
"input": "100 30\n601771 913885 829106 91674 465657 367068 142461 873149 294276 916519 720701 370006 551782 321506 68525 570684 81178 724855 564907 661130 10112 983124 799801 100639 766045 862312 513021 232094 979480 408554",
"output": "72 89 16 26 85 73 29 99 63 30 8 46 70 19 100 93 36 54 65 77 17 79 62 64 21 69 42 82 68 1 "
},
{
"input": "3 2\n20148340 81473314",
"output": "2 3 "
},
{
"input": "3 2\n301633543 643389490",
"output": "2 3 "
},
{
"input": "6 5\n532623340 628883728 583960589 690950241 488468353",
"output": "5 3 6 1 4 "
},
{
"input": "6 2\n458995521 294343587",
"output": "4 1 "
},
{
"input": "68 1\n5",
"output": "6 "
}
] | 62 | 4,608,000 | 3 | 4,583 |
|
981 | Useful Decomposition | [
"implementation",
"trees"
] | null | null | Ramesses knows a lot about problems involving trees (undirected connected graphs without cycles)!
He created a new useful tree decomposition, but he does not know how to construct it, so he asked you for help!
The decomposition is the splitting the edges of the tree in some simple paths in such a way that each two paths have at least one common vertex. Each edge of the tree should be in exactly one path.
Help Remesses, find such a decomposition of the tree or derermine that there is no such decomposition. | The first line contains a single integer $n$ ($2 \leq n \leq 10^{5}$) the number of nodes in the tree.
Each of the next $n<=-<=1$ lines contains two integers $a_i$ and $b_i$ ($1 \leq a_i, b_i \leq n$, $a_i \neq b_i$)Β β the edges of the tree. It is guaranteed that the given edges form a tree. | If there are no decompositions, print the only line containing "No".
Otherwise in the first line print "Yes", and in the second line print the number of paths in the decomposition $m$.
Each of the next $m$ lines should contain two integers $u_i$, $v_i$ ($1 \leq u_i, v_i \leq n$, $u_i \neq v_i$) denoting that one of the paths in the decomposition is the simple path between nodes $u_i$ and $v_i$.
Each pair of paths in the decomposition should have at least one common vertex, and each edge of the tree should be presented in exactly one path. You can print the paths and the ends of each path in arbitrary order.
If there are multiple decompositions, print any. | [
"4\n1 2\n2 3\n3 4\n",
"6\n1 2\n2 3\n3 4\n2 5\n3 6\n",
"5\n1 2\n1 3\n1 4\n1 5\n"
] | [
"Yes\n1\n1 4\n",
"No\n",
"Yes\n4\n1 2\n1 3\n1 4\n1 5\n"
] | The tree from the first example is shown on the picture below: <img class="tex-graphics" src="https://espresso.codeforces.com/9eb4b4c143d3ad267ae05d1e43341bd368b3088b.png" style="max-width: 100.0%;max-height: 100.0%;"/> The number next to each edge corresponds to the path number in the decomposition. It is easy to see that this decomposition suits the required conditions.
The tree from the second example is shown on the picture below: <img class="tex-graphics" src="https://espresso.codeforces.com/20704b97182d9bcde3321c00a16edcae4d772d93.png" style="max-width: 100.0%;max-height: 100.0%;"/> We can show that there are no valid decompositions of this tree.
The tree from the third example is shown on the picture below: <img class="tex-graphics" src="https://espresso.codeforces.com/357ff9496a4ed4746401160ee6ee63f5d57d81b9.png" style="max-width: 100.0%;max-height: 100.0%;"/> The number next to each edge corresponds to the path number in the decomposition. It is easy to see that this decomposition suits the required conditions. | [
{
"input": "4\n1 2\n2 3\n3 4",
"output": "Yes\n1\n1 4"
},
{
"input": "6\n1 2\n2 3\n3 4\n2 5\n3 6",
"output": "No"
},
{
"input": "5\n1 2\n1 3\n1 4\n1 5",
"output": "Yes\n4\n1 2\n1 3\n1 4\n1 5"
},
{
"input": "2\n1 2",
"output": "Yes\n1\n1 2"
},
{
"input": "8\n1 2\n1 3\n1 4\n1 8\n7 8\n6 8\n5 8",
"output": "No"
},
{
"input": "9\n1 2\n1 3\n1 4\n1 5\n1 6\n6 7\n7 8\n7 9",
"output": "No"
},
{
"input": "3\n2 3\n1 2",
"output": "Yes\n1\n1 3"
}
] | 483 | 8,089,600 | 3 | 4,584 |
|
0 | none | [
"none"
] | null | null | Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but *n* different heads that can read data in parallel.
When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the *i*-th reading head is above the track number *h**i*. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered *h*1, *h*2, ..., *h**n* have been read at the beginning of the operation.
Mike needs to read the data on *m* distinct tracks with numbers *p*1, *p*2, ..., *p**m*. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. | The first line of the input contains two space-separated integers *n*, *m* (1<=β€<=*n*,<=*m*<=β€<=105) β the number of disk heads and the number of tracks to read, accordingly. The second line contains *n* distinct integers *h**i* in ascending order (1<=β€<=*h**i*<=β€<=1010, *h**i*<=<<=*h**i*<=+<=1) β the initial positions of the heads. The third line contains *m* distinct integers *p**i* in ascending order (1<=β€<=*p**i*<=β€<=1010, *p**i*<=<<=*p**i*<=+<=1) - the numbers of tracks to read.
Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is recommended to use the cin, cout streams or the %I64d specifier. | Print a single number β the minimum time required, in seconds, to read all the needed tracks. | [
"3 4\n2 5 6\n1 3 6 8\n",
"3 3\n1 2 3\n1 2 3\n",
"1 2\n165\n142 200\n"
] | [
"2\n",
"0\n",
"81\n"
] | The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way:
1. during the first second move the 1-st head to the left and let it stay there; 1. move the second head to the left twice; 1. move the third head to the right twice (note that the 6-th track has already been read at the beginning).
One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. | [
{
"input": "3 4\n2 5 6\n1 3 6 8",
"output": "2"
},
{
"input": "3 3\n1 2 3\n1 2 3",
"output": "0"
},
{
"input": "1 2\n165\n142 200",
"output": "81"
},
{
"input": "1 2\n5000000000\n1 10000000000",
"output": "14999999998"
},
{
"input": "2 4\n3 12\n1 7 8 14",
"output": "8"
},
{
"input": "3 3\n1 2 3\n2 3 4",
"output": "1"
},
{
"input": "2 1\n1 10\n9",
"output": "1"
},
{
"input": "3 19\n7 10 13\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19",
"output": "6"
},
{
"input": "3 3\n2 3 4\n1 3 5",
"output": "1"
},
{
"input": "10 11\n1 909090909 1818181817 2727272725 3636363633 4545454541 5454545449 6363636357 7272727265 8181818173\n454545455 1363636363 2272727271 3181818179 4090909087 4999999995 5909090903 6818181811 7727272719 8636363627 9545454535",
"output": "1363636362"
},
{
"input": "3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 5000000001 6000000000 8000000000 10000000000",
"output": "4999999999"
},
{
"input": "2 4\n4500000000 5500000000\n5 499999999 5000000001 9999999995",
"output": "5499999993"
},
{
"input": "10 10\n331462447 1369967506 1504296131 2061390288 2309640071 3006707770 4530801731 4544099460 7357049371 9704808257\n754193799 3820869903 4594383880 5685752675 6303322854 6384906441 7863448848 8542634752 9573124462 9665646063",
"output": "1840806981"
},
{
"input": "1 1\n10000000000\n1",
"output": "9999999999"
},
{
"input": "1 1\n1\n10000000000",
"output": "9999999999"
},
{
"input": "10 10\n9999999991 9999999992 9999999993 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 4 5 6 7 8 9 10",
"output": "9999999990"
},
{
"input": "3 12\n477702277 4717363935 8947981095\n477702276 477702304 477702312 477702317 4717363895 4717363896 4717363920 4717363936 8947981094 8947981111 8947981112 8947981135",
"output": "42"
},
{
"input": "10 10\n389151626 1885767612 2609703695 3054567325 4421751790 5636236054 6336088034 7961001379 8631992167 9836923433\n389144165 389158510 1885760728 1885775073 2609696234 2609710579 3054559864 3054574209 4421744329 4421758674",
"output": "21229"
},
{
"input": "1 1\n10000000000\n1",
"output": "9999999999"
}
] | 233 | 21,708,800 | 3 | 4,586 |
|
8 | Obsession with Robots | [
"constructive algorithms",
"graphs",
"implementation"
] | B. Obsession with Robots | 2 | 64 | The whole world got obsessed with robots,and to keep pace with the progress, great Berland's programmer Draude decided to build his own robot. He was working hard at the robot. He taught it to walk the shortest path from one point to another, to record all its movements, but like in many Draude's programs, there was a bug β the robot didn't always walk the shortest path. Fortunately, the robot recorded its own movements correctly. Now Draude wants to find out when his robot functions wrong. Heh, if Draude only remembered the map of the field, where he tested the robot, he would easily say if the robot walked in the right direction or not. But the field map was lost never to be found, that's why he asks you to find out if there exist at least one map, where the path recorded by the robot is the shortest.
The map is an infinite checkered field, where each square is either empty, or contains an obstruction. It is also known that the robot never tries to run into the obstruction. By the recorded robot's movements find out if there exist at least one such map, that it is possible to choose for the robot a starting square (the starting square should be empty) such that when the robot moves from this square its movements coincide with the recorded ones (the robot doesn't run into anything, moving along empty squares only), and the path from the starting square to the end one is the shortest.
In one movement the robot can move into the square (providing there are no obstrutions in this square) that has common sides with the square the robot is currently in. | The first line of the input file contains the recording of the robot's movements. This recording is a non-empty string, consisting of uppercase Latin letters L, R, U and D, standing for movements left, right, up and down respectively. The length of the string does not exceed 100. | In the first line output the only word OK (if the above described map exists), or BUG (if such a map does not exist). | [
"LLUUUR\n",
"RRUULLDD\n"
] | [
"OK\n",
"BUG\n"
] | none | [
{
"input": "LLUUUR",
"output": "OK"
},
{
"input": "RRUULLDD",
"output": "BUG"
},
{
"input": "L",
"output": "OK"
},
{
"input": "R",
"output": "OK"
},
{
"input": "R",
"output": "OK"
},
{
"input": "RR",
"output": "OK"
},
{
"input": "DL",
"output": "OK"
},
{
"input": "LD",
"output": "OK"
},
{
"input": "RUL",
"output": "BUG"
},
{
"input": "ULD",
"output": "BUG"
},
{
"input": "DDR",
"output": "OK"
},
{
"input": "RRDD",
"output": "OK"
},
{
"input": "RRLR",
"output": "BUG"
},
{
"input": "RRDL",
"output": "BUG"
},
{
"input": "LRUD",
"output": "BUG"
},
{
"input": "RDRLL",
"output": "BUG"
},
{
"input": "DRDRD",
"output": "OK"
},
{
"input": "ULURL",
"output": "BUG"
},
{
"input": "LUUDU",
"output": "BUG"
},
{
"input": "RDLUR",
"output": "BUG"
},
{
"input": "DLDLDDRR",
"output": "OK"
},
{
"input": "RDRDDD",
"output": "OK"
},
{
"input": "UULLDLUR",
"output": "BUG"
},
{
"input": "LULU",
"output": "OK"
},
{
"input": "LLDDLDLLDDDLLLDLLLLLUU",
"output": "OK"
},
{
"input": "LLDDLDLLDDDLLLDLLLLLUU",
"output": "OK"
},
{
"input": "LLDDLDLLDDDLLLDLLLLLUU",
"output": "OK"
},
{
"input": "URRRRRURRURUURRRRRDDDDLDDDRDDDDLLDLL",
"output": "OK"
},
{
"input": "R",
"output": "OK"
},
{
"input": "UL",
"output": "OK"
},
{
"input": "UDR",
"output": "BUG"
},
{
"input": "DDDR",
"output": "OK"
},
{
"input": "UUUDU",
"output": "BUG"
},
{
"input": "LULULL",
"output": "OK"
},
{
"input": "DLURUUU",
"output": "BUG"
},
{
"input": "UURUURRUUU",
"output": "OK"
},
{
"input": "DDDDRDDLDDDDDDDRDDLD",
"output": "OK"
},
{
"input": "URRRLULUURURLRLLLLULLRLRURLULRLULLULRRUU",
"output": "BUG"
},
{
"input": "RURRRRLURRRURRUURRRRRRRRDDULULRRURRRDRRRRRRRRRRLDR",
"output": "BUG"
},
{
"input": "RLRRRRRDRRDRRRRDLRRRRRRRDLRLDDLRRRRLDLDRDRRRRDRDRDRDLRRURRLRRRRDRRRRRRRRLDDRLRRDRRRRRRRDRDRLDRDDDRDR",
"output": "BUG"
},
{
"input": "DDUL",
"output": "BUG"
},
{
"input": "UUULLLLRDD",
"output": "BUG"
},
{
"input": "LLLLLLLLRRRRDDDDDDDUUUUUU",
"output": "BUG"
},
{
"input": "DDDDDDDDDDDDUUUUUUUUUUUURRRRRRRRRRRRRLLLLLLLLLLLLLLL",
"output": "BUG"
},
{
"input": "DDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRRRRRRRRRRRUUUUUUUUUUUUUUUUUUUUUUUU",
"output": "BUG"
},
{
"input": "DLUR",
"output": "BUG"
},
{
"input": "UUUURDLLLL",
"output": "BUG"
},
{
"input": "RRRRRRRRRRRURLLLLLLLLLLLL",
"output": "BUG"
},
{
"input": "LLLLLLLLLLLLLLLLLLLLLLLLLLRUUUUUUUUUUUUUUUUUUUUUUUUU",
"output": "BUG"
},
{
"input": "UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUURDRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR",
"output": "BUG"
},
{
"input": "DDLDRRR",
"output": "BUG"
},
{
"input": "RRUULLD",
"output": "BUG"
},
{
"input": "LUUUULLLLDDDDRRRD",
"output": "BUG"
},
{
"input": "DDDDLLLDDDRRRUURRRR",
"output": "BUG"
},
{
"input": "DDDDDDDLLDDRRURRRRRRR",
"output": "BUG"
},
{
"input": "DDDDDDDDDDLLLLLLLLLLLDDDDDDDDDDDRRRRRRRRRRRUUUUUUUUUURRRRRRRRRR",
"output": "BUG"
},
{
"input": "DDDLLLLLLLDDDDDDDRRRRRRRUUUUUURRR",
"output": "BUG"
},
{
"input": "RRRUUULLLDD",
"output": "BUG"
},
{
"input": "DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLDDDDRRRRUUURRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR",
"output": "BUG"
},
{
"input": "RRRRRRRRRRRDDDDDDDDDDDDDDDDDDDRRRRRRRRRRRRRRRRRRRUUUUUUUUUUUUUUUUUUULLLLLLLLLLLLLLLLLLUUUUUUUUUUU",
"output": "BUG"
}
] | 312 | 0 | 0 | 4,592 |
137 | History | [
"sortings"
] | null | null | Polycarpus likes studying at school a lot and he is always diligent about his homework. Polycarpus has never had any problems with natural sciences as his great-great-grandfather was the great physicist Seinstein. On the other hand though, Polycarpus has never had an easy time with history.
Everybody knows that the World history encompasses exactly *n* events: the *i*-th event had continued from the year *a**i* to the year *b**i* inclusive (*a**i*<=<<=*b**i*). Polycarpus easily learned the dates when each of *n* events started and ended (Polycarpus inherited excellent memory from his great-great-granddad). But the teacher gave him a more complicated task: Polycaprus should know when all events began and ended and he should also find out for each event whether it includes another event. Polycarpus' teacher thinks that an event *j* includes an event *i* if *a**j*<=<<=*a**i* and *b**i*<=<<=*b**j*. Your task is simpler: find the number of events that are included in some other event. | The first input line contains integer *n* (1<=β€<=*n*<=β€<=105) which represents the number of events. Next *n* lines contain descriptions of the historical events, one event per line. The *i*<=+<=1 line contains two integers *a**i* and *b**i* (1<=β€<=*a**i*<=<<=*b**i*<=β€<=109) β the beginning and the end of the *i*-th event. No two events start or finish in the same year, that is, *a**i*<=β <=*a**j*,<=*a**i*<=β <=*b**j*,<=*b**i*<=β <=*a**j*,<=*b**i*<=β <=*b**j* for all *i*, *j* (where *i*<=β <=*j*). Events are given in arbitrary order. | Print the only integer β the answer to the problem. | [
"5\n1 10\n2 9\n3 8\n4 7\n5 6\n",
"5\n1 100\n2 50\n51 99\n52 98\n10 60\n",
"1\n1 1000000000\n"
] | [
"4\n",
"4\n",
"0\n"
] | In the first example the fifth event is contained in the fourth. Similarly, the fourth event is contained in the third, the third β in the second and the second β in the first.
In the second example all events except the first one are contained in the first.
In the third example only one event, so the answer is 0. | [
{
"input": "5\n1 10\n2 9\n3 8\n4 7\n5 6",
"output": "4"
},
{
"input": "5\n1 100\n2 50\n51 99\n52 98\n10 60",
"output": "4"
},
{
"input": "1\n1 1000000000",
"output": "0"
},
{
"input": "2\n100 1000\n500 1500",
"output": "0"
},
{
"input": "4\n1 100\n50 150\n120 200\n180 220",
"output": "0"
},
{
"input": "10\n1 20\n2 19\n3 18\n4 17\n5 16\n6 15\n7 14\n8 13\n9 12\n10 11",
"output": "9"
},
{
"input": "4\n1 5\n2 4\n10 15\n11 14",
"output": "2"
},
{
"input": "10\n1 2\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20",
"output": "0"
},
{
"input": "10\n58 22116\n112840 772160\n127432 399484\n182031 255417\n459340 548097\n603984 739189\n606173 663033\n280170 366159\n779239 906234\n874623 892907",
"output": "7"
},
{
"input": "2\n2 3\n1 4",
"output": "1"
},
{
"input": "3\n9 10\n1 2\n3 4",
"output": "0"
},
{
"input": "4\n1 2\n3 6\n4 5\n10 11",
"output": "1"
},
{
"input": "2\n5 6\n1 10",
"output": "1"
},
{
"input": "7\n1 10\n2 5\n3 9\n100 1000\n200 500\n1001 1002\n777 7777",
"output": "4"
}
] | 2,000 | 9,523,200 | 0 | 4,595 |
|
429 | Tricky Function | [
"data structures",
"divide and conquer",
"geometry"
] | null | null | Iahub and Sorin are the best competitive programmers in their town. However, they can't both qualify to an important contest. The selection will be made with the help of a single problem. Blatnatalag, a friend of Iahub, managed to get hold of the problem before the contest. Because he wants to make sure Iahub will be the one qualified, he tells Iahub the following task.
You're given an (1-based) array *a* with *n* elements. Let's define function *f*(*i*,<=*j*) (1<=β€<=*i*,<=*j*<=β€<=*n*) as (*i*<=-<=*j*)2<=+<=*g*(*i*,<=*j*)2. Function g is calculated by the following pseudo-code:
Find a value *min**i*<=β <=*j*Β Β *f*(*i*,<=*j*).
Probably by now Iahub already figured out the solution to this problem. Can you? | The first line of input contains a single integer *n* (2<=β€<=*n*<=β€<=100000). Next line contains *n* integers *a*[1], *a*[2], ..., *a*[*n*] (<=-<=104<=β€<=*a*[*i*]<=β€<=104). | Output a single integer β the value of *min**i*<=β <=*j*Β Β *f*(*i*,<=*j*). | [
"4\n1 0 0 -1\n",
"2\n1 -1\n"
] | [
"1\n",
"2\n"
] | none | [
{
"input": "4\n1 0 0 -1",
"output": "1"
},
{
"input": "2\n1 -1",
"output": "2"
},
{
"input": "100\n-57 -64 83 76 80 27 60 76 -80 -56 52 72 -17 92 -96 87 41 -88 94 89 12 42 36 34 -100 -43 -42 62 3 87 -69 -6 -27 -59 -7 5 -90 -23 63 -87 -60 -92 -40 54 -16 -47 67 -64 10 33 -19 53 -7 -62 16 -74 -36 4 -75 -55 92 3 -22 43 -30 48 -27 88 -58 41 36 8 -40 -30 -18 16 22 -66 -91 -46 48 -60 -45 -89 37 -76 52 81 81 15 1 -43 -45 -19 9 -75 -75 -63 41 29",
"output": "2"
},
{
"input": "100\n-1 -3 -3 0 -1 -1 -1 1 2 1 0 -1 -2 0 -2 -2 3 -2 -1 -2 2 -2 -2 3 0 2 3 -1 2 -1 -2 2 -3 2 1 0 -1 1 3 -1 0 2 -3 -2 2 2 3 -2 2 3 0 -3 -2 1 -1 0 3 0 2 0 1 1 0 -3 1 -3 3 0 -1 -3 3 3 1 -2 2 -2 -3 -1 -2 2 -1 0 2 1 2 -1 2 3 -2 -1 0 -3 0 -1 3 2 -2 2 3 0",
"output": "1"
},
{
"input": "4\n200 100 -200 100",
"output": "9"
},
{
"input": "2\n3 -9",
"output": "82"
},
{
"input": "3\n0 -10 10",
"output": "4"
},
{
"input": "2\n10000 10000",
"output": "100000001"
},
{
"input": "2\n5 5",
"output": "26"
},
{
"input": "3\n10 10 -10",
"output": "4"
},
{
"input": "6\n10000 10000 10000 10000 10000 6904",
"output": "47665217"
},
{
"input": "3\n0 10000 -10000",
"output": "4"
},
{
"input": "3\n0 2 3",
"output": "5"
},
{
"input": "2\n0 1",
"output": "2"
},
{
"input": "5\n5865 6072 -4563 5913 -7926",
"output": "254032"
},
{
"input": "2\n1 10000",
"output": "100000001"
},
{
"input": "5\n10 11 12 13 -40",
"output": "32"
},
{
"input": "21\n10 10 10 10 10 10 10 10 10 10 -95 10 10 10 10 10 10 10 10 10 10",
"output": "101"
},
{
"input": "5\n0 4 10 -5 -5",
"output": "9"
},
{
"input": "2\n0 10000",
"output": "100000001"
},
{
"input": "4\n0 100 100 -200",
"output": "9"
},
{
"input": "4\n0 10 -5 -5",
"output": "9"
},
{
"input": "4\n10 10 -10 -10",
"output": "4"
},
{
"input": "3\n1 10 10",
"output": "101"
},
{
"input": "3\n1000 1000 -800",
"output": "40004"
},
{
"input": "3\n0 10 -10",
"output": "4"
},
{
"input": "2\n0 100",
"output": "10001"
}
] | 77 | 4,198,400 | -1 | 4,596 |
|
478 | Red-Green Towers | [
"dp"
] | null | null | There are *r* red and *g* green blocks for construction of the red-green tower. Red-green tower can be built following next rules:
- Red-green tower is consisting of some number of levels; - Let the red-green tower consist of *n* levels, then the first level of this tower should consist of *n* blocks, second level β of *n*<=-<=1 blocks, the third one β of *n*<=-<=2 blocks, and so on β the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one; - Each level of the red-green tower should contain blocks of the same color.
Let *h* be the maximum possible number of levels of red-green tower, that can be built out of *r* red and *g* green blocks meeting the rules above. The task is to determine how many different red-green towers having *h* levels can be built out of the available blocks.
Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.
You are to write a program that will find the number of different red-green towers of height *h* moduloΒ 109<=+<=7. | The only line of input contains two integers *r* and *g*, separated by a single space β the number of available red and green blocks respectively (0<=β€<=*r*,<=*g*<=β€<=2Β·105, *r*<=+<=*g*<=β₯<=1). | Output the only integer β the number of different possible red-green towers of height *h* moduloΒ 109<=+<=7. | [
"4 6\n",
"9 7\n",
"1 1\n"
] | [
"2\n",
"6\n",
"2\n"
] | The image in the problem statement shows all possible red-green towers for the first sample. | [
{
"input": "4 6",
"output": "2"
},
{
"input": "9 7",
"output": "6"
},
{
"input": "1 1",
"output": "2"
},
{
"input": "3 3",
"output": "2"
},
{
"input": "2 19",
"output": "1"
},
{
"input": "18 3",
"output": "2"
},
{
"input": "100000 1",
"output": "2"
},
{
"input": "1 100000",
"output": "2"
},
{
"input": "6 6",
"output": "6"
},
{
"input": "10 10",
"output": "18"
},
{
"input": "200000 200000",
"output": "206874596"
},
{
"input": "0 1",
"output": "1"
},
{
"input": "1 0",
"output": "1"
},
{
"input": "0 200000",
"output": "1"
},
{
"input": "200000 0",
"output": "1"
},
{
"input": "199396 0",
"output": "1"
},
{
"input": "199395 0",
"output": "1"
},
{
"input": "0 199397",
"output": "1"
},
{
"input": "121147 78249",
"output": "64290784"
},
{
"input": "78250 121147",
"output": "981737243"
},
{
"input": "121146 78249",
"output": "832902708"
},
{
"input": "199585 199586",
"output": "438320405"
},
{
"input": "199586 199586",
"output": "876640810"
},
{
"input": "199585 199585",
"output": "199771918"
},
{
"input": "107344 159729",
"output": "849320920"
},
{
"input": "2954 1977",
"output": "835530858"
},
{
"input": "25580 17318",
"output": "263898876"
},
{
"input": "89671 32487",
"output": "654128709"
},
{
"input": "38 36",
"output": "612"
},
{
"input": "136749 183300",
"output": "906576609"
},
{
"input": "10000 10000",
"output": "885988055"
},
{
"input": "200000 199999",
"output": "396481680"
}
] | 62 | 614,400 | -1 | 4,611 |
|
53 | Physical Education | [
"sortings"
] | D. Physical Education | 2 | 256 | Vasya is a school PE teacher. Unlike other PE teachers, Vasya doesn't like it when the students stand in line according to their height. Instead, he demands that the children stand in the following order: *a*1,<=*a*2,<=...,<=*a**n*, where *a**i* is the height of the *i*-th student in the line and *n* is the number of students in the line. The children find it hard to keep in mind this strange arrangement, and today they formed the line in the following order: *b*1,<=*b*2,<=...,<=*b**n*, which upset Vasya immensely. Now Vasya wants to rearrange the children so that the resulting order is like this: *a*1,<=*a*2,<=...,<=*a**n*. During each move Vasya can swap two people who stand next to each other in the line. Help Vasya, find the sequence of swaps leading to the arrangement Vasya needs. It is not required to minimize the number of moves. | The first line contains an integer *n* (1<=β€<=*n*<=β€<=300) which is the number of students. The second line contains *n* space-separated integers *a**i* (1<=β€<=*a**i*<=β€<=109) which represent the height of the student occupying the *i*-th place must possess. The third line contains *n* space-separated integers *b**i* (1<=β€<=*b**i*<=β€<=109) which represent the height of the student occupying the *i*-th place in the initial arrangement. It is possible that some students possess similar heights. It is guaranteed that it is possible to arrange the children in the required order, i.e. *a* and *b* coincide as multisets. | In the first line print an integer *k* (0<=β€<=*k*<=β€<=106) which is the number of moves. It is not required to minimize *k* but it must not exceed 106. Then print *k* lines each containing two space-separated integers. Line *p**i*, *p**i*<=+<=1 (1<=β€<=*p**i*<=β€<=*n*<=-<=1) means that Vasya should swap students occupying places *p**i* and *p**i*<=+<=1. | [
"4\n1 2 3 2\n3 2 1 2\n",
"2\n1 100500\n1 100500\n"
] | [
"4\n2 3\n1 2\n3 4\n2 3\n",
"0\n"
] | none | [
{
"input": "4\n1 2 3 2\n3 2 1 2",
"output": "4\n2 3\n1 2\n3 4\n2 3"
},
{
"input": "2\n1 100500\n1 100500",
"output": "0"
},
{
"input": "3\n652586118 652586118 652586118\n652586118 652586118 652586118",
"output": "3\n2 3\n1 2\n2 3"
},
{
"input": "4\n681106577 681106577 675077178 675077178\n675077178 681106577 681106577 675077178",
"output": "4\n2 3\n1 2\n2 3\n3 4"
},
{
"input": "5\n470138369 747764103 729004864 491957578 874531368\n874531368 729004864 491957578 747764103 470138369",
"output": "9\n4 5\n3 4\n2 3\n1 2\n4 5\n3 4\n2 3\n3 4\n4 5"
},
{
"input": "6\n590202194 293471749 259345095 293471749 18056518 293471749\n293471749 293471749 293471749 18056518 259345095 590202194",
"output": "12\n5 6\n4 5\n3 4\n2 3\n1 2\n3 4\n2 3\n5 6\n4 5\n3 4\n4 5\n5 6"
},
{
"input": "1\n873725529\n873725529",
"output": "0"
},
{
"input": "1\n800950546\n800950546",
"output": "0"
},
{
"input": "2\n344379439 344379439\n344379439 344379439",
"output": "1\n1 2"
},
{
"input": "2\n305292852 305292852\n305292852 305292852",
"output": "1\n1 2"
}
] | 216 | 6,963,200 | 0 | 4,613 |
612 | The Union of k-Segments | [
"greedy",
"sortings"
] | null | null | You are given *n* segments on the coordinate axis Ox and the number *k*. The point is satisfied if it belongs to at least *k* segments. Find the smallest (by the number of segments) set of segments on the coordinate axis Ox which contains all satisfied points and no others. | The first line contains two integers *n* and *k* (1<=β€<=*k*<=β€<=*n*<=β€<=106) β the number of segments and the value of *k*.
The next *n* lines contain two integers *l**i*,<=*r**i* (<=-<=109<=β€<=*l**i*<=β€<=*r**i*<=β€<=109) each β the endpoints of the *i*-th segment. The segments can degenerate and intersect each other. The segments are given in arbitrary order. | First line contains integer *m* β the smallest number of segments.
Next *m* lines contain two integers *a**j*,<=*b**j* (*a**j*<=β€<=*b**j*) β the ends of *j*-th segment in the answer. The segments should be listed in the order from left to right. | [
"3 2\n0 5\n-3 2\n3 8\n",
"3 2\n0 5\n-3 3\n3 8\n"
] | [
"2\n0 2\n3 5\n",
"1\n0 5\n"
] | none | [
{
"input": "3 2\n0 5\n-3 2\n3 8",
"output": "2\n0 2\n3 5"
},
{
"input": "3 2\n0 5\n-3 3\n3 8",
"output": "1\n0 5"
},
{
"input": "1 1\n-1 1",
"output": "1\n-1 1"
},
{
"input": "10 2\n27 96\n-22 45\n-68 26\n46 69\n-91 86\n12 73\n-89 76\n-11 33\n17 47\n-57 78",
"output": "1\n-89 86"
},
{
"input": "10 1\n3 60\n-73 -37\n59 69\n-56 1\n-84 -24\n-14 46\n-65 -23\n-66 -57\n-87 -80\n-21 20",
"output": "1\n-87 69"
},
{
"input": "10 10\n-92 87\n-100 -67\n-88 80\n-82 -59\n-72 81\n-50 30\n30 77\n65 92\n-76 -60\n-29 -15",
"output": "0"
},
{
"input": "1 1\n-941727901 756748222",
"output": "1\n-941727901 756748222"
},
{
"input": "1 1\n-990637865 387517231",
"output": "1\n-990637865 387517231"
},
{
"input": "1 1\n-870080964 571991746",
"output": "1\n-870080964 571991746"
},
{
"input": "10 8\n-749560329 759073394\n-186423470 816422576\n-674251064 742056817\n-342947007 954589677\n-306243234 999298121\n-448636479 409818446\n-885248428 624359061\n-936960294 754851875\n-781500924 984124751\n-342740564 618223559",
"output": "1\n-342740564 624359061"
},
{
"input": "10 1\n-260424665 -168566709\n299109864 663179811\n769984405 942516913\n-998905510 -707148023\n-167958021 60599275\n658861231 718845364\n79407402 279078536\n13652788 79756488\n-676213666 -339118351\n-349156760 -258185154",
"output": "5\n-998905510 -707148023\n-676213666 -168566709\n-167958021 279078536\n299109864 718845364\n769984405 942516913"
},
{
"input": "10 8\n-278661264 757623461\n-751226975 996393413\n-721476675 863607399\n-228431002 643113689\n-209293138 701503607\n-433870703 932866969\n-385182911 667745533\n-661057075 783312740\n-617789923 657076219\n-890369225 990071765",
"output": "1\n-278661264 667745533"
},
{
"input": "4 2\n2 2\n2 2\n2 3\n3 3",
"output": "2\n2 2\n3 3"
},
{
"input": "2 2\n-3 1\n-4 -1",
"output": "1\n-3 -1"
},
{
"input": "1 1\n2 2",
"output": "1\n2 2"
},
{
"input": "2 1\n0 2\n-1 0",
"output": "1\n-1 2"
},
{
"input": "2 2\n-1000000000 1000000000\n-1000000000 100",
"output": "1\n-1000000000 100"
}
] | 62 | 5,632,000 | 0 | 4,627 |
|
0 | none | [
"none"
] | null | null | In the year of $30XX$ participants of some world programming championship live in a single large hotel. The hotel has $n$ floors. Each floor has $m$ sections with a single corridor connecting all of them. The sections are enumerated from $1$ to $m$ along the corridor, and all sections with equal numbers on different floors are located exactly one above the other. Thus, the hotel can be represented as a rectangle of height $n$ and width $m$. We can denote sections with pairs of integers $(i, j)$, where $i$ is the floor, and $j$ is the section number on the floor.
The guests can walk along the corridor on each floor, use stairs and elevators. Each stairs or elevator occupies all sections $(1, x)$, $(2, x)$, $\ldots$, $(n, x)$ for some $x$ between $1$ and $m$. All sections not occupied with stairs or elevators contain guest rooms. It takes one time unit to move between neighboring sections on the same floor or to move one floor up or down using stairs. It takes one time unit to move up to $v$ floors in any direction using an elevator. You can assume you don't have to wait for an elevator, and the time needed to enter or exit an elevator is negligible.
You are to process $q$ queries. Each query is a question "what is the minimum time needed to go from a room in section $(x_1, y_1)$ to a room in section $(x_2, y_2)$?" | The first line contains five integers $n, m, c_l, c_e, v$ ($2 \leq n, m \leq 10^8$, $0 \leq c_l, c_e \leq 10^5$, $1 \leq c_l + c_e \leq m - 1$, $1 \leq v \leq n - 1$)Β β the number of floors and section on each floor, the number of stairs, the number of elevators and the maximum speed of an elevator, respectively.
The second line contains $c_l$ integers $l_1, \ldots, l_{c_l}$ in increasing order ($1 \leq l_i \leq m$), denoting the positions of the stairs. If $c_l = 0$, the second line is empty.
The third line contains $c_e$ integers $e_1, \ldots, e_{c_e}$ in increasing order, denoting the elevators positions in the same format. It is guaranteed that all integers $l_i$ and $e_i$ are distinct.
The fourth line contains a single integer $q$ ($1 \leq q \leq 10^5$)Β β the number of queries.
The next $q$ lines describe queries. Each of these lines contains four integers $x_1, y_1, x_2, y_2$ ($1 \leq x_1, x_2 \leq n$, $1 \leq y_1, y_2 \leq m$)Β β the coordinates of starting and finishing sections for the query. It is guaranteed that the starting and finishing sections are distinct. It is also guaranteed that these sections contain guest rooms, i.Β e. $y_1$ and $y_2$ are not among $l_i$ and $e_i$. | Print $q$ integers, one per lineΒ β the answers for the queries. | [
"5 6 1 1 3\n2\n5\n3\n1 1 5 6\n1 3 5 4\n3 3 5 3\n"
] | [
"7\n5\n4\n"
] | In the first query the optimal way is to go to the elevator in the 5-th section in four time units, use it to go to the fifth floor in two time units and go to the destination in one more time unit.
In the second query it is still optimal to use the elevator, but in the third query it is better to use the stairs in the section 2. | [
{
"input": "5 6 1 1 3\n2\n5\n3\n1 1 5 6\n1 3 5 4\n3 3 5 3",
"output": "7\n5\n4"
},
{
"input": "2 2 0 1 1\n\n1\n1\n1 2 2 2",
"output": "3"
},
{
"input": "4 4 1 0 1\n4\n\n5\n1 1 2 2\n1 3 2 2\n3 3 4 3\n3 2 2 2\n1 2 2 3",
"output": "6\n4\n3\n5\n4"
},
{
"input": "10 10 1 8 4\n10\n2 3 4 5 6 7 8 9\n10\n1 1 3 1\n2 1 7 1\n1 1 9 1\n7 1 4 1\n10 1 7 1\n2 1 7 1\n3 1 2 1\n5 1 2 1\n10 1 5 1\n6 1 9 1",
"output": "3\n4\n4\n3\n3\n4\n3\n3\n4\n3"
},
{
"input": "2 5 1 0 1\n2\n\n1\n1 4 1 5",
"output": "1"
},
{
"input": "2 10 1 1 1\n1\n10\n1\n1 5 1 8",
"output": "3"
},
{
"input": "4 4 1 0 1\n1\n\n1\n1 2 1 4",
"output": "2"
},
{
"input": "2 4 1 1 1\n1\n2\n1\n2 3 2 4",
"output": "1"
},
{
"input": "1000 1000 1 1 10\n1\n2\n1\n1 900 1 1000",
"output": "100"
},
{
"input": "2 4 1 1 1\n1\n4\n1\n1 2 1 3",
"output": "1"
},
{
"input": "5 5 1 1 1\n3\n2\n1\n1 5 1 1",
"output": "4"
}
] | 46 | 0 | 0 | 4,634 |
|
364 | Free Market | [
"dp",
"greedy"
] | null | null | John Doe has recently found a "Free Market" in his city β that is the place where you can exchange some of your possessions for other things for free.
John knows that his city has *n* items in total (each item is unique). You can bring any number of items to the market and exchange them for any other one. Note that each item is one of a kind and that means that you cannot exchange set {*a*,<=*b*} for set {*v*,<=*a*}. However, you can always exchange set *x* for any set *y*, unless there is item *p*, such that *p* occurs in *x* and *p* occurs in *y*.
For each item, John knows its value *c**i*. John's sense of justice doesn't let him exchange a set of items *x* for a set of items *y*, if *s*(*x*)<=+<=*d*<=<<=*s*(*y*) (*s*(*x*) is the total price of items in the set *x*).
During one day John can exchange only one set of items for something else. Initially, he has no items. John wants to get a set of items with the maximum total price. Find the cost of such set and the minimum number of days John can get it in. | The first line contains two space-separated integers *n*, *d* (1<=β€<=*n*<=β€<=50, 1<=β€<=*d*<=β€<=104) β the number of items on the market and John's sense of justice value, correspondingly. The second line contains *n* space-separated integers *c**i* (1<=β€<=*c**i*<=β€<=104). | Print two space-separated integers: the maximum possible price in the set of items John can get and the minimum number of days needed to get such set. | [
"3 2\n1 3 10\n",
"3 5\n1 2 3\n",
"10 10000\n10000 9999 1 10000 10000 10000 1 2 3 4\n"
] | [
"4 3\n",
"6 2\n",
"50010 6\n"
] | In the first sample John can act like this:
- Take the first item (1β-β0ββ€β2). - Exchange the first item for the second one (3β-β1ββ€β2). - Take the first item (1β-β0ββ€β2). | [] | 1,000 | 0 | 0 | 4,639 |
|
876 | Divisiblity of Differences | [
"implementation",
"math",
"number theory"
] | null | null | You are given a multiset of *n* integers. You should select exactly *k* of them in a such way that the difference between any two of them is divisible by *m*, or tell that it is impossible.
Numbers can be repeated in the original multiset and in the multiset of selected numbers, but number of occurrences of any number in multiset of selected numbers should not exceed the number of its occurrences in the original multiset. | First line contains three integers *n*, *k* and *m* (2<=β€<=*k*<=β€<=*n*<=β€<=100<=000, 1<=β€<=*m*<=β€<=100<=000)Β β number of integers in the multiset, number of integers you should select and the required divisor of any pair of selected integers.
Second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=β€<=*a**i*<=β€<=109)Β β the numbers in the multiset. | If it is not possible to select *k* numbers in the desired way, output Β«NoΒ» (without the quotes).
Otherwise, in the first line of output print Β«YesΒ» (without the quotes). In the second line print *k* integers *b*1,<=*b*2,<=...,<=*b**k*Β β the selected numbers. If there are multiple possible solutions, print any of them. | [
"3 2 3\n1 8 4\n",
"3 3 3\n1 8 4\n",
"4 3 5\n2 7 7 7\n"
] | [
"Yes\n1 4 ",
"No",
"Yes\n2 7 7 "
] | none | [
{
"input": "3 2 3\n1 8 4",
"output": "Yes\n1 4 "
},
{
"input": "3 3 3\n1 8 4",
"output": "No"
},
{
"input": "4 3 5\n2 7 7 7",
"output": "Yes\n2 7 7 "
},
{
"input": "9 9 5\n389149775 833127990 969340400 364457730 48649145 316121525 640054660 924273385 973207825",
"output": "Yes\n389149775 833127990 969340400 364457730 48649145 316121525 640054660 924273385 973207825 "
},
{
"input": "15 8 10\n216175135 15241965 611723934 987180005 151601897 403701727 533996295 207637446 875331635 46172555 604086315 350146655 401084142 156540458 982110455",
"output": "Yes\n216175135 15241965 987180005 533996295 875331635 46172555 604086315 350146655 "
},
{
"input": "2 2 100000\n0 1",
"output": "No"
},
{
"input": "101 25 64\n451 230 14 53 7 520 709 102 678 358 166 870 807 230 230 279 166 230 765 176 742 358 924 976 647 806 870 473 976 994 750 146 802 224 503 801 105 614 882 203 390 338 29 587 214 213 405 806 102 102 621 358 521 742 678 205 309 871 796 326 162 693 268 486 68 627 304 829 806 623 748 934 714 672 712 614 587 589 846 260 593 85 839 257 711 395 336 358 472 133 324 527 599 5 845 920 989 494 358 70 882",
"output": "Yes\n230 102 678 358 166 870 230 230 166 230 742 358 806 870 614 806 102 102 358 742 678 486 806 934 614 "
},
{
"input": "108 29 72\n738 619 711 235 288 288 679 36 785 233 706 71 216 144 216 781 338 583 495 648 144 432 72 720 541 288 158 328 154 202 10 533 635 176 707 216 314 397 440 142 326 458 568 701 745 144 61 634 520 720 744 144 409 127 526 476 101 469 72 432 738 432 235 641 695 276 144 144 231 555 630 9 109 319 437 288 288 317 453 432 601 0 449 576 743 352 333 504 504 369 228 288 381 142 500 72 297 359 230 773 216 576 144 244 437 772 483 51",
"output": "Yes\n288 288 216 144 216 648 144 432 72 720 288 216 144 720 144 72 432 432 144 144 288 288 432 0 576 504 504 288 72 "
},
{
"input": "8 2 6\n750462183 165947982 770714338 368445737 363145692 966611485 376672869 678687947",
"output": "Yes\n165947982 363145692 "
},
{
"input": "12 2 1\n512497388 499105388 575265677 864726520 678272195 667107176 809432109 439696443 770034376 873126825 690514828 541499950",
"output": "Yes\n512497388 499105388 "
},
{
"input": "9 3 1\n506004039 471451660 614118177 518013571 43210072 454727076 285905913 543002174 298515615",
"output": "Yes\n506004039 471451660 614118177 "
},
{
"input": "8 4 6\n344417267 377591123 938158786 682031413 804153975 89006697 275945670 735510539",
"output": "No"
},
{
"input": "8 8 1\n314088413 315795280 271532387 241073087 961218399 884234132 419866508 286799253",
"output": "Yes\n314088413 315795280 271532387 241073087 961218399 884234132 419866508 286799253 "
},
{
"input": "7 7 1\n0 0 0 0 0 0 0",
"output": "Yes\n0 0 0 0 0 0 0 "
},
{
"input": "11 4 3\n0 1 0 1 1 0 0 0 0 0 0",
"output": "Yes\n0 0 0 0 "
},
{
"input": "13 4 4\n1 1 0 3 2 4 1 0 3 4 2 4 3",
"output": "Yes\n0 4 0 4 "
},
{
"input": "5 5 1\n6 4 6 0 4",
"output": "Yes\n6 4 6 0 4 "
},
{
"input": "3 2 3\n1 2 3",
"output": "No"
},
{
"input": "6 3 4\n5 9 10 6 7 8",
"output": "No"
},
{
"input": "4 4 3\n4 7 2 5",
"output": "No"
},
{
"input": "4 2 6\n5 5 5 5",
"output": "Yes\n5 5 "
},
{
"input": "4 3 3\n5 1 4 7",
"output": "Yes\n1 4 7 "
},
{
"input": "4 3 10\n0 1 11 11",
"output": "Yes\n1 11 11 "
},
{
"input": "5 2 4\n1 2 2 2 2",
"output": "Yes\n2 2 "
},
{
"input": "5 5 9\n8 17 26 35 44",
"output": "Yes\n8 17 26 35 44 "
},
{
"input": "3 2 2\n1 2 4",
"output": "Yes\n2 4 "
},
{
"input": "5 4 2\n1 3 6 10 12",
"output": "No"
},
{
"input": "3 2 4\n1 2 3",
"output": "No"
},
{
"input": "8 3 5\n1 2 3 4 1 2 3 4",
"output": "No"
},
{
"input": "5 2 9\n8 8 8 8 8",
"output": "Yes\n8 8 "
},
{
"input": "3 3 3\n1 3 6",
"output": "No"
},
{
"input": "5 2 10\n4 5 6 19 29",
"output": "Yes\n19 29 "
},
{
"input": "5 3 3\n3 6 4 7 10",
"output": "Yes\n4 7 10 "
}
] | 1,000 | 5,529,600 | 0 | 4,642 |
|
859 | Lazy Security Guard | [
"brute force",
"geometry",
"math"
] | null | null | Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly *N* city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly *N* blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite. | Input will consist of a single integer *N* (1<=β€<=*N*<=β€<=106), the number of city blocks that must be enclosed by the route. | Print the minimum perimeter that can be achieved. | [
"4\n",
"11\n",
"22\n"
] | [
"8\n",
"14\n",
"20\n"
] | Here are some possible shapes for the examples:
<img class="tex-graphics" src="https://espresso.codeforces.com/e11bef2cf82b55dd583cfc97d12b5aee5e483a65.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "4",
"output": "8"
},
{
"input": "11",
"output": "14"
},
{
"input": "22",
"output": "20"
},
{
"input": "3",
"output": "8"
},
{
"input": "1024",
"output": "128"
},
{
"input": "101",
"output": "42"
},
{
"input": "30",
"output": "22"
},
{
"input": "1000000",
"output": "4000"
},
{
"input": "1",
"output": "4"
},
{
"input": "2",
"output": "6"
},
{
"input": "5",
"output": "10"
},
{
"input": "6",
"output": "10"
},
{
"input": "7",
"output": "12"
},
{
"input": "8",
"output": "12"
},
{
"input": "9",
"output": "12"
},
{
"input": "10",
"output": "14"
},
{
"input": "999000",
"output": "3998"
},
{
"input": "999001",
"output": "4000"
},
{
"input": "999999",
"output": "4000"
},
{
"input": "933206",
"output": "3866"
},
{
"input": "718351",
"output": "3392"
},
{
"input": "607443",
"output": "3118"
},
{
"input": "347887",
"output": "2360"
},
{
"input": "246206",
"output": "1986"
},
{
"input": "151375",
"output": "1558"
},
{
"input": "12639",
"output": "450"
},
{
"input": "3751",
"output": "246"
},
{
"input": "3607",
"output": "242"
},
{
"input": "124",
"output": "46"
},
{
"input": "64",
"output": "32"
},
{
"input": "31",
"output": "24"
},
{
"input": "23",
"output": "20"
},
{
"input": "15",
"output": "16"
},
{
"input": "19",
"output": "18"
},
{
"input": "59637",
"output": "978"
}
] | 62 | 0 | 3 | 4,644 |
|
778 | Peterson Polyglot | [
"brute force",
"dfs and similar",
"dsu",
"hashing",
"strings",
"trees"
] | null | null | Peterson loves to learn new languages, but his favorite hobby is making new ones. Language is a set of words, and word is a sequence of lowercase Latin letters.
Peterson makes new language every morning. It is difficult task to store the whole language, so Peterson have invented new data structure for storing his languages which is called broom. Broom is rooted tree with edges marked with letters. Initially broom is represented by the only vertexΒ β the root of the broom. When Peterson wants to add new word to the language he stands at the root and processes the letters of new word one by one. Consider that Peterson stands at the vertex *u*. If there is an edge from *u* marked with current letter, Peterson goes through this edge. Otherwise Peterson adds new edge from *u* to the new vertex *v*, marks it with the current letter and goes through the new edge. Size of broom is the number of vertices in it.
In the evening after working day Peterson can't understand the language he made this morning. It is too difficult for bored Peterson and he tries to make it simpler. Simplification of the language is the process of erasing some letters from some words of this language. Formally, Peterson takes some positive integer *p* and erases *p*-th letter from all the words of this language having length at least *p*. Letters in words are indexed starting by 1. Peterson considers that simplification should change at least one word, i.e. there has to be at least one word of length at least *p*. Peterson tries to make his language as simple as possible, so he wants to choose *p* such that the size of the broom for his simplified language is as small as possible.
Peterson is pretty annoyed with this task so he asks you for help. Write a program to find the smallest possible size of the broom and integer *p*. | The first line of input contains integer *n* (2<=β€<=*n*<=β€<=3Β·105)Β β the size of the broom.
Next *n*<=-<=1 lines describe the broom: *i*-th of them contains integers *u**i*, *v**i* and letter *x**i*Β β describing the edge from *u**i* to *v**i* marked with letter *x**i*.
Vertices are numbered from 1 to *n*. All *x**i* are lowercase latin letters. Vertex 1 is the root of the broom.
Edges describe correct broom which is made from Peterson's language. | The first line of output should contain the minimum possible size of the broom after its simplification. The second line of output should contain integer *p* to choose. If there are several suitable *p* values, print the smallest one. | [
"5\n1 2 c\n2 3 a\n3 4 t\n2 5 t\n",
"16\n1 2 o\n2 3 f\n1 4 p\n4 5 i\n5 6 e\n6 7 c\n7 8 e\n4 9 r\n9 10 e\n10 11 t\n11 12 t\n12 13 y\n10 14 f\n14 15 i\n15 16 x\n"
] | [
"3\n2\n",
"12\n2\n"
] | <img class="tex-graphics" src="https://espresso.codeforces.com/4b46644a485274790bd64830c23320ae20be3097.png" style="max-width: 100.0%;max-height: 100.0%;"/>
Broom from the second sample test can be built using language "piece", "of", "pie", "pretty", "prefix". Its simplification with *p*β=β2 obtains the language of words "pece", "o", "pe", "petty", "pefix". This language gives us the broom with minimum possible size. | [
{
"input": "5\n1 2 c\n2 3 a\n3 4 t\n2 5 t",
"output": "3\n2"
},
{
"input": "16\n1 2 o\n2 3 f\n1 4 p\n4 5 i\n5 6 e\n6 7 c\n7 8 e\n4 9 r\n9 10 e\n10 11 t\n11 12 t\n12 13 y\n10 14 f\n14 15 i\n15 16 x",
"output": "12\n2"
},
{
"input": "2\n1 2 o",
"output": "1\n1"
},
{
"input": "3\n2 3 w\n1 2 o",
"output": "2\n1"
},
{
"input": "3\n1 3 g\n1 2 o",
"output": "1\n1"
},
{
"input": "5\n1 2 s\n1 5 p\n5 4 w\n2 3 a",
"output": "3\n1"
},
{
"input": "5\n1 2 m\n1 4 v\n4 5 x\n2 3 x",
"output": "2\n1"
}
] | 30 | 0 | 0 | 4,655 |
|
159 | Matchmaker | [
"*special",
"greedy",
"sortings"
] | null | null | Polycarpus has *n* markers and *m* marker caps. Each marker is described by two numbers: *x**i* is the color and *y**i* is the diameter. Correspondingly, each cap is described by two numbers: *a**j* is the color and *b**j* is the diameter. Cap (*a**j*,<=*b**j*) can close marker (*x**i*,<=*y**i*) only if their diameters match, that is, *b**j*<==<=*y**i*. Besides, a marker is considered to be beautifully closed, if the cap color and the marker color match, that is, *a**j*<==<=*x**i*.
Find the way to close the maximum number of markers. If there are several such ways, then choose the one that has the maximum number of beautifully closed markers. | The first input line contains two space-separated integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=105) β the number of markers and the number of caps, correspondingly.
Next *n* lines describe the markers. The *i*-th line contains two space-separated integers *x**i*, *y**i* (1<=β€<=*x**i*,<=*y**i*<=β€<=1000) β the *i*-th marker's color and diameter, correspondingly.
Next *m* lines describe the caps. The *j*-th line contains two space-separated integers *a**j*, *b**j* (1<=β€<=*a**j*,<=*b**j*<=β€<=1000) β the color and diameter of the *j*-th cap, correspondingly. | Print two space-separated integers *u*,<=*v*, where *u* is the number of closed markers and *v* is the number of beautifully closed markers in the sought optimal way. Remember that you have to find the way to close the maximum number of markers, and if there are several such ways, you should choose the one where the number of beautifully closed markers is maximum. | [
"3 4\n1 2\n3 4\n2 4\n5 4\n2 4\n1 1\n1 2\n",
"2 2\n1 2\n2 1\n3 4\n5 1\n"
] | [
"3 2\n",
"1 0\n"
] | In the first test sample the first marker should be closed by the fourth cap, the second marker should be closed by the first cap and the third marker should be closed by the second cap. Thus, three markers will be closed, and two of them will be beautifully closed β the first and the third markers. | [
{
"input": "3 4\n1 2\n3 4\n2 4\n5 4\n2 4\n1 1\n1 2",
"output": "3 2"
},
{
"input": "2 2\n1 2\n2 1\n3 4\n5 1",
"output": "1 0"
},
{
"input": "6 7\n2 1\n2 2\n2 1\n1 1\n2 1\n1 2\n2 2\n2 2\n2 2\n1 2\n2 2\n1 1\n1 2",
"output": "3 3"
},
{
"input": "6 7\n2 1\n1 1\n2 2\n1 2\n1 1\n1 2\n2 1\n1 1\n1 1\n1 1\n1 2\n2 2\n1 1",
"output": "5 5"
},
{
"input": "6 7\n2 1\n2 2\n1 1\n1 2\n2 2\n1 2\n1 2\n1 1\n1 2\n2 2\n2 2\n2 2\n1 1",
"output": "6 5"
},
{
"input": "6 7\n1 1\n1 1\n1 2\n1 2\n2 2\n1 2\n2 1\n2 1\n2 1\n2 1\n1 1\n1 1\n1 2",
"output": "3 3"
},
{
"input": "6 2\n1 1\n2 1\n1 1\n1 1\n1 2\n1 1\n2 2\n1 2",
"output": "1 1"
},
{
"input": "3 3\n1 1\n1 1\n1 1\n1 1\n1 1\n1 1",
"output": "3 3"
},
{
"input": "1 1\n1 1\n1 1",
"output": "1 1"
},
{
"input": "1 1\n1 1\n2 2",
"output": "0 0"
},
{
"input": "1 1\n1 1\n1 2",
"output": "0 0"
},
{
"input": "1 1\n1 2\n2 2",
"output": "1 0"
},
{
"input": "1 5\n1 1\n2 2\n1 1\n2 1\n1 2\n1 1",
"output": "1 1"
}
] | 2,870 | 24,883,200 | 3 | 4,671 |
|
437 | The Child and Homework | [
"implementation"
] | null | null | Once upon a time a child got a test consisting of multiple-choice questions as homework. A multiple-choice question consists of four choices: A, B, C and D. Each choice has a description, and the child should find out the only one that is correct.
Fortunately the child knows how to solve such complicated test. The child will follow the algorithm:
- If there is some choice whose description at least twice shorter than all other descriptions, or at least twice longer than all other descriptions, then the child thinks the choice is great. - If there is exactly one great choice then the child chooses it. Otherwise the child chooses C (the child think it is the luckiest choice).
You are given a multiple-choice questions, can you predict child's choose? | The first line starts with "A." (without quotes), then followed the description of choice A. The next three lines contains the descriptions of the other choices in the same format. They are given in order: B, C, D. Please note, that the description goes after prefix "X.", so the prefix mustn't be counted in description's length.
Each description is non-empty and consists of at most 100 characters. Each character can be either uppercase English letter or lowercase English letter, or "_". | Print a single line with the child's choice: "A", "B", "C" or "D" (without quotes). | [
"A.VFleaKing_is_the_author_of_this_problem\nB.Picks_is_the_author_of_this_problem\nC.Picking_is_the_author_of_this_problem\nD.Ftiasch_is_cute\n",
"A.ab\nB.abcde\nC.ab\nD.abc\n",
"A.c\nB.cc\nC.c\nD.c\n"
] | [
"D\n",
"C\n",
"B\n"
] | In the first sample, the first choice has length 39, the second one has length 35, the third one has length 37, and the last one has length 15. The choice D (length 15) is twice shorter than all other choices', so it is great choice. There is no other great choices so the child will choose D.
In the second sample, no choice is great, so the child will choose the luckiest choice C.
In the third sample, the choice B (length 2) is twice longer than all other choices', so it is great choice. There is no other great choices so the child will choose B. | [
{
"input": "A.VFleaKing_is_the_author_of_this_problem\nB.Picks_is_the_author_of_this_problem\nC.Picking_is_the_author_of_this_problem\nD.Ftiasch_is_cute",
"output": "D"
},
{
"input": "A.ab\nB.abcde\nC.ab\nD.abc",
"output": "C"
},
{
"input": "A.c\nB.cc\nC.c\nD.c",
"output": "B"
},
{
"input": "A.He_nan_de_yang_guang_zhao_yao_zhe_wo_men_mei_guo_ren_lian_shang_dou_xiao_kai_yan_wahaaaaaaaaaaaaaaaa\nB.Li_bai_li_bai_fei_liu_zhi_xia_san_qian_chi_yi_si_yin_he_luo_jiu_tian_li_bai_li_bai_li_bai_li_bai_shi\nC.Peng_yu_xiang_shi_zai_tai_shen_le_jian_zhi_jiu_shi_ye_jie_du_liu_a_si_mi_da_zhen_shi_tai_shen_le_a_a\nD.Wo_huo_le_si_shi_er_nian_zhen_de_shi_cong_lai_ye_mei_you_jian_guo_zhe_me_biao_zhun_de_yi_bai_ge_zi_a",
"output": "C"
},
{
"input": "A.a___FXIcs_gB____dxFFzst_p_P_Xp_vS__cS_C_ei_\nB.fmnmkS_SeZYx_tSys_d__Exbojv_a_YPEL_BPj__I_aYH\nC._nrPx_j\nD.o_A_UwmNbC_sZ_AXk_Y___i_SN_U_UxrBN_qo_____",
"output": "C"
},
{
"input": "A.G_R__iT_ow_Y__Sm_al__u_____l_ltK\nB.CWRe__h__cbCF\nC._QJ_dVHCL_g_WBsMO__LC____hMNE_DoO__xea_ec\nD.___Zh_",
"output": "D"
},
{
"input": "A.a___FXIcs_gB____dxFFzst_p_P_Xp_vS__cS_C_ei_\nB.fmnmkS_SeZYx_tSys_d__Exbojv_a_YPEL_BPj__I_aYH\nC._nrPx_j\nD.o_A_UwmNbC_sZ_AXk_Y___i_SN_U_UxrBN_qo_____",
"output": "C"
},
{
"input": "A.G_R__iT_ow_Y__Sm_al__u_____l_ltK\nB.CWRe__h__cbCF\nC._QJ_dVHCL_g_WBsMO__LC____hMNE_DoO__xea_ec\nD.___Zh_",
"output": "D"
},
{
"input": "A.ejQ_E_E_G_e_SDjZ__lh_f_K__Z_i_B_U__S__S_EMD_ZEU_Sq\nB.o_JpInEdsrAY_T__D_S\nC.E_Vp_s\nD.a_AU_h",
"output": "A"
},
{
"input": "A.PN_m_P_qgOAMwDyxtbH__Yc__bPOh_wYH___n_Fv_qlZp_\nB._gLeDU__rr_vjrm__O_jl_R__DG___u_XqJjW_\nC.___sHLQzdTzT_tZ_Gs\nD.sZNcVa__M_To_bz_clFi_mH_",
"output": "C"
},
{
"input": "A.bR___cCYJg_Wbt____cxfXfC____c_O_\nB.guM\nC.__bzsH_Of__RjG__u_w_i__PXQL_U_Ow_U_n\nD._nHIuZsu_uU_stRC_k___vD_ZOD_u_z_c_Zf__p_iF_uD_Hdg",
"output": "B"
},
{
"input": "A.x_\nB.__RSiDT_\nC.Ci\nD.KLY_Hc_YN_xXg_DynydumheKTw_PFHo_vqXwm_DY_dA___OS_kG___",
"output": "D"
},
{
"input": "A.yYGJ_C__NYq_\nB.ozMUZ_cKKk_zVUPR_b_g_ygv_HoM__yAxvh__iE\nC.sgHJ___MYP__AWejchRvjSD_o\nD.gkfF_GiOqW_psMT_eS",
"output": "C"
},
{
"input": "A._LYm_nvl_E__RCFZ_IdO\nB.k__qIPO_ivvZyIG__L_\nC.D_SabLm_R___j_HS_t__\nD._adj_R_ngix____GSe_aw__SbOOl_",
"output": "C"
},
{
"input": "A.h_WiYTD_C_h___z_Gn_Th_uNh__g___jm\nB.__HeQaudCJcYfVi__Eg_vryuQrDkb_g__oy_BwX_Mu_\nC._MChdMhQA_UKrf_LGZk_ALTo_mnry_GNNza_X_D_u____ueJb__Y_h__CNUNDfmZATck_ad_XTbG\nD.NV___OoL__GfP_CqhD__RB_____v_T_xi",
"output": "C"
},
{
"input": "A.____JGWsfiU\nB.S_LMq__MpE_oFBs_P\nC.U_Rph_VHpUr____X_jWXbk__ElJTu_Z_wlBpKLTD\nD.p_ysvPNmbrF__",
"output": "C"
},
{
"input": "A.ejQ_E_E_G_e_SDjZ__lh_f_K__Z_i_B_U__S__S_EMD_ZEU_Sq\nB.o_JpInEdsrAY_T__D_S\nC.E_Vp_s\nD.a_AU_h",
"output": "A"
},
{
"input": "A.PN_m_P_qgOAMwDyxtbH__Yc__bPOh_wYH___n_Fv_qlZp_\nB._gLeDU__rr_vjrm__O_jl_R__DG___u_XqJjW_\nC.___sHLQzdTzT_tZ_Gs\nD.sZNcVa__M_To_bz_clFi_mH_",
"output": "C"
},
{
"input": "A.bR___cCYJg_Wbt____cxfXfC____c_O_\nB.guM\nC.__bzsH_Of__RjG__u_w_i__PXQL_U_Ow_U_n\nD._nHIuZsu_uU_stRC_k___vD_ZOD_u_z_c_Zf__p_iF_uD_Hdg",
"output": "B"
},
{
"input": "A.x_\nB.__RSiDT_\nC.Ci\nD.KLY_Hc_YN_xXg_DynydumheKTw_PFHo_vqXwm_DY_dA___OS_kG___",
"output": "D"
},
{
"input": "A.yYGJ_C__NYq_\nB.ozMUZ_cKKk_zVUPR_b_g_ygv_HoM__yAxvh__iE\nC.sgHJ___MYP__AWejchRvjSD_o\nD.gkfF_GiOqW_psMT_eS",
"output": "C"
},
{
"input": "A._LYm_nvl_E__RCFZ_IdO\nB.k__qIPO_ivvZyIG__L_\nC.D_SabLm_R___j_HS_t__\nD._adj_R_ngix____GSe_aw__SbOOl_",
"output": "C"
},
{
"input": "A.h_WiYTD_C_h___z_Gn_Th_uNh__g___jm\nB.__HeQaudCJcYfVi__Eg_vryuQrDkb_g__oy_BwX_Mu_\nC._MChdMhQA_UKrf_LGZk_ALTo_mnry_GNNza_X_D_u____ueJb__Y_h__CNUNDfmZATck_ad_XTbG\nD.NV___OoL__GfP_CqhD__RB_____v_T_xi",
"output": "C"
},
{
"input": "A.____JGWsfiU\nB.S_LMq__MpE_oFBs_P\nC.U_Rph_VHpUr____X_jWXbk__ElJTu_Z_wlBpKLTD\nD.p_ysvPNmbrF__",
"output": "C"
},
{
"input": "A.aaaaaa\nB.aaa\nC.aaa\nD.aaa",
"output": "A"
},
{
"input": "A.aaa\nB.aaaaaa\nC.aaaaaa\nD.aaaaaa",
"output": "A"
},
{
"input": "A.a\nB.b\nC.c\nD.d",
"output": "C"
},
{
"input": "A._\nB.__\nC.____\nD.________",
"output": "C"
},
{
"input": "A.____\nB.________\nC.________\nD._______",
"output": "C"
},
{
"input": "A.h\nB.asdf\nC.asqw\nD.qwertasdfg",
"output": "C"
},
{
"input": "A.aa\nB.aaaaa\nC.aaaaaa\nD.aaaaaaaaaaaaa",
"output": "C"
},
{
"input": "A.ccc\nB.ccccccc\nC.ccc\nD.c",
"output": "C"
},
{
"input": "A.c\nB.ccc\nC.cccccccccccccccccc\nD.cccccc",
"output": "C"
},
{
"input": "A.aa\nB.bb\nC.cc\nD.ddd",
"output": "C"
},
{
"input": "A.QW\nB.WERT\nC.QWER\nD.QWERTYUI",
"output": "C"
}
] | 108 | 6,963,200 | 0 | 4,688 |
|
631 | Report | [
"data structures",
"sortings"
] | null | null | Each month Blake gets the report containing main economic indicators of the company "Blake Technologies". There are *n* commodities produced by the company. For each of them there is exactly one integer in the final report, that denotes corresponding revenue. Before the report gets to Blake, it passes through the hands of *m* managers. Each of them may reorder the elements in some order. Namely, the *i*-th manager either sorts first *r**i* numbers in non-descending or non-ascending order and then passes the report to the manager *i*<=+<=1, or directly to Blake (if this manager has number *i*<==<=*m*).
Employees of the "Blake Technologies" are preparing the report right now. You know the initial sequence *a**i* of length *n* and the description of each manager, that is value *r**i* and his favourite order. You are asked to speed up the process and determine how the final report will look like. | The first line of the input contains two integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=200<=000)Β β the number of commodities in the report and the number of managers, respectively.
The second line contains *n* integers *a**i* (|*a**i*|<=β€<=109)Β β the initial report before it gets to the first manager.
Then follow *m* lines with the descriptions of the operations managers are going to perform. The *i*-th of these lines contains two integers *t**i* and *r**i* (, 1<=β€<=*r**i*<=β€<=*n*), meaning that the *i*-th manager sorts the first *r**i* numbers either in the non-descending (if *t**i*<==<=1) or non-ascending (if *t**i*<==<=2) order. | Print *n* integersΒ β the final report, which will be passed to Blake by manager number *m*. | [
"3 1\n1 2 3\n2 2\n",
"4 2\n1 2 4 3\n2 3\n1 2\n"
] | [
"2 1 3 ",
"2 4 1 3 "
] | In the first sample, the initial report looked like: 1 2 3. After the first manager the first two numbers were transposed: 2 1 3. The report got to Blake in this form.
In the second sample the original report was like this: 1 2 4 3. After the first manager the report changed to: 4 2 1 3. After the second manager the report changed to: 2 4 1 3. This report was handed over to Blake. | [
{
"input": "3 1\n1 2 3\n2 2",
"output": "2 1 3 "
},
{
"input": "4 2\n1 2 4 3\n2 3\n1 2",
"output": "2 4 1 3 "
},
{
"input": "4 1\n4 3 2 1\n1 4",
"output": "1 2 3 4 "
},
{
"input": "5 1\n1 2 3 4 5\n2 5",
"output": "5 4 3 2 1 "
},
{
"input": "6 2\n3 1 2 6 4 5\n1 6\n2 3",
"output": "3 2 1 4 5 6 "
},
{
"input": "10 3\n6 4 0 2 -3 7 8 -9 1 5\n1 8\n1 4\n2 2",
"output": "-3 -9 0 2 4 6 7 8 1 5 "
},
{
"input": "100 30\n65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 74 57 115 16 55 88 79 97 21 80 41 56 49 103 61 66 1 36 44 43 82 37 38 106 27 114 51 112 55 87 41 69 31 86 58 27 46 99 18 105 91 38 5 9 2 109 39 2 27 47\n2 38\n2 32\n1 46\n1 37\n1 20\n1 5\n2 42\n2 18\n1 35\n1 36\n2 44\n1 36\n1 20\n2 21\n2 14\n1 13\n2 2\n1 15\n2 50\n2 35\n1 42\n1 21\n1 50\n2 50\n1 1\n2 48\n2 24\n1 34\n1 23\n2 9",
"output": "65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 74 57 115 16 55 88 79 97 21 80 41 56 49 103 61 66 1 36 44 43 82 37 38 106 27 114 51 112 55 87 41 69 31 86 58 27 46 99 18 105 91 38 5 9 2 109 39 2 27 47 "
},
{
"input": "1 1\n1234\n1 1",
"output": "1234 "
},
{
"input": "1 1\n1000000000\n2 1",
"output": "1000000000 "
},
{
"input": "1 2\n-1000000000\n1 1\n2 1",
"output": "-1000000000 "
},
{
"input": "30 13\n15 44 5 56 84 15 24 72 97 3 61 97 36 33 98 49 1 40 76 94 7 46 85 53 79 68 78 54 80 33\n2 18\n1 9\n1 6\n2 30\n2 15\n2 4\n2 17\n2 16\n2 20\n2 16\n2 7\n2 12\n1 20",
"output": "40 44 46 49 53 54 56 61 68 72 76 78 79 80 84 85 94 97 97 98 36 33 33 24 15 15 7 5 3 1 "
}
] | 2,000 | 30,515,200 | 0 | 4,697 |
|
898 | Proper Nutrition | [
"brute force",
"implementation",
"number theory"
] | null | null | Vasya has *n* burles. One bottle of Ber-Cola costs *a* burles and one Bars bar costs *b* burles. He can buy any non-negative integer number of bottles of Ber-Cola and any non-negative integer number of Bars bars.
Find out if it's possible to buy some amount of bottles of Ber-Cola and Bars bars and spend exactly *n* burles.
In other words, you should find two non-negative integers *x* and *y* such that Vasya can buy *x* bottles of Ber-Cola and *y* Bars bars and *x*Β·*a*<=+<=*y*Β·*b*<==<=*n* or tell that it's impossible. | First line contains single integer *n* (1<=β€<=*n*<=β€<=10<=000<=000)Β β amount of money, that Vasya has.
Second line contains single integer *a* (1<=β€<=*a*<=β€<=10<=000<=000)Β β cost of one bottle of Ber-Cola.
Third line contains single integer *b* (1<=β€<=*b*<=β€<=10<=000<=000)Β β cost of one Bars bar. | If Vasya can't buy Bars and Ber-Cola in such a way to spend exactly *n* burles print Β«NOΒ» (without quotes).
Otherwise in first line print Β«YESΒ» (without quotes). In second line print two non-negative integers *x* and *y*Β β number of bottles of Ber-Cola and number of Bars bars Vasya should buy in order to spend exactly *n* burles, i.e. *x*Β·*a*<=+<=*y*Β·*b*<==<=*n*. If there are multiple answers print any of them.
Any of numbers *x* and *y* can be equal 0. | [
"7\n2\n3\n",
"100\n25\n10\n",
"15\n4\n8\n",
"9960594\n2551\n2557\n"
] | [
"YES\n2 1\n",
"YES\n0 10\n",
"NO\n",
"YES\n1951 1949\n"
] | In first example Vasya can buy two bottles of Ber-Cola and one Bars bar. He will spend exactly 2Β·2β+β1Β·3β=β7 burles.
In second example Vasya can spend exactly *n* burles multiple ways:
- buy two bottles of Ber-Cola and five Bars bars; - buy four bottles of Ber-Cola and don't buy Bars bars; - don't buy Ber-Cola and buy 10 Bars bars.
In third example it's impossible to but Ber-Cola and Bars bars in order to spend exactly *n* burles. | [
{
"input": "7\n2\n3",
"output": "YES\n2 1"
},
{
"input": "100\n25\n10",
"output": "YES\n0 10"
},
{
"input": "15\n4\n8",
"output": "NO"
},
{
"input": "9960594\n2551\n2557",
"output": "YES\n1951 1949"
},
{
"input": "10000000\n1\n1",
"output": "YES\n0 10000000"
},
{
"input": "9999999\n9999\n9999",
"output": "NO"
},
{
"input": "9963629\n2591\n2593",
"output": "YES\n635 3208"
},
{
"input": "1\n7\n8",
"output": "NO"
},
{
"input": "9963630\n2591\n2593",
"output": "YES\n1931 1913"
},
{
"input": "7516066\n1601\n4793",
"output": "YES\n4027 223"
},
{
"input": "6509546\n1607\n6221",
"output": "YES\n617 887"
},
{
"input": "2756250\n8783\n29",
"output": "YES\n21 88683"
},
{
"input": "7817510\n2377\n743",
"output": "YES\n560 8730"
},
{
"input": "6087210\n1583\n1997",
"output": "YES\n1070 2200"
},
{
"input": "4\n2\n2",
"output": "YES\n0 2"
},
{
"input": "7996960\n4457\n5387",
"output": "YES\n727 883"
},
{
"input": "7988988\n4021\n3169",
"output": "YES\n1789 251"
},
{
"input": "4608528\n9059\n977",
"output": "YES\n349 1481"
},
{
"input": "8069102\n2789\n47",
"output": "YES\n3 171505"
},
{
"input": "3936174\n4783\n13",
"output": "YES\n5 300943"
},
{
"input": "10000000\n9999999\n1",
"output": "YES\n0 10000000"
},
{
"input": "10000000\n1\n9999999",
"output": "YES\n1 1"
},
{
"input": "4\n1\n3",
"output": "YES\n1 1"
},
{
"input": "4\n1\n2",
"output": "YES\n0 2"
},
{
"input": "4\n3\n1",
"output": "YES\n0 4"
},
{
"input": "4\n2\n1",
"output": "YES\n0 4"
},
{
"input": "100\n10\n20",
"output": "YES\n0 5"
},
{
"input": "101\n11\n11",
"output": "NO"
},
{
"input": "121\n11\n11",
"output": "YES\n0 11"
},
{
"input": "25\n5\n6",
"output": "YES\n5 0"
},
{
"input": "1\n1\n1",
"output": "YES\n0 1"
},
{
"input": "10000000\n2\n1",
"output": "YES\n0 10000000"
},
{
"input": "10000000\n1234523\n1",
"output": "YES\n0 10000000"
},
{
"input": "10000000\n5000000\n5000000",
"output": "YES\n0 2"
},
{
"input": "10000000\n5000001\n5000000",
"output": "YES\n0 2"
},
{
"input": "10000000\n5000000\n5000001",
"output": "YES\n2 0"
},
{
"input": "9999999\n9999999\n9999999",
"output": "YES\n0 1"
},
{
"input": "10000000\n10000000\n10000000",
"output": "YES\n0 1"
},
{
"input": "10\n1\n3",
"output": "YES\n1 3"
},
{
"input": "97374\n689\n893",
"output": "NO"
},
{
"input": "100096\n791\n524",
"output": "NO"
},
{
"input": "75916\n651\n880",
"output": "NO"
},
{
"input": "110587\n623\n806",
"output": "NO"
},
{
"input": "5600\n670\n778",
"output": "NO"
},
{
"input": "81090\n527\n614",
"output": "NO"
},
{
"input": "227718\n961\n865",
"output": "NO"
},
{
"input": "10000000\n3\n999999",
"output": "NO"
},
{
"input": "3\n4\n5",
"output": "NO"
},
{
"input": "9999999\n2\n2",
"output": "NO"
},
{
"input": "9999999\n2\n4",
"output": "NO"
},
{
"input": "9999997\n2\n5",
"output": "YES\n1 1999999"
},
{
"input": "9366189\n4326262\n8994187",
"output": "NO"
},
{
"input": "1000000\n1\n10000000",
"output": "YES\n1000000 0"
},
{
"input": "9999991\n2\n2",
"output": "NO"
},
{
"input": "10000000\n7\n7",
"output": "NO"
},
{
"input": "9999991\n2\n4",
"output": "NO"
},
{
"input": "10000000\n3\n6",
"output": "NO"
},
{
"input": "10000000\n11\n11",
"output": "NO"
},
{
"input": "4\n7\n3",
"output": "NO"
},
{
"input": "1000003\n2\n2",
"output": "NO"
},
{
"input": "1000000\n7\n7",
"output": "NO"
},
{
"input": "999999\n2\n2",
"output": "NO"
},
{
"input": "8\n13\n5",
"output": "NO"
},
{
"input": "1000003\n15\n3",
"output": "NO"
},
{
"input": "7\n7\n2",
"output": "YES\n1 0"
},
{
"input": "9999999\n2\n8",
"output": "NO"
},
{
"input": "1000000\n3\n7",
"output": "YES\n5 142855"
},
{
"input": "9999999\n1\n10000000",
"output": "YES\n9999999 0"
},
{
"input": "100\n1\n1000000",
"output": "YES\n100 0"
},
{
"input": "10000000\n9999999\n9999997",
"output": "NO"
},
{
"input": "2\n1\n3",
"output": "YES\n2 0"
},
{
"input": "3\n5\n2",
"output": "NO"
},
{
"input": "5\n2\n3",
"output": "YES\n1 1"
},
{
"input": "10000000\n7\n14",
"output": "NO"
},
{
"input": "10000000\n2\n9999999",
"output": "YES\n5000000 0"
},
{
"input": "10000000\n3\n3",
"output": "NO"
},
{
"input": "1\n3\n2",
"output": "NO"
},
{
"input": "25\n27\n2",
"output": "NO"
},
{
"input": "3\n2\n17",
"output": "NO"
},
{
"input": "999997\n4\n8",
"output": "NO"
},
{
"input": "2000000\n1\n2000001",
"output": "YES\n2000000 0"
},
{
"input": "8\n7\n3",
"output": "NO"
},
{
"input": "7005920\n5705\n28145",
"output": "NO"
},
{
"input": "2\n6\n4",
"output": "NO"
},
{
"input": "10000000\n9999999\n3",
"output": "NO"
},
{
"input": "10000000\n77\n99",
"output": "NO"
},
{
"input": "100\n8\n70",
"output": "NO"
},
{
"input": "99999\n2\n2",
"output": "NO"
},
{
"input": "5\n7\n2",
"output": "NO"
},
{
"input": "999999\n12\n14",
"output": "NO"
},
{
"input": "100\n1\n1000",
"output": "YES\n100 0"
},
{
"input": "10000000\n123\n321",
"output": "NO"
},
{
"input": "9369319\n4\n2",
"output": "NO"
},
{
"input": "9999998\n3\n3",
"output": "NO"
},
{
"input": "85\n5\n85",
"output": "YES\n0 1"
},
{
"input": "64549\n9999999\n2",
"output": "NO"
},
{
"input": "10000000\n3\n7",
"output": "YES\n1 1428571"
},
{
"input": "9999889\n2\n2",
"output": "NO"
},
{
"input": "10000000\n9999999\n123",
"output": "NO"
},
{
"input": "64549\n2\n9999999",
"output": "NO"
}
] | 670 | 1,638,400 | 0 | 4,714 |
|
558 | A Simple Task | [
"data structures",
"sortings",
"strings"
] | null | null | This task is very simple. Given a string *S* of length *n* and *q* queries each query is on the format *i* *j* *k* which means sort the substring consisting of the characters from *i* to *j* in non-decreasing order if *k*<==<=1 or in non-increasing order if *k*<==<=0.
Output the final string after applying the queries. | The first line will contain two integers *n*,<=*q* (1<=β€<=*n*<=β€<=105, 0<=β€<=*q*<=β€<=50<=000), the length of the string and the number of queries respectively.
Next line contains a string *S* itself. It contains only lowercase English letters.
Next *q* lines will contain three integers each *i*,<=*j*,<=*k* (1<=β€<=*i*<=β€<=*j*<=β€<=*n*, ). | Output one line, the string *S* after applying the queries. | [
"10 5\nabacdabcda\n7 10 0\n5 8 1\n1 4 0\n3 6 0\n7 10 1\n",
"10 1\nagjucbvdfk\n1 10 1\n"
] | [
"cbcaaaabdd",
"abcdfgjkuv"
] | First sample test explanation:
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/3ac4e8cc7e335675a4a2b7b4758bfb3865377cea.png" style="max-width: 100.0%;max-height: 100.0%;"/>
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a90b5b03cf59288d8861f0142ecbdf6b12f69e5c.png" style="max-width: 100.0%;max-height: 100.0%;"/>
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/1f482a91a275b6bce07eaed85312eac0cfcc6ccf.png" style="max-width: 100.0%;max-height: 100.0%;"/>
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/33b1a4a924f4bd562551ba4e40309f180dbe22e0.png" style="max-width: 100.0%;max-height: 100.0%;"/>
<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bddc77fd5b02858eb2ff29819cd16a93dbd241e6.png" style="max-width: 100.0%;max-height: 100.0%;"/> | [
{
"input": "10 5\nabacdabcda\n7 10 0\n5 8 1\n1 4 0\n3 6 0\n7 10 1",
"output": "cbcaaaabdd"
},
{
"input": "10 1\nagjucbvdfk\n1 10 1",
"output": "abcdfgjkuv"
},
{
"input": "10 6\nrmaahmdmuo\n1 3 1\n4 6 0\n5 6 1\n7 8 0\n8 10 0\n8 9 1",
"output": "amrmahmoud"
},
{
"input": "10 5\nhbtngdflmj\n1 10 1\n2 9 0\n3 8 1\n4 7 0\n5 6 1",
"output": "bnflhjgmdt"
},
{
"input": "13 0\nokaywearedone",
"output": "okaywearedone"
}
] | 5,000 | 2,560,000 | 0 | 4,715 |
|
630 | Selection of Personnel | [
"combinatorics",
"math"
] | null | null | One company of IT City decided to create a group of innovative developments consisting from 5 to 7 people and hire new employees for it. After placing an advertisment the company received *n* resumes. Now the HR department has to evaluate each possible group composition and select one of them. Your task is to count the number of variants of group composition to evaluate. | The only line of the input contains one integer *n* (7<=β€<=*n*<=β€<=777) β the number of potential employees that sent resumes. | Output one integer β the number of different variants of group composition. | [
"7\n"
] | [
"29"
] | none | [
{
"input": "7",
"output": "29"
},
{
"input": "8",
"output": "92"
},
{
"input": "9",
"output": "246"
},
{
"input": "10",
"output": "582"
},
{
"input": "321",
"output": "66715035255088"
},
{
"input": "624",
"output": "7147161340917624"
},
{
"input": "666",
"output": "11292070960994226"
},
{
"input": "700",
"output": "16017044425409540"
},
{
"input": "776",
"output": "33019955679376860"
},
{
"input": "777",
"output": "33319741730082870"
}
] | 46 | 0 | 3 | 4,732 |
|
578 | "Or" Game | [
"brute force",
"greedy"
] | null | null | You are given *n* numbers *a*1,<=*a*2,<=...,<=*a**n*. You can perform at most *k* operations. For each operation you can multiply one of the numbers by *x*. We want to make as large as possible, where denotes the bitwise OR.
Find the maximum possible value of after performing at most *k* operations optimally. | The first line contains three integers *n*, *k* and *x* (1<=β€<=*n*<=β€<=200<=000, 1<=β€<=*k*<=β€<=10, 2<=β€<=*x*<=β€<=8).
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=β€<=*a**i*<=β€<=109). | Output the maximum value of a bitwise OR of sequence elements after performing operations. | [
"3 1 2\n1 1 1\n",
"4 2 3\n1 2 4 8\n"
] | [
"3\n",
"79\n"
] | For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2 so the result is <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/1ee73b671ed4bc53f2f96ed1a85fd98388e1712b.png" style="max-width: 100.0%;max-height: 100.0%;"/>.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result. | [
{
"input": "3 1 2\n1 1 1",
"output": "3"
},
{
"input": "4 2 3\n1 2 4 8",
"output": "79"
},
{
"input": "2 1 2\n12 9",
"output": "30"
},
{
"input": "2 1 2\n12 7",
"output": "31"
},
{
"input": "3 1 3\n3 2 0",
"output": "11"
},
{
"input": "5 10 8\n1000000000 1000000000 1000000000 1000000000 1000000000",
"output": "1073741825000000000"
},
{
"input": "1 2 3\n612635770",
"output": "5513721930"
},
{
"input": "3 2 5\n0 2 3",
"output": "75"
},
{
"input": "2 1 8\n18 17",
"output": "154"
},
{
"input": "5 10 8\n0 0 0 0 0",
"output": "0"
},
{
"input": "1 1 2\n1",
"output": "2"
},
{
"input": "1 1 2\n0",
"output": "0"
},
{
"input": "3 2 6\n724148075 828984987 810015532",
"output": "29996605423"
},
{
"input": "3 1 2\n17 18 4",
"output": "54"
},
{
"input": "3 1 2\n4 17 18",
"output": "54"
},
{
"input": "2 2 2\n60 59",
"output": "252"
},
{
"input": "2 2 2\n9 10",
"output": "46"
},
{
"input": "3 1 2\n10 12 5",
"output": "31"
},
{
"input": "3 1 2\n20 17 8",
"output": "62"
},
{
"input": "3 1 2\n5 12 10",
"output": "31"
},
{
"input": "3 1 8\n10 17 18",
"output": "155"
},
{
"input": "3 1 2\n17 20 28",
"output": "62"
},
{
"input": "5 1 3\n1 5 13 8 16",
"output": "63"
}
] | 124 | 0 | 0 | 4,738 |
|
268 | Beautiful Sets of Points | [
"constructive algorithms",
"implementation"
] | null | null | Manao has invented a new mathematical term β a beautiful set of points. He calls a set of points on a plane beautiful if it meets the following conditions:
1. The coordinates of each point in the set are integers. 1. For any two points from the set, the distance between them is a non-integer.
Consider all points (*x*,<=*y*) which satisfy the inequations: 0<=β€<=*x*<=β€<=*n*; 0<=β€<=*y*<=β€<=*m*; *x*<=+<=*y*<=><=0. Choose their subset of maximum size such that it is also a beautiful set of points. | The single line contains two space-separated integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=100). | In the first line print a single integer β the size *k* of the found beautiful set. In each of the next *k* lines print a pair of space-separated integers β the *x*- and *y*- coordinates, respectively, of a point from the set.
If there are several optimal solutions, you may print any of them. | [
"2 2\n",
"4 3\n"
] | [
"3\n0 1\n1 2\n2 0\n",
"4\n0 3\n2 1\n3 0\n4 2\n"
] | Consider the first sample. The distance between points (0, 1) and (1, 2) equals <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/bfe16f27ebc966df6f10ba356a1547b6e7242dd7.png" style="max-width: 100.0%;max-height: 100.0%;"/>, between (0, 1) and (2, 0) β <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/23d63d8a57cddda72562a512c05111054cd85870.png" style="max-width: 100.0%;max-height: 100.0%;"/>, between (1, 2) and (2, 0) β <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/23d63d8a57cddda72562a512c05111054cd85870.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Thus, these points form a beautiful set. You cannot form a beautiful set with more than three points out of the given points. Note that this is not the only solution. | [
{
"input": "2 2",
"output": "3\n0 1\n1 2\n2 0"
},
{
"input": "4 3",
"output": "4\n0 3\n2 1\n3 0\n4 2"
},
{
"input": "21 21",
"output": "22\n21 0\n20 1\n19 2\n18 3\n17 4\n16 5\n15 6\n14 7\n13 8\n12 9\n11 10\n10 11\n9 12\n8 13\n7 14\n6 15\n5 16\n4 17\n3 18\n2 19\n1 20\n0 21"
},
{
"input": "10 1",
"output": "2\n1 0\n0 1"
},
{
"input": "4 4",
"output": "5\n4 0\n3 1\n2 2\n1 3\n0 4"
},
{
"input": "1 1",
"output": "2\n1 0\n0 1"
},
{
"input": "5 5",
"output": "6\n5 0\n4 1\n3 2\n2 3\n1 4\n0 5"
},
{
"input": "100 100",
"output": "101\n100 0\n99 1\n98 2\n97 3\n96 4\n95 5\n94 6\n93 7\n92 8\n91 9\n90 10\n89 11\n88 12\n87 13\n86 14\n85 15\n84 16\n83 17\n82 18\n81 19\n80 20\n79 21\n78 22\n77 23\n76 24\n75 25\n74 26\n73 27\n72 28\n71 29\n70 30\n69 31\n68 32\n67 33\n66 34\n65 35\n64 36\n63 37\n62 38\n61 39\n60 40\n59 41\n58 42\n57 43\n56 44\n55 45\n54 46\n53 47\n52 48\n51 49\n50 50\n49 51\n48 52\n47 53\n46 54\n45 55\n44 56\n43 57\n42 58\n41 59\n40 60\n39 61\n38 62\n37 63\n36 64\n35 65\n34 66\n33 67\n32 68\n31 69\n30 70\n29 71\n28 72\n27 7..."
},
{
"input": "96 96",
"output": "97\n96 0\n95 1\n94 2\n93 3\n92 4\n91 5\n90 6\n89 7\n88 8\n87 9\n86 10\n85 11\n84 12\n83 13\n82 14\n81 15\n80 16\n79 17\n78 18\n77 19\n76 20\n75 21\n74 22\n73 23\n72 24\n71 25\n70 26\n69 27\n68 28\n67 29\n66 30\n65 31\n64 32\n63 33\n62 34\n61 35\n60 36\n59 37\n58 38\n57 39\n56 40\n55 41\n54 42\n53 43\n52 44\n51 45\n50 46\n49 47\n48 48\n47 49\n46 50\n45 51\n44 52\n43 53\n42 54\n41 55\n40 56\n39 57\n38 58\n37 59\n36 60\n35 61\n34 62\n33 63\n32 64\n31 65\n30 66\n29 67\n28 68\n27 69\n26 70\n25 71\n24 72\n23 73\n..."
},
{
"input": "99 100",
"output": "100\n99 0\n98 1\n97 2\n96 3\n95 4\n94 5\n93 6\n92 7\n91 8\n90 9\n89 10\n88 11\n87 12\n86 13\n85 14\n84 15\n83 16\n82 17\n81 18\n80 19\n79 20\n78 21\n77 22\n76 23\n75 24\n74 25\n73 26\n72 27\n71 28\n70 29\n69 30\n68 31\n67 32\n66 33\n65 34\n64 35\n63 36\n62 37\n61 38\n60 39\n59 40\n58 41\n57 42\n56 43\n55 44\n54 45\n53 46\n52 47\n51 48\n50 49\n49 50\n48 51\n47 52\n46 53\n45 54\n44 55\n43 56\n42 57\n41 58\n40 59\n39 60\n38 61\n37 62\n36 63\n35 64\n34 65\n33 66\n32 67\n31 68\n30 69\n29 70\n28 71\n27 72\n26 73..."
},
{
"input": "67 58",
"output": "59\n58 0\n57 1\n56 2\n55 3\n54 4\n53 5\n52 6\n51 7\n50 8\n49 9\n48 10\n47 11\n46 12\n45 13\n44 14\n43 15\n42 16\n41 17\n40 18\n39 19\n38 20\n37 21\n36 22\n35 23\n34 24\n33 25\n32 26\n31 27\n30 28\n29 29\n28 30\n27 31\n26 32\n25 33\n24 34\n23 35\n22 36\n21 37\n20 38\n19 39\n18 40\n17 41\n16 42\n15 43\n14 44\n13 45\n12 46\n11 47\n10 48\n9 49\n8 50\n7 51\n6 52\n5 53\n4 54\n3 55\n2 56\n1 57\n0 58"
},
{
"input": "67 59",
"output": "60\n59 0\n58 1\n57 2\n56 3\n55 4\n54 5\n53 6\n52 7\n51 8\n50 9\n49 10\n48 11\n47 12\n46 13\n45 14\n44 15\n43 16\n42 17\n41 18\n40 19\n39 20\n38 21\n37 22\n36 23\n35 24\n34 25\n33 26\n32 27\n31 28\n30 29\n29 30\n28 31\n27 32\n26 33\n25 34\n24 35\n23 36\n22 37\n21 38\n20 39\n19 40\n18 41\n17 42\n16 43\n15 44\n14 45\n13 46\n12 47\n11 48\n10 49\n9 50\n8 51\n7 52\n6 53\n5 54\n4 55\n3 56\n2 57\n1 58\n0 59"
},
{
"input": "80 91",
"output": "81\n80 0\n79 1\n78 2\n77 3\n76 4\n75 5\n74 6\n73 7\n72 8\n71 9\n70 10\n69 11\n68 12\n67 13\n66 14\n65 15\n64 16\n63 17\n62 18\n61 19\n60 20\n59 21\n58 22\n57 23\n56 24\n55 25\n54 26\n53 27\n52 28\n51 29\n50 30\n49 31\n48 32\n47 33\n46 34\n45 35\n44 36\n43 37\n42 38\n41 39\n40 40\n39 41\n38 42\n37 43\n36 44\n35 45\n34 46\n33 47\n32 48\n31 49\n30 50\n29 51\n28 52\n27 53\n26 54\n25 55\n24 56\n23 57\n22 58\n21 59\n20 60\n19 61\n18 62\n17 63\n16 64\n15 65\n14 66\n13 67\n12 68\n11 69\n10 70\n9 71\n8 72\n7 73\n6 ..."
},
{
"input": "100 11",
"output": "12\n11 0\n10 1\n9 2\n8 3\n7 4\n6 5\n5 6\n4 7\n3 8\n2 9\n1 10\n0 11"
},
{
"input": "16 55",
"output": "17\n16 0\n15 1\n14 2\n13 3\n12 4\n11 5\n10 6\n9 7\n8 8\n7 9\n6 10\n5 11\n4 12\n3 13\n2 14\n1 15\n0 16"
},
{
"input": "13 71",
"output": "14\n13 0\n12 1\n11 2\n10 3\n9 4\n8 5\n7 6\n6 7\n5 8\n4 9\n3 10\n2 11\n1 12\n0 13"
},
{
"input": "30 40",
"output": "31\n30 0\n29 1\n28 2\n27 3\n26 4\n25 5\n24 6\n23 7\n22 8\n21 9\n20 10\n19 11\n18 12\n17 13\n16 14\n15 15\n14 16\n13 17\n12 18\n11 19\n10 20\n9 21\n8 22\n7 23\n6 24\n5 25\n4 26\n3 27\n2 28\n1 29\n0 30"
},
{
"input": "77 77",
"output": "78\n77 0\n76 1\n75 2\n74 3\n73 4\n72 5\n71 6\n70 7\n69 8\n68 9\n67 10\n66 11\n65 12\n64 13\n63 14\n62 15\n61 16\n60 17\n59 18\n58 19\n57 20\n56 21\n55 22\n54 23\n53 24\n52 25\n51 26\n50 27\n49 28\n48 29\n47 30\n46 31\n45 32\n44 33\n43 34\n42 35\n41 36\n40 37\n39 38\n38 39\n37 40\n36 41\n35 42\n34 43\n33 44\n32 45\n31 46\n30 47\n29 48\n28 49\n27 50\n26 51\n25 52\n24 53\n23 54\n22 55\n21 56\n20 57\n19 58\n18 59\n17 60\n16 61\n15 62\n14 63\n13 64\n12 65\n11 66\n10 67\n9 68\n8 69\n7 70\n6 71\n5 72\n4 73\n3 74\n..."
},
{
"input": "6 6",
"output": "7\n6 0\n5 1\n4 2\n3 3\n2 4\n1 5\n0 6"
},
{
"input": "37 42",
"output": "38\n37 0\n36 1\n35 2\n34 3\n33 4\n32 5\n31 6\n30 7\n29 8\n28 9\n27 10\n26 11\n25 12\n24 13\n23 14\n22 15\n21 16\n20 17\n19 18\n18 19\n17 20\n16 21\n15 22\n14 23\n13 24\n12 25\n11 26\n10 27\n9 28\n8 29\n7 30\n6 31\n5 32\n4 33\n3 34\n2 35\n1 36\n0 37"
},
{
"input": "88 88",
"output": "89\n88 0\n87 1\n86 2\n85 3\n84 4\n83 5\n82 6\n81 7\n80 8\n79 9\n78 10\n77 11\n76 12\n75 13\n74 14\n73 15\n72 16\n71 17\n70 18\n69 19\n68 20\n67 21\n66 22\n65 23\n64 24\n63 25\n62 26\n61 27\n60 28\n59 29\n58 30\n57 31\n56 32\n55 33\n54 34\n53 35\n52 36\n51 37\n50 38\n49 39\n48 40\n47 41\n46 42\n45 43\n44 44\n43 45\n42 46\n41 47\n40 48\n39 49\n38 50\n37 51\n36 52\n35 53\n34 54\n33 55\n32 56\n31 57\n30 58\n29 59\n28 60\n27 61\n26 62\n25 63\n24 64\n23 65\n22 66\n21 67\n20 68\n19 69\n18 70\n17 71\n16 72\n15 73\n..."
},
{
"input": "95 99",
"output": "96\n95 0\n94 1\n93 2\n92 3\n91 4\n90 5\n89 6\n88 7\n87 8\n86 9\n85 10\n84 11\n83 12\n82 13\n81 14\n80 15\n79 16\n78 17\n77 18\n76 19\n75 20\n74 21\n73 22\n72 23\n71 24\n70 25\n69 26\n68 27\n67 28\n66 29\n65 30\n64 31\n63 32\n62 33\n61 34\n60 35\n59 36\n58 37\n57 38\n56 39\n55 40\n54 41\n53 42\n52 43\n51 44\n50 45\n49 46\n48 47\n47 48\n46 49\n45 50\n44 51\n43 52\n42 53\n41 54\n40 55\n39 56\n38 57\n37 58\n36 59\n35 60\n34 61\n33 62\n32 63\n31 64\n30 65\n29 66\n28 67\n27 68\n26 69\n25 70\n24 71\n23 72\n22 73\n..."
},
{
"input": "93 70",
"output": "71\n70 0\n69 1\n68 2\n67 3\n66 4\n65 5\n64 6\n63 7\n62 8\n61 9\n60 10\n59 11\n58 12\n57 13\n56 14\n55 15\n54 16\n53 17\n52 18\n51 19\n50 20\n49 21\n48 22\n47 23\n46 24\n45 25\n44 26\n43 27\n42 28\n41 29\n40 30\n39 31\n38 32\n37 33\n36 34\n35 35\n34 36\n33 37\n32 38\n31 39\n30 40\n29 41\n28 42\n27 43\n26 44\n25 45\n24 46\n23 47\n22 48\n21 49\n20 50\n19 51\n18 52\n17 53\n16 54\n15 55\n14 56\n13 57\n12 58\n11 59\n10 60\n9 61\n8 62\n7 63\n6 64\n5 65\n4 66\n3 67\n2 68\n1 69\n0 70"
},
{
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},
{
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"output": "2\n1 0\n0 1"
},
{
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"output": "3\n2 0\n1 1\n0 2"
},
{
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"output": "7\n6 0\n5 1\n4 2\n3 3\n2 4\n1 5\n0 6"
},
{
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"output": "29\n28 0\n27 1\n26 2\n25 3\n24 4\n23 5\n22 6\n21 7\n20 8\n19 9\n18 10\n17 11\n16 12\n15 13\n14 14\n13 15\n12 16\n11 17\n10 18\n9 19\n8 20\n7 21\n6 22\n5 23\n4 24\n3 25\n2 26\n1 27\n0 28"
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},
{
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"output": "49\n48 0\n47 1\n46 2\n45 3\n44 4\n43 5\n42 6\n41 7\n40 8\n39 9\n38 10\n37 11\n36 12\n35 13\n34 14\n33 15\n32 16\n31 17\n30 18\n29 19\n28 20\n27 21\n26 22\n25 23\n24 24\n23 25\n22 26\n21 27\n20 28\n19 29\n18 30\n17 31\n16 32\n15 33\n14 34\n13 35\n12 36\n11 37\n10 38\n9 39\n8 40\n7 41\n6 42\n5 43\n4 44\n3 45\n2 46\n1 47\n0 48"
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},
{
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},
{
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},
{
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{
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{
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{
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},
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},
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{
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},
{
"input": "10 10",
"output": "11\n10 0\n9 1\n8 2\n7 3\n6 4\n5 5\n4 6\n3 7\n2 8\n1 9\n0 10"
},
{
"input": "3 7",
"output": "4\n3 0\n2 1\n1 2\n0 3"
},
{
"input": "98 76",
"output": "77\n76 0\n75 1\n74 2\n73 3\n72 4\n71 5\n70 6\n69 7\n68 8\n67 9\n66 10\n65 11\n64 12\n63 13\n62 14\n61 15\n60 16\n59 17\n58 18\n57 19\n56 20\n55 21\n54 22\n53 23\n52 24\n51 25\n50 26\n49 27\n48 28\n47 29\n46 30\n45 31\n44 32\n43 33\n42 34\n41 35\n40 36\n39 37\n38 38\n37 39\n36 40\n35 41\n34 42\n33 43\n32 44\n31 45\n30 46\n29 47\n28 48\n27 49\n26 50\n25 51\n24 52\n23 53\n22 54\n21 55\n20 56\n19 57\n18 58\n17 59\n16 60\n15 61\n14 62\n13 63\n12 64\n11 65\n10 66\n9 67\n8 68\n7 69\n6 70\n5 71\n4 72\n3 73\n2 74\n..."
},
{
"input": "10 100",
"output": "11\n10 0\n9 1\n8 2\n7 3\n6 4\n5 5\n4 6\n3 7\n2 8\n1 9\n0 10"
}
] | 122 | 1,638,400 | 0 | 4,757 |
|
746 | Green and Black Tea | [
"constructive algorithms",
"greedy",
"math"
] | null | null | Innokentiy likes tea very much and today he wants to drink exactly *n* cups of tea. He would be happy to drink more but he had exactly *n* tea bags, *a* of them are green and *b* are black.
Innokentiy doesn't like to drink the same tea (green or black) more than *k* times in a row. Your task is to determine the order of brewing tea bags so that Innokentiy will be able to drink *n* cups of tea, without drinking the same tea more than *k* times in a row, or to inform that it is impossible. Each tea bag has to be used exactly once. | The first line contains four integers *n*, *k*, *a* and *b* (1<=β€<=*k*<=β€<=*n*<=β€<=105, 0<=β€<=*a*,<=*b*<=β€<=*n*)Β β the number of cups of tea Innokentiy wants to drink, the maximum number of cups of same tea he can drink in a row, the number of tea bags of green and black tea. It is guaranteed that *a*<=+<=*b*<==<=*n*. | If it is impossible to drink *n* cups of tea, print "NO" (without quotes).
Otherwise, print the string of the length *n*, which consists of characters 'G' and 'B'. If some character equals 'G', then the corresponding cup of tea should be green. If some character equals 'B', then the corresponding cup of tea should be black.
If there are multiple answers, print any of them. | [
"5 1 3 2\n",
"7 2 2 5\n",
"4 3 4 0\n"
] | [
"GBGBG\n",
"BBGBGBB",
"NO\n"
] | none | [
{
"input": "5 1 3 2",
"output": "GBGBG"
},
{
"input": "7 2 2 5",
"output": "BBGBBGB"
},
{
"input": "4 3 4 0",
"output": "NO"
},
{
"input": "2 2 0 2",
"output": "BB"
},
{
"input": "3 2 0 3",
"output": "NO"
},
{
"input": "1 1 0 1",
"output": "B"
},
{
"input": "1 1 1 0",
"output": "G"
},
{
"input": "11 2 3 8",
"output": "BBGBBGBBGBB"
},
{
"input": "100000 39 24855 75145",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "2 2 2 0",
"output": "GG"
},
{
"input": "2 2 1 1",
"output": "GB"
},
{
"input": "3 2 2 1",
"output": "GGB"
},
{
"input": "3 2 1 2",
"output": "BBG"
},
{
"input": "5 1 4 1",
"output": "NO"
},
{
"input": "10 1 7 3",
"output": "NO"
},
{
"input": "20 1 5 15",
"output": "NO"
},
{
"input": "1000 123 447 553",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB..."
},
{
"input": "3000 70 2946 54",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGG..."
},
{
"input": "10000 590 4020 5980",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "10001 1841 1052 8949",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "50000 104 31045 18955",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "59999 16660 46835 13164",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "70000 3017 31589 38411",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "99999 15805 82842 17157",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "100000 6397 59122 40878",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "100000 856 69042 30958",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "6 1 3 3",
"output": "GBGBGB"
},
{
"input": "9 2 3 6",
"output": "BBGBBGBBG"
},
{
"input": "9 1 6 3",
"output": "NO"
},
{
"input": "10 1 4 6",
"output": "NO"
},
{
"input": "10 1 3 7",
"output": "NO"
},
{
"input": "10 1 2 8",
"output": "NO"
},
{
"input": "10 1 5 5",
"output": "GBGBGBGBGB"
},
{
"input": "11 1 2 9",
"output": "NO"
},
{
"input": "11 2 4 7",
"output": "BBGBBGBBGBG"
},
{
"input": "11 2 5 6",
"output": "BBGBGBGBGBG"
},
{
"input": "11 2 6 5",
"output": "GGBGBGBGBGB"
},
{
"input": "11 1 7 4",
"output": "NO"
},
{
"input": "11 2 8 3",
"output": "GGBGGBGGBGG"
},
{
"input": "11 1 9 2",
"output": "NO"
},
{
"input": "99999 10760 33333 66666",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "99999 3434 66666 33333",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "99999 7343 33332 66667",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "99999 177 33334 66665",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB..."
},
{
"input": "99999 3580 66665 33334",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "99999 1681 66667 33332",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG..."
},
{
"input": "7 3 2 5",
"output": "BBBGBBG"
},
{
"input": "9 2 7 2",
"output": "NO"
},
{
"input": "10 2 8 2",
"output": "NO"
},
{
"input": "100000 50000 50000 50000",
"output": "GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBG..."
}
] | 46 | 0 | 0 | 4,763 |
|
0 | none | [
"none"
] | null | null | As a German University in Cairo (GUC) student and a basketball player, Herr Wafa was delighted once he heard the news. GUC is finally participating in the Annual Basketball Competition (ABC).
A team is to be formed of *n* players, all of which are GUC students. However, the team might have players belonging to different departments. There are *m* departments in GUC, numbered from 1 to *m*. Herr Wafa's department has number *h*. For each department *i*, Herr Wafa knows number *s**i* β how many students who play basketball belong to this department.
Herr Wafa was also able to guarantee a spot on the team, using his special powers. But since he hates floating-point numbers, he needs your help at finding the probability that he will have at least one teammate belonging to his department.
Note that every possible team containing Herr Wafa is equally probable. Consider all the students different from each other. | The first line contains three integers *n*, *m* and *h* (1<=β€<=*n*<=β€<=100,<=1<=β€<=*m*<=β€<=1000,<=1<=β€<=*h*<=β€<=*m*) β the number of players on the team, the number of departments in GUC and Herr Wafa's department, correspondingly.
The second line contains a single-space-separated list of *m* integers *s**i* (1<=β€<=*s**i*<=β€<=100), denoting the number of students in the *i*-th department. Note that *s**h* includes Herr Wafa. | Print the probability that Herr Wafa will have at least one teammate from his department. If there is not enough basketball players in GUC to participate in ABC, print -1. The answer will be accepted if it has absolute or relative error not exceeding 10<=-<=6. | [
"3 2 1\n2 1\n",
"3 2 1\n1 1\n",
"3 2 1\n2 2\n"
] | [
"1\n",
"-1\n",
"0.666667\n"
] | In the first example all 3 players (2 from department 1 and 1 from department 2) must be chosen for the team. Both players from Wafa's departments will be chosen, so he's guaranteed to have a teammate from his department.
In the second example, there are not enough players.
In the third example, there are three possibilities to compose the team containing Herr Wafa. In two of them the other player from Herr Wafa's department is part of the team. | [
{
"input": "3 2 1\n2 1",
"output": "1"
},
{
"input": "3 2 1\n1 1",
"output": "-1"
},
{
"input": "3 2 1\n2 2",
"output": "0.666667"
},
{
"input": "3 2 1\n1 2",
"output": "0.000000"
},
{
"input": "6 5 3\n5 2 3 10 5",
"output": "0.380435"
},
{
"input": "7 10 6\n9 10 2 3 3 6 9 9 3 7",
"output": "0.420946"
},
{
"input": "17 5 1\n10 4 9 6 2",
"output": "0.999860"
},
{
"input": "5 8 3\n9 7 2 5 2 10 3 4",
"output": "0.097561"
},
{
"input": "14 8 4\n6 2 10 6 2 8 4 2",
"output": "0.885750"
},
{
"input": "14 9 9\n9 4 7 2 1 2 4 3 9",
"output": "0.971132"
},
{
"input": "46 73 68\n4 2 6 4 1 9 8 10 7 8 7 2 6 4 7 9 7 9 9 1 5 1 5 1 8 2 10 2 1 7 10 2 8 3 5 3 8 9 10 5 3 4 10 4 9 6 8 1 1 6 3 1 9 6 9 4 4 3 4 5 8 1 6 2 4 10 5 7 2 6 7 4 2",
"output": "0.525158"
},
{
"input": "24 55 54\n8 3 6 4 8 9 10 2 2 6 6 8 3 4 5 6 6 6 10 4 8 2 3 2 2 2 10 7 10 1 6 1 6 8 10 9 2 8 9 6 6 4 1 2 7 2 2 9 3 7 3 7 6 8 4",
"output": "0.433479"
},
{
"input": "63 25 24\n6 7 7 1 2 5 5 9 9 1 9 8 1 2 10 10 5 10 2 9 5 4 9 5 7",
"output": "0.891560"
},
{
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"output": "-1"
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"output": "-1"
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{
"input": "1 1 1\n1",
"output": "0.000000"
},
{
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"output": "0.000000"
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{
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"output": "0.000000"
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{
"input": "100 1 1\n100",
"output": "1"
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"output": "1"
}
] | 0 | 0 | -1 | 4,778 |
|
789 | Masha and geometric depression | [
"brute force",
"implementation",
"math"
] | null | null | Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.
You are given geometric progression *b* defined by two integers *b*1 and *q*. Remind that a geometric progression is a sequence of integers *b*1,<=*b*2,<=*b*3,<=..., where for each *i*<=><=1 the respective term satisfies the condition *b**i*<==<=*b**i*<=-<=1Β·*q*, where *q* is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both *b*1 and *q* can equal 0. Also, Dvastan gave Masha *m* "bad" integers *a*1,<=*a*2,<=...,<=*a**m*, and an integer *l*.
Masha writes all progression terms one by one onto the board (including repetitive) while condition |*b**i*|<=β€<=*l* is satisfied (|*x*| means absolute value of *x*). There is an exception: if a term equals one of the "bad" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.
But the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print "inf" in case she needs to write infinitely many integers. | The first line of input contains four integers *b*1, *q*, *l*, *m* (-109<=β€<=*b*1,<=*q*<=β€<=109, 1<=β€<=*l*<=β€<=109, 1<=β€<=*m*<=β€<=105)Β β the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of "bad" integers, respectively.
The second line contains *m* distinct integers *a*1,<=*a*2,<=...,<=*a**m* (-109<=β€<=*a**i*<=β€<=109)Β β numbers that will never be written on the board. | Print the only integer, meaning the number of progression terms that will be written on the board if it is finite, or "inf" (without quotes) otherwise. | [
"3 2 30 4\n6 14 25 48\n",
"123 1 2143435 4\n123 11 -5453 141245\n",
"123 1 2143435 4\n54343 -13 6 124\n"
] | [
"3",
"0",
"inf"
] | In the first sample case, Masha will write integers 3,β12,β24. Progression term 6 will be skipped because it is a "bad" integer. Terms bigger than 24 won't be written because they exceed *l* by absolute value.
In the second case, Masha won't write any number because all terms are equal 123 and this is a "bad" integer.
In the third case, Masha will write infinitely integers 123. | [
{
"input": "3 2 30 4\n6 14 25 48",
"output": "3"
},
{
"input": "123 1 2143435 4\n123 11 -5453 141245",
"output": "0"
},
{
"input": "123 1 2143435 4\n54343 -13 6 124",
"output": "inf"
},
{
"input": "3 2 25 2\n379195692 -69874783",
"output": "4"
},
{
"input": "3 2 30 3\n-691070108 -934106649 -220744807",
"output": "4"
},
{
"input": "3 3 104 17\n9 -73896485 -290898562 5254410 409659728 -916522518 -435516126 94354167 262981034 -375897180 -80186684 -173062070 -288705544 -699097793 -11447747 320434295 503414250",
"output": "3"
},
{
"input": "-1000000000 -1000000000 1 1\n232512888",
"output": "0"
},
{
"input": "11 0 228 5\n-1 0 1 5 -11245",
"output": "1"
},
{
"input": "11 0 228 5\n-1 -17 1 5 -11245",
"output": "inf"
},
{
"input": "0 0 2143435 5\n-1 -153 1 5 -11245",
"output": "inf"
},
{
"input": "123 0 2143435 4\n5433 0 123 -645",
"output": "0"
},
{
"input": "123 -1 2143435 5\n-123 0 12 5 -11245",
"output": "inf"
},
{
"input": "123 0 21 4\n543453 -123 6 1424",
"output": "0"
},
{
"input": "3 2 115 16\n24 48 12 96 3 720031148 -367712651 -838596957 558177735 -963046495 -313322487 -465018432 -618984128 -607173835 144854086 178041956",
"output": "1"
},
{
"input": "-3 0 92055 36\n-92974174 -486557474 -663622151 695596393 177960746 -563227474 -364263320 -676254242 -614140218 71456762 -764104225 705056581 -106398436 332755134 -199942822 -732751692 658942664 677739866 886535704 183687802 -784248291 -22550621 -938674499 637055091 -704750213 780395802 778342470 -999059668 -794361783 796469192 215667969 354336794 -60195289 -885080928 -290279020 201221317",
"output": "inf"
},
{
"input": "0 -3 2143435 5\n-1 0 1 5 -11245",
"output": "0"
},
{
"input": "123 -1 2143435 5\n-123 0 123 -5453 141245",
"output": "0"
},
{
"input": "123 0 2143435 4\n5433 0 -123 -645",
"output": "1"
},
{
"input": "11 0 2 5\n-1 0 1 5 -11245",
"output": "0"
},
{
"input": "2 2 4 1\n2",
"output": "1"
},
{
"input": "1 -2 1000000000 1\n0",
"output": "30"
},
{
"input": "0 8 10 1\n5",
"output": "inf"
},
{
"input": "-1000 0 10 1\n5",
"output": "0"
},
{
"input": "0 2 2143435 4\n54343 -13 6 124",
"output": "inf"
},
{
"input": "0 8 5 1\n9",
"output": "inf"
},
{
"input": "-10 1 5 1\n100",
"output": "0"
},
{
"input": "123 -1 2143435 4\n54343 -13 6 123",
"output": "inf"
},
{
"input": "-5 -1 10 1\n-5",
"output": "inf"
},
{
"input": "2 0 1 1\n2",
"output": "0"
},
{
"input": "0 5 8 1\n10",
"output": "inf"
},
{
"input": "0 5 100 2\n34 56",
"output": "inf"
},
{
"input": "15 -1 15 4\n15 -15 1 2",
"output": "0"
},
{
"input": "10 -1 2 1\n1",
"output": "0"
},
{
"input": "2 0 2 1\n2",
"output": "inf"
},
{
"input": "4 0 4 1\n0",
"output": "1"
},
{
"input": "10 10 10 1\n123",
"output": "1"
},
{
"input": "2 2 4 1\n3",
"output": "2"
},
{
"input": "0 1 1 1\n0",
"output": "0"
},
{
"input": "3 2 30 1\n3",
"output": "3"
},
{
"input": "1000000000 100000 1000000000 4\n5433 13 6 0",
"output": "1"
},
{
"input": "-2 0 1 1\n1",
"output": "0"
},
{
"input": "2 -1 10 1\n2",
"output": "inf"
},
{
"input": "1 -1 2 1\n1",
"output": "inf"
},
{
"input": "0 10 10 1\n2",
"output": "inf"
},
{
"input": "0 35 2 1\n3",
"output": "inf"
},
{
"input": "3 1 3 1\n5",
"output": "inf"
},
{
"input": "3 2 3 4\n6 14 25 48",
"output": "1"
},
{
"input": "0 69 12 1\n1",
"output": "inf"
},
{
"input": "100 0 100000 1\n100",
"output": "inf"
},
{
"input": "0 4 1000 3\n5 6 7",
"output": "inf"
},
{
"input": "0 2 100 1\n5",
"output": "inf"
},
{
"input": "3 2 24 4\n6 14 25 48",
"output": "3"
},
{
"input": "0 4 1 1\n2",
"output": "inf"
},
{
"input": "1 5 10000 1\n125",
"output": "5"
},
{
"input": "2 -1 1 1\n1",
"output": "0"
},
{
"input": "0 3 100 1\n5",
"output": "inf"
},
{
"input": "0 3 3 1\n1",
"output": "inf"
},
{
"input": "0 2 5 1\n1",
"output": "inf"
},
{
"input": "5 -1 100 1\n5",
"output": "inf"
},
{
"input": "-20 0 10 1\n0",
"output": "0"
},
{
"input": "3 0 1 1\n3",
"output": "0"
},
{
"input": "2 -1 3 1\n2",
"output": "inf"
},
{
"input": "1 1 1000000000 1\n100",
"output": "inf"
},
{
"input": "5 -1 3 1\n0",
"output": "0"
},
{
"input": "0 5 10 1\n2",
"output": "inf"
},
{
"input": "123 0 125 1\n123",
"output": "inf"
},
{
"input": "2 -1 100 1\n2",
"output": "inf"
},
{
"input": "5 2 100 1\n5",
"output": "4"
},
{
"input": "-5 0 1 1\n1",
"output": "0"
},
{
"input": "-3 0 1 1\n-3",
"output": "0"
},
{
"input": "2 -2 10 1\n1",
"output": "3"
},
{
"input": "0 2 30 4\n6 14 25 48",
"output": "inf"
},
{
"input": "1 -1 1 1\n1",
"output": "inf"
},
{
"input": "2 -1 6 1\n2",
"output": "inf"
},
{
"input": "-3 1 100 1\n-3",
"output": "0"
},
{
"input": "1 0 2 1\n1",
"output": "inf"
},
{
"input": "1000000000 999999998 1000000000 1\n0",
"output": "1"
},
{
"input": "1 0 2143435 4\n1 -123 -5453 141245",
"output": "inf"
},
{
"input": "-1000 0 100 1\n-1000",
"output": "0"
},
{
"input": "100 10 2 1\n100",
"output": "0"
},
{
"input": "-3 1 100 1\n3",
"output": "inf"
},
{
"input": "123 -1 10000 1\n123",
"output": "inf"
},
{
"input": "1 -1 2143435 4\n1 -123 -5453 141245",
"output": "inf"
},
{
"input": "5 1 5 5\n1 2 3 4 0",
"output": "inf"
},
{
"input": "-100 -1 1 1\n1",
"output": "0"
},
{
"input": "10 -1 3 2\n10 8",
"output": "0"
},
{
"input": "-10 0 5 1\n0",
"output": "0"
},
{
"input": "3 0 3 1\n0",
"output": "1"
},
{
"input": "2 0 2 1\n-1",
"output": "inf"
},
{
"input": "5 0 20 1\n5",
"output": "inf"
},
{
"input": "-4 1 1 1\n0",
"output": "0"
},
{
"input": "11 0 1111 1\n11",
"output": "inf"
},
{
"input": "2 0 3 1\n2",
"output": "inf"
},
{
"input": "-1 -1 2143435 4\n-1 -123 -5453 141245",
"output": "inf"
},
{
"input": "-100 0 50 1\n0",
"output": "0"
},
{
"input": "5 1 2 1\n2",
"output": "0"
},
{
"input": "3 0 3 1\n4",
"output": "inf"
},
{
"input": "0 23 3 1\n3",
"output": "inf"
},
{
"input": "-1000 0 100 1\n2",
"output": "0"
},
{
"input": "1 -1 10 1\n1",
"output": "inf"
}
] | 46 | 4,608,000 | 0 | 4,779 |
|
868 | Race Against Time | [
"implementation"
] | null | null | Have you ever tried to explain to the coordinator, why it is eight hours to the contest and not a single problem has been prepared yet? Misha had. And this time he has a really strong excuse: he faced a space-time paradox! Space and time replaced each other.
The entire universe turned into an enormous clock face with three handsΒ β hour, minute, and second. Time froze, and clocks now show the time *h* hours, *m* minutes, *s* seconds.
Last time Misha talked with the coordinator at *t*1 o'clock, so now he stands on the number *t*1 on the clock face. The contest should be ready by *t*2 o'clock. In the terms of paradox it means that Misha has to go to number *t*2 somehow. Note that he doesn't have to move forward only: in these circumstances time has no direction.
Clock hands are very long, and Misha cannot get round them. He also cannot step over as it leads to the collapse of space-time. That is, if hour clock points 12 and Misha stands at 11 then he cannot move to 1 along the top arc. He has to follow all the way round the clock center (of course, if there are no other hands on his way).
Given the hands' positions, *t*1, and *t*2, find if Misha can prepare the contest on time (or should we say on space?). That is, find if he can move from *t*1 to *t*2 by the clock face. | Five integers *h*, *m*, *s*, *t*1, *t*2 (1<=β€<=*h*<=β€<=12, 0<=β€<=*m*,<=*s*<=β€<=59, 1<=β€<=*t*1,<=*t*2<=β€<=12, *t*1<=β <=*t*2).
Misha's position and the target time do not coincide with the position of any hand. | Print "YES" (quotes for clarity), if Misha can prepare the contest on time, and "NO" otherwise.
You can print each character either upper- or lowercase ("YeS" and "yes" are valid when the answer is "YES"). | [
"12 30 45 3 11\n",
"12 0 1 12 1\n",
"3 47 0 4 9\n"
] | [
"NO\n",
"YES\n",
"YES\n"
] | The three examples are shown on the pictures below from left to right. The starting position of Misha is shown with green, the ending position is shown with pink. Note that the positions of the hands on the pictures are not exact, but are close to the exact and the answer is the same. | [
{
"input": "12 30 45 3 11",
"output": "NO"
},
{
"input": "12 0 1 12 1",
"output": "YES"
},
{
"input": "3 47 0 4 9",
"output": "YES"
},
{
"input": "10 22 59 6 10",
"output": "YES"
},
{
"input": "3 1 13 12 3",
"output": "NO"
},
{
"input": "11 19 28 9 10",
"output": "YES"
},
{
"input": "9 38 22 6 1",
"output": "NO"
},
{
"input": "5 41 11 5 8",
"output": "NO"
},
{
"input": "11 2 53 10 4",
"output": "YES"
},
{
"input": "9 41 17 10 1",
"output": "YES"
},
{
"input": "6 54 48 12 6",
"output": "YES"
},
{
"input": "12 55 9 5 1",
"output": "NO"
},
{
"input": "8 55 35 9 3",
"output": "NO"
},
{
"input": "3 21 34 3 10",
"output": "YES"
},
{
"input": "2 52 1 12 3",
"output": "NO"
},
{
"input": "7 17 11 1 7",
"output": "NO"
},
{
"input": "11 6 37 6 4",
"output": "YES"
},
{
"input": "9 6 22 8 1",
"output": "NO"
},
{
"input": "3 10 5 5 9",
"output": "YES"
},
{
"input": "7 12 22 11 2",
"output": "YES"
},
{
"input": "7 19 4 7 3",
"output": "NO"
},
{
"input": "11 36 21 4 6",
"output": "NO"
},
{
"input": "10 32 49 1 3",
"output": "YES"
},
{
"input": "1 9 43 11 3",
"output": "NO"
},
{
"input": "1 8 33 4 8",
"output": "NO"
},
{
"input": "3 0 33 9 4",
"output": "NO"
},
{
"input": "7 15 9 10 3",
"output": "NO"
},
{
"input": "8 3 57 11 1",
"output": "NO"
},
{
"input": "1 33 49 5 9",
"output": "NO"
},
{
"input": "3 40 0 5 7",
"output": "YES"
},
{
"input": "5 50 9 2 7",
"output": "NO"
},
{
"input": "10 0 52 6 1",
"output": "YES"
},
{
"input": "3 10 4 1 11",
"output": "NO"
},
{
"input": "2 41 53 4 6",
"output": "YES"
},
{
"input": "10 29 30 4 7",
"output": "NO"
},
{
"input": "5 13 54 9 11",
"output": "NO"
},
{
"input": "1 0 23 3 9",
"output": "NO"
},
{
"input": "1 0 41 12 1",
"output": "NO"
},
{
"input": "6 30 30 3 9",
"output": "YES"
},
{
"input": "3 7 32 11 10",
"output": "YES"
},
{
"input": "1 0 25 12 4",
"output": "NO"
},
{
"input": "12 0 0 5 6",
"output": "YES"
},
{
"input": "1 5 4 3 2",
"output": "YES"
},
{
"input": "6 30 30 9 10",
"output": "YES"
},
{
"input": "6 0 0 2 8",
"output": "NO"
},
{
"input": "10 50 59 9 10",
"output": "YES"
},
{
"input": "12 59 59 12 6",
"output": "NO"
},
{
"input": "3 0 30 3 4",
"output": "NO"
},
{
"input": "2 10 10 1 11",
"output": "YES"
},
{
"input": "10 5 30 1 12",
"output": "YES"
},
{
"input": "5 29 31 5 10",
"output": "YES"
},
{
"input": "5 2 2 11 2",
"output": "NO"
},
{
"input": "5 15 46 3 10",
"output": "YES"
},
{
"input": "1 30 50 1 2",
"output": "NO"
},
{
"input": "5 26 14 1 12",
"output": "YES"
},
{
"input": "1 58 43 12 1",
"output": "YES"
},
{
"input": "12 0 12 11 1",
"output": "NO"
},
{
"input": "6 52 41 6 5",
"output": "YES"
},
{
"input": "5 8 2 1 3",
"output": "NO"
},
{
"input": "2 0 0 1 3",
"output": "NO"
},
{
"input": "1 5 6 2 1",
"output": "YES"
},
{
"input": "9 5 5 11 12",
"output": "YES"
},
{
"input": "12 5 19 3 4",
"output": "NO"
},
{
"input": "6 14 59 1 3",
"output": "NO"
},
{
"input": "10 38 34 4 12",
"output": "YES"
},
{
"input": "2 54 14 2 12",
"output": "YES"
},
{
"input": "5 31 0 6 7",
"output": "NO"
},
{
"input": "6 15 30 3 9",
"output": "YES"
},
{
"input": "3 54 41 8 10",
"output": "NO"
},
{
"input": "3 39 10 10 12",
"output": "YES"
},
{
"input": "1 11 50 1 2",
"output": "NO"
},
{
"input": "5 40 24 8 1",
"output": "NO"
},
{
"input": "9 5 59 1 3",
"output": "NO"
},
{
"input": "5 0 0 6 7",
"output": "YES"
},
{
"input": "4 40 59 6 8",
"output": "YES"
},
{
"input": "10 13 55 12 1",
"output": "YES"
},
{
"input": "6 50 0 5 6",
"output": "YES"
},
{
"input": "7 59 3 7 4",
"output": "YES"
},
{
"input": "6 0 1 6 7",
"output": "NO"
},
{
"input": "6 15 55 3 5",
"output": "NO"
},
{
"input": "12 9 55 10 2",
"output": "YES"
},
{
"input": "2 0 1 11 2",
"output": "NO"
},
{
"input": "8 45 17 12 9",
"output": "NO"
},
{
"input": "5 30 31 11 3",
"output": "YES"
},
{
"input": "6 43 0 10 6",
"output": "NO"
},
{
"input": "6 30 30 1 11",
"output": "YES"
},
{
"input": "11 59 59 11 12",
"output": "YES"
},
{
"input": "5 45 35 9 5",
"output": "NO"
},
{
"input": "2 43 4 9 7",
"output": "NO"
},
{
"input": "12 30 50 6 9",
"output": "NO"
},
{
"input": "1 10 1 2 3",
"output": "NO"
},
{
"input": "10 5 55 9 1",
"output": "NO"
},
{
"input": "1 59 59 2 3",
"output": "YES"
},
{
"input": "1 49 14 10 3",
"output": "NO"
},
{
"input": "3 15 15 2 4",
"output": "YES"
},
{
"input": "10 5 55 1 5",
"output": "NO"
},
{
"input": "6 33 45 12 6",
"output": "YES"
},
{
"input": "1 20 20 11 1",
"output": "YES"
},
{
"input": "2 30 45 1 11",
"output": "YES"
},
{
"input": "1 55 1 11 10",
"output": "YES"
},
{
"input": "3 0 1 11 1",
"output": "NO"
},
{
"input": "1 5 6 1 12",
"output": "YES"
},
{
"input": "12 10 5 11 4",
"output": "YES"
},
{
"input": "6 5 59 12 1",
"output": "YES"
},
{
"input": "12 0 20 11 12",
"output": "YES"
},
{
"input": "3 25 30 4 5",
"output": "YES"
},
{
"input": "2 15 18 11 1",
"output": "YES"
},
{
"input": "12 5 48 11 9",
"output": "NO"
},
{
"input": "6 30 30 10 2",
"output": "YES"
},
{
"input": "1 0 11 1 2",
"output": "NO"
},
{
"input": "10 0 1 10 11",
"output": "NO"
},
{
"input": "3 30 45 10 1",
"output": "YES"
},
{
"input": "11 21 56 3 12",
"output": "YES"
},
{
"input": "3 16 16 3 4",
"output": "YES"
},
{
"input": "11 55 55 1 12",
"output": "YES"
},
{
"input": "12 12 12 11 12",
"output": "YES"
},
{
"input": "3 5 1 1 2",
"output": "NO"
},
{
"input": "3 30 45 10 11",
"output": "YES"
},
{
"input": "10 0 1 9 10",
"output": "YES"
},
{
"input": "3 0 5 3 6",
"output": "NO"
},
{
"input": "1 1 49 1 10",
"output": "NO"
},
{
"input": "9 45 15 11 12",
"output": "YES"
},
{
"input": "12 15 59 3 8",
"output": "NO"
},
{
"input": "5 0 5 3 6",
"output": "NO"
},
{
"input": "3 30 45 1 2",
"output": "YES"
},
{
"input": "2 10 11 2 4",
"output": "YES"
},
{
"input": "2 10 10 4 3",
"output": "YES"
},
{
"input": "3 30 59 1 2",
"output": "YES"
},
{
"input": "11 59 59 12 11",
"output": "YES"
},
{
"input": "10 25 50 5 6",
"output": "NO"
},
{
"input": "6 30 30 9 3",
"output": "YES"
},
{
"input": "8 14 40 12 3",
"output": "NO"
},
{
"input": "2 10 10 1 6",
"output": "YES"
}
] | 62 | 0 | 0 | 4,803 |
|
825 | Suitable Replacement | [
"binary search",
"greedy",
"implementation"
] | null | null | You are given two strings *s* and *t* consisting of small Latin letters, string *s* can also contain '?' characters.
Suitability of string *s* is calculated by following metric:
Any two letters can be swapped positions, these operations can be performed arbitrary number of times over any pair of positions. Among all resulting strings *s*, you choose the one with the largest number of non-intersecting occurrences of string *t*. Suitability is this number of occurrences.
You should replace all '?' characters with small Latin letters in such a way that the suitability of string *s* is maximal. | The first line contains string *s* (1<=β€<=|*s*|<=β€<=106).
The second line contains string *t* (1<=β€<=|*t*|<=β€<=106). | Print string *s* with '?' replaced with small Latin letters in such a way that suitability of that string is maximal.
If there are multiple strings with maximal suitability then print any of them. | [
"?aa?\nab\n",
"??b?\nza\n",
"abcd\nabacaba\n"
] | [
"baab\n",
"azbz\n",
"abcd\n"
] | In the first example string "baab" can be transformed to "abab" with swaps, this one has suitability of 2. That means that string "baab" also has suitability of 2.
In the second example maximal suitability you can achieve is 1 and there are several dozens of such strings, "azbz" is just one of them.
In the third example there are no '?' characters and the suitability of the string is 0. | [
{
"input": "?aa?\nab",
"output": "baab"
},
{
"input": "??b?\nza",
"output": "azbz"
},
{
"input": "abcd\nabacaba",
"output": "abcd"
},
{
"input": "mqwstphetbfrsyxuzdww\nrutseqtsbh",
"output": "mqwstphetbfrsyxuzdww"
},
{
"input": "????????????????????\nxwkxsxlrre",
"output": "eekkllrrrrsswwxxxxxx"
},
{
"input": "fzjqgrgzzzghrwgwhfjq\nggwfrjzzqh",
"output": "fzjqgrgzzzghrwgwhfjq"
},
{
"input": "ng?\nvu",
"output": "ngz"
},
{
"input": "???\nb",
"output": "bbb"
},
{
"input": "??a?\na",
"output": "aaaa"
},
{
"input": "c?aa???a?cdcc??\nabcadbaccb",
"output": "cbaabbzazcdcczz"
},
{
"input": "cc?cdb?????b?cc?b?\ncabdacd",
"output": "ccacdbaaaddbdcczbz"
},
{
"input": "ccaaa?bc?baccbccccbca?cccab??aacccbaac?bccacc?accccaccbcbbcbc\ncbaaacccc",
"output": "ccaaaabcabaccbccccbcaacccabaaaacccbaaczbccacczaccccaccbcbbcbc"
},
{
"input": "aacaacbabc?bcca?ccca\nbc",
"output": "aacaacbabcbbccabccca"
}
] | 514 | 60,006,400 | 3 | 4,816 |
|
429 | Working out | [
"dp"
] | null | null | Summer is coming! It's time for Iahub and Iahubina to work out, as they both want to look hot at the beach. The gym where they go is a matrix *a* with *n* lines and *m* columns. Let number *a*[*i*][*j*] represents the calories burned by performing workout at the cell of gym in the *i*-th line and the *j*-th column.
Iahub starts with workout located at line 1 and column 1. He needs to finish with workout *a*[*n*][*m*]. After finishing workout *a*[*i*][*j*], he can go to workout *a*[*i*<=+<=1][*j*] or *a*[*i*][*j*<=+<=1]. Similarly, Iahubina starts with workout *a*[*n*][1] and she needs to finish with workout *a*[1][*m*]. After finishing workout from cell *a*[*i*][*j*], she goes to either *a*[*i*][*j*<=+<=1] or *a*[*i*<=-<=1][*j*].
There is one additional condition for their training. They have to meet in exactly one cell of gym. At that cell, none of them will work out. They will talk about fast exponentiation (pretty odd small talk) and then both of them will move to the next workout.
If a workout was done by either Iahub or Iahubina, it counts as total gain. Please plan a workout for Iahub and Iahubina such as total gain to be as big as possible. Note, that Iahub and Iahubina can perform workouts with different speed, so the number of cells that they use to reach meet cell may differs. | The first line of the input contains two integers *n* and *m* (3<=β€<=*n*,<=*m*<=β€<=1000). Each of the next *n* lines contains *m* integers: *j*-th number from *i*-th line denotes element *a*[*i*][*j*] (0<=β€<=*a*[*i*][*j*]<=β€<=105). | The output contains a single number β the maximum total gain possible. | [
"3 3\n100 100 100\n100 1 100\n100 100 100\n"
] | [
"800"
] | Iahub will choose exercises *a*[1][1]βββ*a*[1][2]βββ*a*[2][2]βββ*a*[3][2]βββ*a*[3][3]. Iahubina will choose exercises *a*[3][1]βββ*a*[2][1]βββ*a*[2][2]βββ*a*[2][3]βββ*a*[1][3]. | [
{
"input": "3 3\n100 100 100\n100 1 100\n100 100 100",
"output": "800"
},
{
"input": "4 5\n87882 40786 3691 85313 46694\n28884 16067 3242 97367 78518\n4250 35501 9780 14435 19004\n64673 65438 56977 64495 27280",
"output": "747898"
},
{
"input": "3 3\n3 1 2\n3 2 0\n2 3 2",
"output": "16"
},
{
"input": "3 3\n1 10 1\n1 10 1\n1 10 1",
"output": "26"
},
{
"input": "3 3\n0 0 0\n0 10000 0\n0 0 0",
"output": "0"
},
{
"input": "3 3\n1 1 1\n0 10000 0\n1 1 1",
"output": "6"
},
{
"input": "3 3\n9 0 9\n0 9 9\n9 9 9",
"output": "54"
},
{
"input": "3 3\n0 0 0\n0 100 0\n0 0 0",
"output": "0"
},
{
"input": "3 3\n100000 100000 100000\n1 100000 100000\n1 1 100000",
"output": "500003"
},
{
"input": "3 3\n100 0 100\n1 100 100\n0 100 100",
"output": "501"
}
] | 312 | 10,035,200 | 0 | 4,847 |
|
267 | Subtractions | [
"math",
"number theory"
] | null | null | You've got two numbers. As long as they are both larger than zero, they go through the same operation: subtract the lesser number from the larger one. If they equal substract one number from the another. For example, one operation transforms pair (4,17) to pair (4,13), it transforms (5,5) to (0,5).
You've got some number of pairs (*a**i*,<=*b**i*). How many operations will be performed for each of them? | The first line contains the number of pairs *n* (1<=<=β€<=<=*n*<=<=β€<=<=1000). Then follow *n* lines, each line contains a pair of positive integers *a**i*,<=*b**i* (1<=<=β€<=<=*a**i*,<=<=*b**i*<=<=β€<=<=109). | Print the sought number of operations for each pair on a single line. | [
"2\n4 17\n7 987654321\n"
] | [
"8\n141093479\n"
] | none | [
{
"input": "2\n4 17\n7 987654321",
"output": "8\n141093479"
},
{
"input": "10\n7 987654321\n7 987654321\n7 987654321\n7 987654321\n7 987654321\n7 987654321\n7 987654321\n7 987654321\n7 987654321\n7 987654321",
"output": "141093479\n141093479\n141093479\n141093479\n141093479\n141093479\n141093479\n141093479\n141093479\n141093479"
},
{
"input": "1\n536870912 32",
"output": "16777216"
},
{
"input": "20\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999\n1000000000 999999999",
"output": "1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000\n1000000000"
},
{
"input": "3\n1000000000 1\n1000000000 1\n1 100000000",
"output": "1000000000\n1000000000\n100000000"
}
] | 30 | 0 | 0 | 4,848 |
|
940 | Cashback | [
"data structures",
"dp",
"greedy",
"math"
] | null | null | Since you are the best Wraith King, Nizhniy Magazin Β«MirΒ» at the centre of Vinnytsia is offering you a discount.
You are given an array *a* of length *n* and an integer *c*.
The value of some array *b* of length *k* is the sum of its elements except for the smallest. For example, the value of the array [3,<=1,<=6,<=5,<=2] with *c*<==<=2 is 3<=+<=6<=+<=5<==<=14.
Among all possible partitions of *a* into contiguous subarrays output the smallest possible sum of the values of these subarrays. | The first line contains integers *n* and *c* (1<=β€<=*n*,<=*c*<=β€<=100<=000).
The second line contains *n* integers *a**i* (1<=β€<=*a**i*<=β€<=109)Β β elements of *a*. | Output a single integer Β β the smallest possible sum of values of these subarrays of some partition of *a*. | [
"3 5\n1 2 3\n",
"12 10\n1 1 10 10 10 10 10 10 9 10 10 10\n",
"7 2\n2 3 6 4 5 7 1\n",
"8 4\n1 3 4 5 5 3 4 1\n"
] | [
"6\n",
"92\n",
"17\n",
"23\n"
] | In the first example any partition yields 6 as the sum.
In the second example one of the optimal partitions is [1,β1],β[10,β10,β10,β10,β10,β10,β9,β10,β10,β10] with the values 2 and 90 respectively.
In the third example one of the optimal partitions is [2,β3],β[6,β4,β5,β7],β[1] with the values 3, 13 and 1 respectively.
In the fourth example one of the optimal partitions is [1],β[3,β4,β5,β5,β3,β4],β[1] with the values 1, 21 and 1 respectively. | [
{
"input": "3 5\n1 2 3",
"output": "6"
},
{
"input": "12 10\n1 1 10 10 10 10 10 10 9 10 10 10",
"output": "92"
},
{
"input": "7 2\n2 3 6 4 5 7 1",
"output": "17"
},
{
"input": "8 4\n1 3 4 5 5 3 4 1",
"output": "23"
},
{
"input": "15 5\n11 15 16 24 24 28 36 40 49 49 53 55 66 73 100",
"output": "547"
},
{
"input": "11 10\n58 97 93 74 59 59 76 59 59 59 30",
"output": "665"
},
{
"input": "1 1\n1",
"output": "0"
},
{
"input": "15 5\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1",
"output": "12"
},
{
"input": "15 10\n2 3 3 3 3 3 3 3 3 3 3 3 3 3 1",
"output": "39"
},
{
"input": "15 10\n4 5 5 5 5 5 5 5 5 5 5 5 5 5 1",
"output": "65"
},
{
"input": "15 15\n47 48 48 48 48 48 48 48 48 48 48 48 48 48 25",
"output": "671"
},
{
"input": "15 10\n94 87 72 62 55 53 51 50 48 41 39 24 15 7 2",
"output": "659"
},
{
"input": "15 5\n1 67 1 100 67 34 67 34 34 1 1 34 34 1 67",
"output": "508"
},
{
"input": "9 10\n20 54 35 72 35 35 64 39 34",
"output": "388"
},
{
"input": "10 10\n48 87 96 87 87 87 87 87 87 86",
"output": "791"
},
{
"input": "12 10\n76 77 82 77 97 77 77 77 77 77 77 48",
"output": "842"
},
{
"input": "13 10\n94 95 95 95 95 95 95 95 95 95 95 95 76",
"output": "1120"
},
{
"input": "14 10\n16 82 72 72 72 72 72 72 72 72 72 72 81 71",
"output": "898"
},
{
"input": "15 10\n31 91 91 91 91 91 91 91 91 99 91 91 91 91 90",
"output": "1221"
},
{
"input": "100 5\n3 4 9 4 2 6 3 3 9 4 4 1 9 9 9 6 10 9 3 7 7 1 5 7 1 8 2 10 10 5 6 3 5 7 8 9 7 5 4 6 5 3 2 10 1 8 9 5 7 6 10 6 3 9 5 3 8 8 7 3 1 8 8 4 4 4 6 2 2 5 5 3 5 3 4 10 7 7 6 4 6 5 10 9 4 5 9 4 1 2 2 4 8 1 3 5 6 9 1 2",
"output": "488"
},
{
"input": "100 20\n9149 9142 7686 5769 1871 4565 5670 8587 663 637 3421 4267 6884 8142 7634 5748 936 316 9300 771 6906 9230 8994 9690 7155 9393 6274 3183 932 7460 1611 6122 4031 6922 5466 1499 5290 4907 4673 5665 9744 1602 9891 8260 6351 4640 9930 9756 5242 3752 82 3287 824 6897 5579 9095 883 6231 5738 6690 7547 1195 8888 7328 8433 926 5138 3793 2412 2634 9735 9060 3431 2921 3454 513 5345 4748 9261 7920 939 6741 4227 4896 9518 3277 2783 7521 8578 3599 6726 3946 568 7739 9905 2532 9938 3668 6876 7116",
"output": "543544"
},
{
"input": "100 25\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1",
"output": "96"
}
] | 436 | 18,432,000 | 3 | 4,849 |
|
46 | Ball Game | [
"brute force",
"implementation"
] | A. Ball Game | 2 | 256 | A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to *n* clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if *n*<==<=5, then after the third throw the child number 2 has the ball again. Overall, *n*<=-<=1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw. | The first line contains integer *n* (2<=β€<=*n*<=β€<=100) which indicates the number of kids in the circle. | In the single line print *n*<=-<=1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces. | [
"10\n",
"3\n"
] | [
"2 4 7 1 6 2 9 7 6\n",
"2 1\n"
] | none | [
{
"input": "10",
"output": "2 4 7 1 6 2 9 7 6"
},
{
"input": "3",
"output": "2 1"
},
{
"input": "4",
"output": "2 4 3"
},
{
"input": "5",
"output": "2 4 2 1"
},
{
"input": "6",
"output": "2 4 1 5 4"
},
{
"input": "7",
"output": "2 4 7 4 2 1"
},
{
"input": "8",
"output": "2 4 7 3 8 6 5"
},
{
"input": "9",
"output": "2 4 7 2 7 4 2 1"
},
{
"input": "2",
"output": "2"
},
{
"input": "11",
"output": "2 4 7 11 5 11 7 4 2 1"
},
{
"input": "12",
"output": "2 4 7 11 4 10 5 1 10 8 7"
},
{
"input": "13",
"output": "2 4 7 11 3 9 3 11 7 4 2 1"
},
{
"input": "20",
"output": "2 4 7 11 16 2 9 17 6 16 7 19 12 6 1 17 14 12 11"
},
{
"input": "25",
"output": "2 4 7 11 16 22 4 12 21 6 17 4 17 6 21 12 4 22 16 11 7 4 2 1"
},
{
"input": "30",
"output": "2 4 7 11 16 22 29 7 16 26 7 19 2 16 1 17 4 22 11 1 22 14 7 1 26 22 19 17 16"
},
{
"input": "35",
"output": "2 4 7 11 16 22 29 2 11 21 32 9 22 1 16 32 14 32 16 1 22 9 32 21 11 2 29 22 16 11 7 4 2 1"
},
{
"input": "40",
"output": "2 4 7 11 16 22 29 37 6 16 27 39 12 26 1 17 34 12 31 11 32 14 37 21 6 32 19 7 36 26 17 9 2 36 31 27 24 22 21"
},
{
"input": "45",
"output": "2 4 7 11 16 22 29 37 1 11 22 34 2 16 31 2 19 37 11 31 7 29 7 31 11 37 19 2 31 16 2 34 22 11 1 37 29 22 16 11 7 4 2 1"
},
{
"input": "50",
"output": "2 4 7 11 16 22 29 37 46 6 17 29 42 6 21 37 4 22 41 11 32 4 27 1 26 2 29 7 36 16 47 29 12 46 31 17 4 42 31 21 12 4 47 41 36 32 29 27 26"
},
{
"input": "55",
"output": "2 4 7 11 16 22 29 37 46 1 12 24 37 51 11 27 44 7 26 46 12 34 2 26 51 22 49 22 51 26 2 34 12 46 26 7 44 27 11 51 37 24 12 1 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "60",
"output": "2 4 7 11 16 22 29 37 46 56 7 19 32 46 1 17 34 52 11 31 52 14 37 1 26 52 19 47 16 46 17 49 22 56 31 7 44 22 1 41 22 4 47 31 16 2 49 37 26 16 7 59 52 46 41 37 34 32 31"
},
{
"input": "65",
"output": "2 4 7 11 16 22 29 37 46 56 2 14 27 41 56 7 24 42 61 16 37 59 17 41 1 27 54 17 46 11 42 9 42 11 46 17 54 27 1 41 17 59 37 16 61 42 24 7 56 41 27 14 2 56 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "70",
"output": "2 4 7 11 16 22 29 37 46 56 67 9 22 36 51 67 14 32 51 1 22 44 67 21 46 2 29 57 16 46 7 39 2 36 1 37 4 42 11 51 22 64 37 11 56 32 9 57 36 16 67 49 32 16 1 57 44 32 21 11 2 64 57 51 46 42 39 37 36"
},
{
"input": "75",
"output": "2 4 7 11 16 22 29 37 46 56 67 4 17 31 46 62 4 22 41 61 7 29 52 1 26 52 4 32 61 16 47 4 37 71 31 67 29 67 31 71 37 4 47 16 61 32 4 52 26 1 52 29 7 61 41 22 4 62 46 31 17 4 67 56 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "80",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 12 26 41 57 74 12 31 51 72 14 37 61 6 32 59 7 36 66 17 49 2 36 71 27 64 22 61 21 62 24 67 31 76 42 9 57 26 76 47 19 72 46 21 77 54 32 11 71 52 34 17 1 66 52 39 27 16 6 77 69 62 56 51 47 44 42 41"
},
{
"input": "85",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 7 21 36 52 69 2 21 41 62 84 22 46 71 12 39 67 11 41 72 19 52 1 36 72 24 62 16 56 12 54 12 56 16 62 24 72 36 1 52 19 72 41 11 67 39 12 71 46 22 84 62 41 21 2 69 52 36 21 7 79 67 56 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "90",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 2 16 31 47 64 82 11 31 52 74 7 31 56 82 19 47 76 16 47 79 22 56 1 37 74 22 61 11 52 4 47 1 46 2 49 7 56 16 67 29 82 46 11 67 34 2 61 31 2 64 37 11 76 52 29 7 76 56 37 19 2 76 61 47 34 22 11 1 82 74 67 61 56 52 49 47 46"
},
{
"input": "95",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 92 11 26 42 59 77 1 21 42 64 87 16 41 67 94 27 56 86 22 54 87 26 61 2 39 77 21 61 7 49 92 41 86 37 84 37 86 41 92 49 7 61 21 77 39 2 61 26 87 54 22 86 56 27 94 67 41 16 87 64 42 21 1 77 59 42 26 11 92 79 67 56 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "96",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 92 10 25 41 58 76 95 19 40 62 85 13 38 64 91 23 52 82 17 49 82 20 55 91 32 70 13 53 94 40 83 31 76 26 73 25 74 28 79 35 88 46 5 61 22 80 43 7 68 34 1 65 34 4 71 43 16 86 61 37 14 88 67 47 28 10 89 73 58 44 31 19 8 94 85 77 70 64 59 55 52 50 49"
},
{
"input": "97",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 92 9 24 40 57 75 94 17 38 60 83 10 35 61 88 19 48 78 12 44 77 14 49 85 25 63 5 45 86 31 74 21 66 15 62 13 62 15 66 21 74 31 86 45 5 63 25 85 49 14 77 44 12 78 48 19 88 61 35 10 83 60 38 17 94 75 57 40 24 9 92 79 67 56 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "98",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 92 8 23 39 56 74 93 15 36 58 81 7 32 58 85 15 44 74 7 39 72 8 43 79 18 56 95 37 78 22 65 11 56 4 51 1 50 2 53 7 60 16 71 29 86 46 7 67 30 92 57 23 88 56 25 93 64 36 9 81 56 32 9 85 64 44 25 7 88 72 57 43 30 18 7 95 86 78 71 65 60 56 53 51 50"
},
{
"input": "99",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 92 7 22 38 55 73 92 13 34 56 79 4 29 55 82 11 40 70 2 34 67 2 37 73 11 49 88 29 70 13 56 1 46 92 40 88 38 88 40 92 46 1 56 13 70 29 88 49 11 73 37 2 67 34 2 70 40 11 82 55 29 4 79 56 34 13 92 73 55 38 22 7 92 79 67 56 46 37 29 22 16 11 7 4 2 1"
},
{
"input": "100",
"output": "2 4 7 11 16 22 29 37 46 56 67 79 92 6 21 37 54 72 91 11 32 54 77 1 26 52 79 7 36 66 97 29 62 96 31 67 4 42 81 21 62 4 47 91 36 82 29 77 26 76 27 79 32 86 41 97 54 12 71 31 92 54 17 81 46 12 79 47 16 86 57 29 2 76 51 27 4 82 61 41 22 4 87 71 56 42 29 17 6 96 87 79 72 66 61 57 54 52 51"
}
] | 92 | 0 | 0 | 4,851 |
0 | none | [
"none"
] | null | null | The mobile application store has a new game called "Subway Roller".
The protagonist of the game Philip is located in one end of the tunnel and wants to get out of the other one. The tunnel is a rectangular field consisting of three rows and *n* columns. At the beginning of the game the hero is in some cell of the leftmost column. Some number of trains rides towards the hero. Each train consists of two or more neighbouring cells in some row of the field.
All trains are moving from right to left at a speed of two cells per second, and the hero runs from left to right at the speed of one cell per second. For simplicity, the game is implemented so that the hero and the trains move in turns. First, the hero moves one cell to the right, then one square up or down, or stays idle. Then all the trains move twice simultaneously one cell to the left. Thus, in one move, Philip definitely makes a move to the right and can move up or down. If at any point, Philip is in the same cell with a train, he loses. If the train reaches the left column, it continues to move as before, leaving the tunnel.
Your task is to answer the question whether there is a sequence of movements of Philip, such that he would be able to get to the rightmost column. | Each test contains from one to ten sets of the input data. The first line of the test contains a single integer *t* (1<=β€<=*t*<=β€<=10 for pretests and tests or *t*<==<=1 for hacks; see the Notes section for details) β the number of sets.
Then follows the description of *t* sets of the input data.
The first line of the description of each set contains two integers *n*,<=*k* (2<=β€<=*n*<=β€<=100,<=1<=β€<=*k*<=β€<=26) β the number of columns on the field and the number of trains. Each of the following three lines contains the sequence of *n* character, representing the row of the field where the game is on. Philip's initial position is marked as 's', he is in the leftmost column. Each of the *k* trains is marked by some sequence of identical uppercase letters of the English alphabet, located in one line. Distinct trains are represented by distinct letters. Character '.' represents an empty cell, that is, the cell that doesn't contain either Philip or the trains. | For each set of the input data print on a single line word YES, if it is possible to win the game and word NO otherwise. | [
"2\n16 4\n...AAAAA........\ns.BBB......CCCCC\n........DDDDD...\n16 4\n...AAAAA........\ns.BBB....CCCCC..\n.......DDDDD....\n",
"2\n10 4\ns.ZZ......\n.....AAABB\n.YYYYYY...\n10 4\ns.ZZ......\n....AAAABB\n.YYYYYY...\n"
] | [
"YES\nNO\n",
"YES\nNO\n"
] | In the first set of the input of the first sample Philip must first go forward and go down to the third row of the field, then go only forward, then go forward and climb to the second row, go forward again and go up to the first row. After that way no train blocks Philip's path, so he can go straight to the end of the tunnel.
Note that in this problem the challenges are restricted to tests that contain only one testset. | [] | 77 | 512,000 | 3 | 4,854 |
|
847 | Weather Tomorrow | [
"implementation",
"math"
] | null | null | Vasya came up with his own weather forecasting method. He knows the information about the average air temperature for each of the last *n* days. Assume that the average air temperature for each day is integral.
Vasya believes that if the average temperatures over the last *n* days form an arithmetic progression, where the first term equals to the average temperature on the first day, the second term equals to the average temperature on the second day and so on, then the average temperature of the next (*n*<=+<=1)-th day will be equal to the next term of the arithmetic progression. Otherwise, according to Vasya's method, the temperature of the (*n*<=+<=1)-th day will be equal to the temperature of the *n*-th day.
Your task is to help Vasya predict the average temperature for tomorrow, i. e. for the (*n*<=+<=1)-th day. | The first line contains a single integer *n* (2<=β€<=*n*<=β€<=100) β the number of days for which the average air temperature is known.
The second line contains a sequence of integers *t*1,<=*t*2,<=...,<=*t**n* (<=-<=1000<=β€<=*t**i*<=β€<=1000)Β β where *t**i* is the average temperature in the *i*-th day. | Print the average air temperature in the (*n*<=+<=1)-th day, which Vasya predicts according to his method. Note that the absolute value of the predicted temperature can exceed 1000. | [
"5\n10 5 0 -5 -10\n",
"4\n1 1 1 1\n",
"3\n5 1 -5\n",
"2\n900 1000\n"
] | [
"-15\n",
"1\n",
"-5\n",
"1100\n"
] | In the first example the sequence of the average temperatures is an arithmetic progression where the first term is 10 and each following terms decreases by 5. So the predicted average temperature for the sixth day is β-β10β-β5β=ββ-β15.
In the second example the sequence of the average temperatures is an arithmetic progression where the first term is 1 and each following terms equals to the previous one. So the predicted average temperature in the fifth day is 1.
In the third example the average temperatures do not form an arithmetic progression, so the average temperature of the fourth day equals to the temperature of the third day and equals to β-β5.
In the fourth example the sequence of the average temperatures is an arithmetic progression where the first term is 900 and each the following terms increase by 100. So predicted average temperature in the third day is 1000β+β100β=β1100. | [
{
"input": "5\n10 5 0 -5 -10",
"output": "-15"
},
{
"input": "4\n1 1 1 1",
"output": "1"
},
{
"input": "3\n5 1 -5",
"output": "-5"
},
{
"input": "2\n900 1000",
"output": "1100"
},
{
"input": "2\n1 2",
"output": "3"
},
{
"input": "3\n2 5 8",
"output": "11"
},
{
"input": "4\n4 1 -2 -5",
"output": "-8"
},
{
"input": "10\n-1000 -995 -990 -985 -980 -975 -970 -965 -960 -955",
"output": "-950"
},
{
"input": "11\n-1000 -800 -600 -400 -200 0 200 400 600 800 1000",
"output": "1200"
},
{
"input": "31\n1000 978 956 934 912 890 868 846 824 802 780 758 736 714 692 670 648 626 604 582 560 538 516 494 472 450 428 406 384 362 340",
"output": "318"
},
{
"input": "5\n1000 544 88 -368 -824",
"output": "-1280"
},
{
"input": "100\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"output": "0"
},
{
"input": "33\n456 411 366 321 276 231 186 141 96 51 6 -39 -84 -129 -174 -219 -264 -309 -354 -399 -444 -489 -534 -579 -624 -669 -714 -759 -804 -849 -894 -939 -984",
"output": "-1029"
},
{
"input": "77\n-765 -742 -719 -696 -673 -650 -627 -604 -581 -558 -535 -512 -489 -466 -443 -420 -397 -374 -351 -328 -305 -282 -259 -236 -213 -190 -167 -144 -121 -98 -75 -52 -29 -6 17 40 63 86 109 132 155 178 201 224 247 270 293 316 339 362 385 408 431 454 477 500 523 546 569 592 615 638 661 684 707 730 753 776 799 822 845 868 891 914 937 960 983",
"output": "1006"
},
{
"input": "3\n2 4 8",
"output": "8"
},
{
"input": "4\n4 1 -3 -5",
"output": "-5"
},
{
"input": "10\n-1000 -995 -990 -984 -980 -975 -970 -965 -960 -955",
"output": "-955"
},
{
"input": "11\n-999 -800 -600 -400 -200 0 200 400 600 800 1000",
"output": "1000"
},
{
"input": "51\n-9 10 30 50 70 90 110 130 150 170 190 210 230 250 270 290 310 330 350 370 390 410 430 450 470 490 510 530 550 570 590 610 630 650 670 690 710 730 750 770 790 810 830 850 870 890 910 930 950 970 990",
"output": "990"
},
{
"input": "100\n10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 194 196 198 200 202 204 206 207",
"output": "207"
},
{
"input": "2\n1000 1000",
"output": "1000"
},
{
"input": "2\n-1000 1000",
"output": "3000"
},
{
"input": "2\n1000 -1000",
"output": "-3000"
},
{
"input": "2\n-1000 -1000",
"output": "-1000"
},
{
"input": "100\n-85 -80 -76 -72 -68 -64 -60 -56 -52 -48 -44 -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132 136 140 144 148 152 156 160 164 168 172 176 180 184 188 192 196 200 204 208 212 216 220 224 228 232 236 240 244 248 252 256 260 264 268 272 276 280 284 288 292 296 300 304 308 312",
"output": "312"
},
{
"input": "4\n1 2 4 5",
"output": "5"
}
] | 46 | 0 | 3 | 4,865 |
|
0 | none | [
"none"
] | null | null | On vacations *n* pupils decided to go on excursion and gather all together. They need to overcome the path with the length *l* meters. Each of the pupils will go with the speed equal to *v*1. To get to the excursion quickly, it was decided to rent a bus, which has seats for *k* people (it means that it can't fit more than *k* people at the same time) and the speed equal to *v*2. In order to avoid seasick, each of the pupils want to get into the bus no more than once.
Determine the minimum time required for all *n* pupils to reach the place of excursion. Consider that the embarkation and disembarkation of passengers, as well as the reversal of the bus, take place immediately and this time can be neglected. | The first line of the input contains five positive integers *n*, *l*, *v*1, *v*2 and *k* (1<=β€<=*n*<=β€<=10<=000, 1<=β€<=*l*<=β€<=109, 1<=β€<=*v*1<=<<=*v*2<=β€<=109, 1<=β€<=*k*<=β€<=*n*)Β β the number of pupils, the distance from meeting to the place of excursion, the speed of each pupil, the speed of bus and the number of seats in the bus. | Print the real numberΒ β the minimum time in which all pupils can reach the place of excursion. Your answer will be considered correct if its absolute or relative error won't exceed 10<=-<=6. | [
"5 10 1 2 5\n",
"3 6 1 2 1\n"
] | [
"5.0000000000\n",
"4.7142857143\n"
] | In the first sample we should immediately put all five pupils to the bus. The speed of the bus equals 2 and the distance is equal to 10, so the pupils will reach the place of excursion in time 10β/β2β=β5. | [
{
"input": "5 10 1 2 5",
"output": "5.0000000000"
},
{
"input": "3 6 1 2 1",
"output": "4.7142857143"
},
{
"input": "39 252 51 98 26",
"output": "3.5344336938"
},
{
"input": "59 96 75 98 9",
"output": "1.2315651330"
},
{
"input": "87 237 3 21 40",
"output": "33.8571428571"
},
{
"input": "11 81 31 90 1",
"output": "2.3331983806"
},
{
"input": "39 221 55 94 1",
"output": "3.9608012268"
},
{
"input": "59 770 86 94 2",
"output": "8.9269481589"
},
{
"input": "10000 1000000000 1 2 1",
"output": "999925003.7498125093"
},
{
"input": "10000 1 999999999 1000000000 1",
"output": "0.0000000010"
},
{
"input": "9102 808807765 95894 96529 2021",
"output": "8423.2676366126"
},
{
"input": "87 422 7 90 3",
"output": "49.2573051579"
},
{
"input": "15 563 38 51 5",
"output": "13.4211211456"
},
{
"input": "39 407 62 63 2",
"output": "6.5592662969"
},
{
"input": "18 518 99 100 4",
"output": "5.2218163471"
},
{
"input": "8367 515267305 49370 57124 723",
"output": "10310.3492287628"
},
{
"input": "6592 724149457 54877 85492 6302",
"output": "10543.9213545882"
},
{
"input": "8811 929128198 57528 84457 6629",
"output": "13306.2878107183"
},
{
"input": "8861 990217735 49933 64765 6526",
"output": "17403.1926037323"
},
{
"input": "9538 765513348 52584 86675 8268",
"output": "11295.6497404812"
},
{
"input": "9274 783669740 44989 60995 6973",
"output": "14946.9402371816"
},
{
"input": "9103 555078149 86703 93382 8235",
"output": "6168.7893283125"
},
{
"input": "9750 980765213 40044 94985 4226",
"output": "18012.2266672490"
},
{
"input": "5884 943590784 42695 98774 3117",
"output": "14275.9991046103"
},
{
"input": "1 1 1 2 1",
"output": "0.5000000000"
},
{
"input": "10000 1000000000 1 1000000000 1",
"output": "19998.6000479986"
},
{
"input": "10000 1000000000 1 1000000000 10000",
"output": "1.0000000000"
},
{
"input": "10000 1000000000 999999999 1000000000 3",
"output": "1.0000000010"
},
{
"input": "9999 1000000 10 20 3",
"output": "99977.5011249438"
},
{
"input": "1 1 1 1000000000 1",
"output": "0.0000000010"
},
{
"input": "1 1 999999999 1000000000 1",
"output": "0.0000000010"
},
{
"input": "1 1000000000 1 2 1",
"output": "500000000.0000000000"
},
{
"input": "1 1000000000 1 1000000000 1",
"output": "1.0000000000"
},
{
"input": "1 1000000000 999999999 1000000000 1",
"output": "1.0000000000"
},
{
"input": "10000 1 1 2 1",
"output": "0.9999250037"
},
{
"input": "10000 1 1 2 10000",
"output": "0.5000000000"
},
{
"input": "10000 1 1 1000000000 1",
"output": "0.0000199986"
},
{
"input": "10000 1 1 1000000000 10000",
"output": "0.0000000010"
},
{
"input": "10000 1 999999999 1000000000 10000",
"output": "0.0000000010"
},
{
"input": "10000 1000000000 1 2 10000",
"output": "500000000.0000000000"
},
{
"input": "10000 1000000000 999999999 1000000000 1",
"output": "1.0000000010"
},
{
"input": "10000 1000000000 999999999 1000000000 10000",
"output": "1.0000000000"
}
] | 124 | 0 | 0 | 4,869 |
|
621 | Wet Shark and Bishops | [
"combinatorics",
"implementation"
] | null | null | Today, Wet Shark is given *n* bishops on a 1000 by 1000 grid. Both rows and columns of the grid are numbered from 1 to 1000. Rows are numbered from top to bottom, while columns are numbered from left to right.
Wet Shark thinks that two bishops attack each other if they share the same diagonal. Note, that this is the only criteria, so two bishops may attack each other (according to Wet Shark) even if there is another bishop located between them. Now Wet Shark wants to count the number of pairs of bishops that attack each other. | The first line of the input contains *n* (1<=β€<=*n*<=β€<=200<=000)Β β the number of bishops.
Each of next *n* lines contains two space separated integers *x**i* and *y**i* (1<=β€<=*x**i*,<=*y**i*<=β€<=1000)Β β the number of row and the number of column where *i*-th bishop is positioned. It's guaranteed that no two bishops share the same position. | Output one integerΒ β the number of pairs of bishops which attack each other. | [
"5\n1 1\n1 5\n3 3\n5 1\n5 5\n",
"3\n1 1\n2 3\n3 5\n"
] | [
"6\n",
"0\n"
] | In the first sample following pairs of bishops attack each other: (1,β3), (1,β5), (2,β3), (2,β4), (3,β4) and (3,β5). Pairs (1,β2), (1,β4), (2,β5) and (4,β5) do not attack each other because they do not share the same diagonal. | [
{
"input": "5\n1 1\n1 5\n3 3\n5 1\n5 5",
"output": "6"
},
{
"input": "3\n1 1\n2 3\n3 5",
"output": "0"
},
{
"input": "3\n859 96\n634 248\n808 72",
"output": "0"
},
{
"input": "3\n987 237\n891 429\n358 145",
"output": "0"
},
{
"input": "3\n411 81\n149 907\n611 114",
"output": "0"
},
{
"input": "3\n539 221\n895 89\n673 890",
"output": "0"
},
{
"input": "3\n259 770\n448 54\n926 667",
"output": "0"
},
{
"input": "3\n387 422\n898 532\n988 636",
"output": "0"
},
{
"input": "10\n515 563\n451 713\n537 709\n343 819\n855 779\n457 60\n650 359\n631 42\n788 639\n710 709",
"output": "0"
},
{
"input": "10\n939 407\n197 191\n791 486\n30 807\n11 665\n600 100\n445 496\n658 959\n510 389\n729 950",
"output": "0"
},
{
"input": "10\n518 518\n71 971\n121 862\n967 607\n138 754\n513 337\n499 873\n337 387\n647 917\n76 417",
"output": "0"
},
{
"input": "10\n646 171\n816 449\n375 934\n950 299\n702 232\n657 81\n885 306\n660 304\n369 371\n798 657",
"output": "0"
},
{
"input": "10\n70 311\n74 927\n732 711\n126 583\n857 118\n97 928\n975 843\n175 221\n284 929\n816 602",
"output": "0"
},
{
"input": "2\n1 1\n1 1000",
"output": "0"
},
{
"input": "2\n1 1\n1000 1",
"output": "0"
},
{
"input": "2\n1 1\n1000 1000",
"output": "1"
},
{
"input": "2\n1000 1\n1 1000",
"output": "1"
},
{
"input": "2\n1000 1\n1000 1000",
"output": "0"
},
{
"input": "2\n1 1000\n1000 1000",
"output": "0"
},
{
"input": "1\n6 3",
"output": "0"
},
{
"input": "1\n1 1",
"output": "0"
},
{
"input": "1\n1 1000",
"output": "0"
},
{
"input": "1\n1000 1",
"output": "0"
},
{
"input": "1\n1000 1000",
"output": "0"
},
{
"input": "2\n1 1\n3 1",
"output": "0"
},
{
"input": "2\n999 1\n1000 2",
"output": "1"
},
{
"input": "5\n1 1000\n2 999\n3 998\n4 997\n5 996",
"output": "10"
}
] | 1,185 | 11,468,800 | 3 | 4,876 |
|
0 | none | [
"none"
] | null | null | Old MacDonald has a farm and a large potato field, (1010<=+<=1)<=Γ<=(1010<=+<=1) square meters in size. The field is divided into square garden beds, each bed takes up one square meter.
Old McDonald knows that the Colorado potato beetle is about to invade his farm and can destroy the entire harvest. To fight the insects, Old McDonald wants to spray some beds with insecticides.
So Old McDonald went to the field, stood at the center of the central field bed and sprayed this bed with insecticides. Now he's going to make a series of movements and spray a few more beds. During each movement Old McDonald moves left, right, up or down the field some integer number of meters. As Old McDonald moves, he sprays all the beds he steps on. In other words, the beds that have any intersection at all with Old McDonald's trajectory, are sprayed with insecticides.
When Old McDonald finished spraying, he wrote out all his movements on a piece of paper. Now he wants to know how many beds won't be infected after the invasion of the Colorado beetles.
It is known that the invasion of the Colorado beetles goes as follows. First some bed on the field border gets infected. Than any bed that hasn't been infected, hasn't been sprayed with insecticides and has a common side with an infected bed, gets infected as well. Help Old McDonald and determine the number of beds that won't be infected by the Colorado potato beetle. | The first line contains an integer *n* (1<=β€<=*n*<=β€<=1000) β the number of Old McDonald's movements.
Next *n* lines contain the description of Old McDonald's movements. The *i*-th of these lines describes the *i*-th movement. Each movement is given in the format "*d**i* *x**i*", where *d**i* is the character that determines the direction of the movement ("L", "R", "U" or "D" for directions "left", "right", "up" and "down", correspondingly), and *x**i* (1<=β€<=*x**i*<=β€<=106) is an integer that determines the number of meters in the movement. | Print a single integer β the number of beds that won't be infected by the Colorado potato beetle.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier. | [
"5\nR 8\nU 9\nL 9\nD 8\nL 2\n",
"7\nR 10\nD 2\nL 7\nU 9\nD 2\nR 3\nD 10\n"
] | [
"101",
"52"
] | none | [] | 62 | 0 | 0 | 4,880 |
|
0 | none | [
"none"
] | null | null | Vasya the programmer lives in the middle of the Programming subway branch. He has two girlfriends: Dasha and Masha, who live at the different ends of the branch, each one is unaware of the other one's existence.
When Vasya has some free time, he goes to one of his girlfriends. He descends into the subway at some time, waits the first train to come and rides on it to the end of the branch to the corresponding girl. However, the trains run with different frequencies: a train goes to Dasha's direction every *a* minutes, but a train goes to Masha's direction every *b* minutes. If two trains approach at the same time, Vasya goes toward the direction with the lower frequency of going trains, that is, to the girl, to whose directions the trains go less frequently (see the note to the third sample).
We know that the trains begin to go simultaneously before Vasya appears. That is the train schedule is such that there exists a moment of time when the two trains arrive simultaneously.
Help Vasya count to which girlfriend he will go more often. | The first line contains two integers *a* and *b* (*a*<=β <=*b*,<=1<=β€<=*a*,<=*b*<=β€<=106). | Print "Dasha" if Vasya will go to Dasha more frequently, "Masha" if he will go to Masha more frequently, or "Equal" if he will go to both girlfriends with the same frequency. | [
"3 7\n",
"5 3\n",
"2 3\n"
] | [
"Dasha\n",
"Masha\n",
"Equal\n"
] | Let's take a look at the third sample. Let the trains start to go at the zero moment of time. It is clear that the moments of the trains' arrival will be periodic with period 6. That's why it is enough to show that if Vasya descends to the subway at a moment of time inside the interval (0,β6], he will go to both girls equally often.
If he descends to the subway at a moment of time from 0 to 2, he leaves for Dasha on the train that arrives by the second minute.
If he descends to the subway at a moment of time from 2 to 3, he leaves for Masha on the train that arrives by the third minute.
If he descends to the subway at a moment of time from 3 to 4, he leaves for Dasha on the train that arrives by the fourth minute.
If he descends to the subway at a moment of time from 4 to 6, he waits for both trains to arrive by the sixth minute and goes to Masha as trains go less often in Masha's direction.
In sum Masha and Dasha get equal time β three minutes for each one, thus, Vasya will go to both girlfriends equally often. | [
{
"input": "3 7",
"output": "Dasha"
},
{
"input": "5 3",
"output": "Masha"
},
{
"input": "2 3",
"output": "Equal"
},
{
"input": "31 88",
"output": "Dasha"
},
{
"input": "8 75",
"output": "Dasha"
},
{
"input": "32 99",
"output": "Dasha"
},
{
"input": "77 4",
"output": "Masha"
},
{
"input": "27 1",
"output": "Masha"
},
{
"input": "84 11",
"output": "Masha"
},
{
"input": "4 6",
"output": "Equal"
},
{
"input": "52 53",
"output": "Equal"
},
{
"input": "397 568",
"output": "Dasha"
},
{
"input": "22 332",
"output": "Dasha"
},
{
"input": "419 430",
"output": "Dasha"
},
{
"input": "638 619",
"output": "Masha"
},
{
"input": "393 325",
"output": "Masha"
},
{
"input": "876 218",
"output": "Masha"
},
{
"input": "552 551",
"output": "Equal"
},
{
"input": "906 912",
"output": "Equal"
},
{
"input": "999 996",
"output": "Equal"
},
{
"input": "652 653",
"output": "Equal"
},
{
"input": "3647 7698",
"output": "Dasha"
},
{
"input": "2661 8975",
"output": "Dasha"
},
{
"input": "251 9731",
"output": "Dasha"
},
{
"input": "9886 8671",
"output": "Masha"
},
{
"input": "8545 7312",
"output": "Masha"
},
{
"input": "4982 2927",
"output": "Masha"
},
{
"input": "7660 7658",
"output": "Equal"
},
{
"input": "9846 9844",
"output": "Equal"
},
{
"input": "9632 9640",
"output": "Equal"
},
{
"input": "5036 5037",
"output": "Equal"
},
{
"input": "64854 77725",
"output": "Dasha"
},
{
"input": "4965 85708",
"output": "Dasha"
},
{
"input": "20393 86640",
"output": "Dasha"
},
{
"input": "99207 30728",
"output": "Masha"
},
{
"input": "77545 13842",
"output": "Masha"
},
{
"input": "30362 10712",
"output": "Masha"
},
{
"input": "51291 51292",
"output": "Equal"
},
{
"input": "55381 55382",
"output": "Equal"
},
{
"input": "91560 91550",
"output": "Equal"
},
{
"input": "99087 99090",
"output": "Equal"
},
{
"input": "983794 986389",
"output": "Dasha"
},
{
"input": "779183 786727",
"output": "Dasha"
},
{
"input": "450766 610961",
"output": "Dasha"
},
{
"input": "664690 630787",
"output": "Masha"
},
{
"input": "461363 256765",
"output": "Masha"
},
{
"input": "638067 409048",
"output": "Masha"
},
{
"input": "929061 929052",
"output": "Equal"
},
{
"input": "996219 996216",
"output": "Equal"
},
{
"input": "716249 716248",
"output": "Equal"
},
{
"input": "782250 782252",
"output": "Equal"
},
{
"input": "1 2",
"output": "Equal"
},
{
"input": "2 1",
"output": "Equal"
},
{
"input": "999999 1000000",
"output": "Equal"
},
{
"input": "999997 1000000",
"output": "Dasha"
},
{
"input": "1000000 999993",
"output": "Masha"
},
{
"input": "999983 999979",
"output": "Masha"
}
] | 62 | 0 | 0 | 4,883 |
|
549 | Haar Features | [
"greedy",
"implementation"
] | null | null | The first algorithm for detecting a face on the image working in realtime was developed by Paul Viola and Michael Jones in 2001. A part of the algorithm is a procedure that computes Haar features. As part of this task, we consider a simplified model of this concept.
Let's consider a rectangular image that is represented with a table of size *n*<=Γ<=*m*. The table elements are integers that specify the brightness of each pixel in the image.
A feature also is a rectangular table of size *n*<=Γ<=*m*. Each cell of a feature is painted black or white.
To calculate the value of the given feature at the given image, you must perform the following steps. First the table of the feature is put over the table of the image (without rotations or reflections), thus each pixel is entirely covered with either black or white cell. The value of a feature in the image is the value of *W*<=-<=*B*, where *W* is the total brightness of the pixels in the image, covered with white feature cells, and *B* is the total brightness of the pixels covered with black feature cells.
Some examples of the most popular Haar features are given below.
Your task is to determine the number of operations that are required to calculate the feature by using the so-called prefix rectangles.
A prefix rectangle is any rectangle on the image, the upper left corner of which coincides with the upper left corner of the image.
You have a variable *value*, whose value is initially zero. In one operation you can count the sum of pixel values ββat any prefix rectangle, multiply it by any integer and add to variable *value*.
You are given a feature. It is necessary to calculate the minimum number of operations required to calculate the values of this attribute at an arbitrary image. For a better understanding of the statement, read the explanation of the first sample. | The first line contains two space-separated integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=100) β the number of rows and columns in the feature.
Next *n* lines contain the description of the feature. Each line consists of *m* characters, the *j*-th character of the *i*-th line equals to "W", if this element of the feature is white and "B" if it is black. | Print a single number β the minimum number of operations that you need to make to calculate the value of the feature. | [
"6 8\nBBBBBBBB\nBBBBBBBB\nBBBBBBBB\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\n",
"3 3\nWBW\nBWW\nWWW\n",
"3 6\nWWBBWW\nWWBBWW\nWWBBWW\n",
"4 4\nBBBB\nBBBB\nBBBB\nBBBW\n"
] | [
"2\n",
"4\n",
"3\n",
"4\n"
] | The first sample corresponds to feature *B*, the one shown in the picture. The value of this feature in an image of size 6βΓβ8 equals to the difference of the total brightness of the pixels in the lower and upper half of the image. To calculate its value, perform the following two operations:
1. add the sum of pixels in the prefix rectangle with the lower right corner in the 6-th row and 8-th column with coefficient 1 to the variable *value* (the rectangle is indicated by a red frame); <img class="tex-graphics" src="https://espresso.codeforces.com/59e6d843dfb74d53c1bdfa004d277d661dbfb8fc.png" style="max-width: 100.0%;max-height: 100.0%;"/>1. add the number of pixels in the prefix rectangle with the lower right corner in the 3-rd row and 8-th column with coefficient β-β2 and variable *value*. <img class="tex-graphics" src="https://espresso.codeforces.com/91d79402e81fce528454fd33ea193676082cf259.png" style="max-width: 100.0%;max-height: 100.0%;"/>
Thus, all the pixels in the lower three rows of the image will be included with factor 1, and all pixels in the upper three rows of the image will be included with factor 1β-β2β=ββ-β1, as required. | [
{
"input": "6 8\nBBBBBBBB\nBBBBBBBB\nBBBBBBBB\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW",
"output": "2"
},
{
"input": "3 3\nWBW\nBWW\nWWW",
"output": "4"
},
{
"input": "3 6\nWWBBWW\nWWBBWW\nWWBBWW",
"output": "3"
},
{
"input": "4 4\nBBBB\nBBBB\nBBBB\nBBBW",
"output": "4"
},
{
"input": "10 9\nBWWWBWWBB\nBBWWBWBBW\nBBWBWBWBB\nBWBWBBBBB\nBBWBWBWBW\nBWWBWWBBW\nWBWWWBWWW\nWBBWBWBWW\nBBWWBWWBB\nBBWWBWWBW",
"output": "61"
},
{
"input": "4 1\nW\nW\nB\nB",
"output": "2"
},
{
"input": "2 10\nBBWBWWBWBB\nBBBBBBBBBW",
"output": "10"
},
{
"input": "100 1\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nW\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB\nB",
"output": "2"
},
{
"input": "1 100\nWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB",
"output": "2"
},
{
"input": "4 5\nBWWBB\nBWBBW\nWBWWW\nWBWWB",
"output": "13"
},
{
"input": "2 9\nWBBBWBBBW\nBWWBBBBBB",
"output": "9"
},
{
"input": "6 6\nBBWWWB\nWBBBWB\nBBBBBW\nWWWWWW\nBBBBBW\nBWWBBB",
"output": "16"
},
{
"input": "1 1\nW",
"output": "1"
},
{
"input": "1 1\nB",
"output": "1"
},
{
"input": "1 8\nWWBWWWWW",
"output": "3"
},
{
"input": "2 8\nBBBBBBBB\nBBBBBBBB",
"output": "1"
},
{
"input": "1 52\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB",
"output": "1"
},
{
"input": "11 8\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWBWWWW\nWWWWWWWW\nWBWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW",
"output": "9"
}
] | 124 | 0 | 3 | 4,898 |
|
173 | Chamber of Secrets | [
"dfs and similar",
"shortest paths"
] | null | null | "The Chamber of Secrets has been opened again" β this news has spread all around Hogwarts and some of the students have been petrified due to seeing the basilisk. Dumbledore got fired and now Harry is trying to enter the Chamber of Secrets. These aren't good news for Lord Voldemort. The problem is, he doesn't want anybody to be able to enter the chamber. The Dark Lord is going to be busy sucking life out of Ginny.
The Chamber of Secrets is an *n*<=Γ<=*m* rectangular grid in which some of the cells are columns. A light ray (and a basilisk's gaze) passes through the columns without changing its direction. But with some spell we can make a column magic to reflect the light ray (or the gaze) in all four directions when it receives the ray. This is shown in the figure below.
The basilisk is located at the right side of the lower right cell of the grid and is looking to the left (in the direction of the lower left cell). According to the legend, anyone who meets a basilisk's gaze directly dies immediately. But if someone meets a basilisk's gaze through a column, this person will get petrified. We know that the door to the Chamber is located on the left side of the upper left corner of the grid and anyone who wants to enter will look in the direction of its movement (in the direction of the upper right cell) from that position.
Given the dimensions of the chamber and the location of regular columns, Lord Voldemort has asked you to find the minimum number of columns that we need to make magic so that anyone who wants to enter the chamber would be petrified or just declare that it's impossible to secure the chamber. | The first line of the input contains two integer numbers *n* and *m* (2<=β€<=*n*,<=*m*<=β€<=1000). Each of the next *n* lines contains *m* characters. Each character is either "." or "#" and represents one cell of the Chamber grid. It's "." if the corresponding cell is empty and "#" if it's a regular column. | Print the minimum number of columns to make magic or -1 if it's impossible to do. | [
"3 3\n.#.\n...\n.#.\n",
"4 3\n##.\n...\n.#.\n.#.\n"
] | [
"2\n",
"2\n"
] | The figure above shows the first sample test. In the first sample we should make both columns magic. The dragon figure represents the basilisk and the binoculars represent the person who will enter the Chamber of secrets. The black star shows the place where the person will be petrified. Yellow lines represent basilisk gaze moving through columns. | [
{
"input": "3 3\n.#.\n...\n.#.",
"output": "2"
},
{
"input": "4 3\n##.\n...\n.#.\n.#.",
"output": "2"
},
{
"input": "3 3\n###\n###\n###",
"output": "2"
},
{
"input": "3 4\n..##\n....\n..#.",
"output": "2"
},
{
"input": "4 3\n#.#\n...\n...\n.##",
"output": "2"
},
{
"input": "4 4\n##..\n..#.\n...#\n...#",
"output": "-1"
},
{
"input": "5 5\n...#.\n.....\n.....\n.....\n..#.#",
"output": "-1"
},
{
"input": "5 5\n.....\n.#...\n.....\n.....\n#.###",
"output": "-1"
},
{
"input": "5 5\n.....\n.###.\n..##.\n..##.\n...#.",
"output": "-1"
},
{
"input": "5 5\n.##..\n.##..\n.#.#.\n..#..\n..#..",
"output": "2"
},
{
"input": "5 5\n...#.\n.#..#\n#.#.#\n#....\n#.#..",
"output": "-1"
},
{
"input": "5 5\n.#.#.\n#..#.\n.#.##\n.#.##\n##.#.",
"output": "2"
},
{
"input": "5 5\n.####\n#.###\n#####\n#.###\n#####",
"output": "2"
},
{
"input": "5 5\n.####\n#.#.#\n#####\n#####\n#####",
"output": "2"
},
{
"input": "5 5\n#####\n#####\n#####\n#####\n#####",
"output": "2"
},
{
"input": "2 42\n.########.#.########.#..#############.##..\n#####.#############.#####.#.#.#####.####..",
"output": "2"
},
{
"input": "2 2\n##\n.#",
"output": "2"
},
{
"input": "4 3\n.#.\n...\n##.\n#.#",
"output": "4"
},
{
"input": "4 3\n..#\n#.#\n...\n#..",
"output": "4"
},
{
"input": "10 10\n#.........\n...#..#...\n..........\n..........\n.......#.#\n..........\n..........\n......##..\n#..#......\n.........#",
"output": "10"
},
{
"input": "4 4\n.#..\n..##\n.#.#\n..#.",
"output": "6"
},
{
"input": "4 3\n#.#\n.##\n...\n.#.",
"output": "4"
},
{
"input": "4 4\n...#\n.##.\n.#.#\n..#.",
"output": "6"
},
{
"input": "4 4\n#...\n.##.\n#.#.\n.#..",
"output": "6"
},
{
"input": "3 3\n..#\n#.#\n#..",
"output": "4"
},
{
"input": "4 4\n#...\n.#.#\n##..\n...#",
"output": "6"
},
{
"input": "5 5\n#....\n.....\n..##.\n#.#..\n...#.",
"output": "6"
},
{
"input": "4 4\n..#.\n#.#.\n#..#\n...#",
"output": "6"
},
{
"input": "4 7\n..#....\n##.##.#\n.##....\n...##.#",
"output": "6"
},
{
"input": "5 2\n.#\n##\n..\n#.\n#.",
"output": "4"
},
{
"input": "4 3\n.#.\n#.#\n##.\n..#",
"output": "6"
}
] | 2,000 | 1,843,200 | 0 | 4,900 |
|
978 | Almost Arithmetic Progression | [
"brute force",
"implementation",
"math"
] | null | null | Polycarp likes arithmetic progressions. A sequence $[a_1, a_2, \dots, a_n]$ is called an arithmetic progression if for each $i$ ($1 \le i < n$) the value $a_{i+1} - a_i$ is the same. For example, the sequences $[42]$, $[5, 5, 5]$, $[2, 11, 20, 29]$ and $[3, 2, 1, 0]$ are arithmetic progressions, but $[1, 0, 1]$, $[1, 3, 9]$ and $[2, 3, 1]$ are not.
It follows from the definition that any sequence of length one or two is an arithmetic progression.
Polycarp found some sequence of positive integers $[b_1, b_2, \dots, b_n]$. He agrees to change each element by at most one. In the other words, for each element there are exactly three options: an element can be decreased by $1$, an element can be increased by $1$, an element can be left unchanged.
Determine a minimum possible number of elements in $b$ which can be changed (by exactly one), so that the sequence $b$ becomes an arithmetic progression, or report that it is impossible.
It is possible that the resulting sequence contains element equals $0$. | The first line contains a single integer $n$ $(1 \le n \le 100\,000)$ β the number of elements in $b$.
The second line contains a sequence $b_1, b_2, \dots, b_n$ $(1 \le b_i \le 10^{9})$. | If it is impossible to make an arithmetic progression with described operations, print -1. In the other case, print non-negative integer β the minimum number of elements to change to make the given sequence becomes an arithmetic progression. The only allowed operation is to add/to subtract one from an element (can't use operation twice to the same position). | [
"4\n24 21 14 10\n",
"2\n500 500\n",
"3\n14 5 1\n",
"5\n1 3 6 9 12\n"
] | [
"3\n",
"0\n",
"-1\n",
"1\n"
] | In the first example Polycarp should increase the first number on $1$, decrease the second number on $1$, increase the third number on $1$, and the fourth number should left unchanged. So, after Polycarp changed three elements by one, his sequence became equals to $[25, 20, 15, 10]$, which is an arithmetic progression.
In the second example Polycarp should not change anything, because his sequence is an arithmetic progression.
In the third example it is impossible to make an arithmetic progression.
In the fourth example Polycarp should change only the first element, he should decrease it on one. After that his sequence will looks like $[0, 3, 6, 9, 12]$, which is an arithmetic progression. | [
{
"input": "4\n24 21 14 10",
"output": "3"
},
{
"input": "2\n500 500",
"output": "0"
},
{
"input": "3\n14 5 1",
"output": "-1"
},
{
"input": "5\n1 3 6 9 12",
"output": "1"
},
{
"input": "1\n1000000000",
"output": "0"
},
{
"input": "2\n1000000000 1",
"output": "0"
},
{
"input": "3\n34 70 52",
"output": "-1"
},
{
"input": "3\n1 2 1",
"output": "1"
},
{
"input": "6\n1 1 3 5 6 5",
"output": "4"
},
{
"input": "3\n2 1 2",
"output": "1"
},
{
"input": "10\n9 5 3 4 7 1 2 8 10 6",
"output": "-1"
},
{
"input": "4\n20 15 20 15",
"output": "-1"
},
{
"input": "4\n10 21 14 24",
"output": "-1"
},
{
"input": "3\n5 9 5",
"output": "-1"
},
{
"input": "10\n10 9 8 7 6 1 2 3 4 5",
"output": "-1"
},
{
"input": "4\n2 6 3 1",
"output": "-1"
},
{
"input": "5\n1 3 6 8 10",
"output": "2"
},
{
"input": "4\n1 3 1 3",
"output": "4"
},
{
"input": "3\n3 1 2",
"output": "2"
},
{
"input": "3\n33 69 51",
"output": "-1"
},
{
"input": "4\n1 1000000000 1000000000 1000000000",
"output": "-1"
},
{
"input": "5\n2 1 3 4 5",
"output": "2"
},
{
"input": "3\n1 9 4",
"output": "-1"
},
{
"input": "3\n2 1 3",
"output": "2"
},
{
"input": "3\n9 3 6",
"output": "-1"
},
{
"input": "3\n1 10 5",
"output": "-1"
}
] | 108 | 14,745,600 | 3 | 4,902 |
|
233 | Non-square Equation | [
"binary search",
"brute force",
"math"
] | null | null | Let's consider equation:
where *x*,<=*n* are positive integers, *s*(*x*) is the function, equal to the sum of digits of number *x* in the decimal number system.
You are given an integer *n*, find the smallest positive integer root of equation *x*, or else determine that there are no such roots. | A single line contains integer *n* (1<=β€<=*n*<=β€<=1018) β the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier. | Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer *x* (*x*<=><=0), that the equation given in the statement holds. | [
"2\n",
"110\n",
"4\n"
] | [
"1\n",
"10\n",
"-1\n"
] | In the first test case *x*β=β1 is the minimum root. As *s*(1)β=β1 and 1<sup class="upper-index">2</sup>β+β1Β·1β-β2β=β0.
In the second test case *x*β=β10 is the minimum root. As *s*(10)β=β1β+β0β=β1 and 10<sup class="upper-index">2</sup>β+β1Β·10β-β110β=β0.
In the third test case the equation has no roots. | [
{
"input": "2",
"output": "1"
},
{
"input": "110",
"output": "10"
},
{
"input": "4",
"output": "-1"
},
{
"input": "8",
"output": "2"
},
{
"input": "10000000100000000",
"output": "100000000"
},
{
"input": "10000006999999929",
"output": "99999999"
},
{
"input": "172541340",
"output": "13131"
},
{
"input": "172580744",
"output": "13132"
},
{
"input": "10000100000",
"output": "100000"
},
{
"input": "1000001000000",
"output": "1000000"
},
{
"input": "100000010000000",
"output": "10000000"
},
{
"input": "425",
"output": "17"
},
{
"input": "1085",
"output": "31"
},
{
"input": "4296409065",
"output": "65535"
},
{
"input": "9211004165221796",
"output": "95973949"
},
{
"input": "1245131330556680",
"output": "35286397"
},
{
"input": "40000000400000000",
"output": "200000000"
},
{
"input": "90000000900000000",
"output": "300000000"
},
{
"input": "160000001600000000",
"output": "400000000"
},
{
"input": "250000002500000000",
"output": "500000000"
},
{
"input": "360000003600000000",
"output": "600000000"
},
{
"input": "490000004900000000",
"output": "700000000"
},
{
"input": "640000006400000000",
"output": "800000000"
},
{
"input": "810000008100000000",
"output": "900000000"
},
{
"input": "902500013300000000",
"output": "950000000"
},
{
"input": "790123519209876480",
"output": "888888888"
},
{
"input": "100000609999938",
"output": "9999999"
},
{
"input": "1000051999947",
"output": "999999"
},
{
"input": "10004299956",
"output": "99999"
},
{
"input": "40000014199999928",
"output": "199999999"
},
{
"input": "90000021599999927",
"output": "299999999"
},
{
"input": "160000029199999926",
"output": "399999999"
},
{
"input": "250000036999999925",
"output": "499999999"
},
{
"input": "360000044999999924",
"output": "599999999"
},
{
"input": "810000070199999921",
"output": "899999999"
},
{
"input": "1000000000000000000",
"output": "-1"
},
{
"input": "980100017820000000",
"output": "990000000"
},
{
"input": "990025022885000000",
"output": "995000000"
},
{
"input": "9999999900000001",
"output": "-1"
},
{
"input": "99999999999999999",
"output": "-1"
},
{
"input": "89997012024799500",
"output": "299994990"
},
{
"input": "1000000000000000000",
"output": "-1"
},
{
"input": "999999999999999997",
"output": "-1"
},
{
"input": "999999887000001932",
"output": "999999908"
},
{
"input": "162",
"output": "9"
},
{
"input": "999920076596999923",
"output": "-1"
},
{
"input": "9999956110095370",
"output": "-1"
},
{
"input": "999999863000003700",
"output": "999999900"
}
] | 92 | 0 | 0 | 4,904 |
|
0 | none | [
"none"
] | null | null | ΠΡΡΡ *n*-ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π½ΡΠΉ Π΄ΠΎΠΌ, Π² ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ ΠΏΠΎ *m* ΡΡΠ°ΠΆΠ΅ΠΉ, ΠΈ Π½Π° ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΡΡΠ°ΠΆΠ΅ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° ΡΠΎΠ²Π½ΠΎ *k* ΠΊΠ²Π°ΡΡΠΈΡ. Π’Π°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, Π² Π΄ΠΎΠΌΠ΅ Π²ΡΠ΅Π³ΠΎ *n*Β·*m*Β·*k* ΠΊΠ²Π°ΡΡΠΈΡ. ΠΠ½ΠΈ ΠΏΡΠΎΠ½ΡΠΌΠ΅ΡΠΎΠ²Π°Π½Ρ Π΅ΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ ΠΎΡ 1 Π΄ΠΎ *n*Β·*m*Β·*k*, ΡΠΎ Π΅ΡΡΡ ΠΏΠ΅ΡΠ²Π°Ρ ΠΊΠ²Π°ΡΡΠΈΡΠ° Π½Π° ΠΏΠ΅ΡΠ²ΠΎΠΌ ΡΡΠ°ΠΆΠ΅ Π² ΠΏΠ΅ΡΠ²ΠΎΠΌ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ ΠΈΠΌΠ΅Π΅Ρ Π½ΠΎΠΌΠ΅Ρ 1, ΠΏΠ΅ΡΠ²Π°Ρ ΠΊΠ²Π°ΡΡΠΈΡΠ° Π½Π° Π²ΡΠΎΡΠΎΠΌ ΡΡΠ°ΠΆΠ΅ ΠΏΠ΅ΡΠ²ΠΎΠ³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° ΠΈΠΌΠ΅Π΅Ρ Π½ΠΎΠΌΠ΅Ρ *k*<=+<=1 ΠΈ ΡΠ°ΠΊ Π΄Π°Π»Π΅Π΅. ΠΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡ ΡΡΠΎΠ³ΠΎ Π΄ΠΎΠΌΠ° ΡΠΎΡΡΠΎΠΈΡ Π² ΡΠΎΠΌ, ΡΡΠΎ ΠΎΠ½ ΠΊΡΡΠ³Π»ΡΠΉ. Π’ΠΎ Π΅ΡΡΡ Π΅ΡΠ»ΠΈ ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΡΡ Π΅Π³ΠΎ ΠΏΠΎ ΡΠ°ΡΠΎΠ²ΠΎΠΉ ΡΡΡΠ΅Π»ΠΊΠ΅, ΡΠΎ ΠΏΠΎΡΠ»Π΅ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° Π½ΠΎΠΌΠ΅Ρ 1 ΡΠ»Π΅Π΄ΡΠ΅Ρ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄ Π½ΠΎΠΌΠ΅Ρ 2, Π·Π°ΡΠ΅ΠΌ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄ Π½ΠΎΠΌΠ΅Ρ 3 ΠΈ ΡΠ°ΠΊ Π΄Π°Π»Π΅Π΅ Π΄ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° Π½ΠΎΠΌΠ΅Ρ *n*. ΠΠΎΡΠ»Π΅ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° Π½ΠΎΠΌΠ΅Ρ *n* ΡΠ½ΠΎΠ²Π° ΠΈΠ΄ΡΡ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄ Π½ΠΎΠΌΠ΅Ρ 1.
ΠΠ΄Π²Π°ΡΠ΄ ΠΆΠΈΠ²ΡΡ Π² ΠΊΠ²Π°ΡΡΠΈΡΠ΅ Π½ΠΎΠΌΠ΅Ρ *a*, Π° ΠΠ°ΡΠ°ΡΠ°Β β Π² ΠΊΠ²Π°ΡΡΠΈΡΠ΅ Π½ΠΎΠΌΠ΅Ρ *b*. ΠΠ΅ΡΠ΅Ρ
ΠΎΠ΄ Π½Π° 1 ΡΡΠ°ΠΆ Π²Π²Π΅ΡΡ
ΠΈΠ»ΠΈ Π²Π½ΠΈΠ· ΠΏΠΎ Π»Π΅ΡΡΠ½ΠΈΡΠ΅ Π·Π°Π½ΠΈΠΌΠ°Π΅Ρ 5 ΡΠ΅ΠΊΡΠ½Π΄, ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄ ΠΎΡ Π΄Π²Π΅ΡΠΈ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° ΠΊ Π΄Π²Π΅ΡΠΈ ΡΠΎΡΠ΅Π΄Π½Π΅Π³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π°Β β 15 ΡΠ΅ΠΊΡΠ½Π΄, Π° ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄ Π² ΠΏΡΠ΅Π΄Π΅Π»Π°Ρ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΡΡΠ°ΠΆΠ° ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ ΠΌΠ³Π½ΠΎΠ²Π΅Π½Π½ΠΎ. Π’Π°ΠΊΠΆΠ΅ Π² ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ Π΄ΠΎΠΌΠ° Π΅ΡΡΡ Π»ΠΈΡΡ. ΠΠ½ ΡΡΡΡΠΎΠ΅Π½ ΡΠ»Π΅Π΄ΡΡΡΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ: ΠΎΠ½ Π²ΡΠ΅Π³Π΄Π° ΠΏΡΠΈΠ΅Π·ΠΆΠ°Π΅Ρ ΡΠΎΠ²Π½ΠΎ ΡΠ΅ΡΠ΅Π· 10 ΡΠ΅ΠΊΡΠ½Π΄ ΠΏΠΎΡΠ»Π΅ Π²ΡΠ·ΠΎΠ²Π°, Π° ΡΡΠΎΠ±Ρ ΠΏΠ΅ΡΠ΅ΠΌΠ΅ΡΡΠΈΡΡ ΠΏΠ°ΡΡΠ°ΠΆΠΈΡΠ° Π½Π° ΠΎΠ΄ΠΈΠ½ ΡΡΠ°ΠΆ Π²Π²Π΅ΡΡ
ΠΈΠ»ΠΈ Π²Π½ΠΈΠ·, Π»ΠΈΡΡ ΡΡΠ°ΡΠΈΡ ΡΠΎΠ²Π½ΠΎ 1 ΡΠ΅ΠΊΡΠ½Π΄Ρ. ΠΠΎΡΠ°Π΄ΠΊΠ° ΠΈ Π²ΡΡΠ°Π΄ΠΊΠ° ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΡΡ ΠΌΠ³Π½ΠΎΠ²Π΅Π½Π½ΠΎ.
ΠΠΎΠΌΠΎΠ³ΠΈΡΠ΅ ΠΠ΄Π²Π°ΡΠ΄Ρ Π½Π°ΠΉΡΠΈ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ΅ Π²ΡΠ΅ΠΌΡ, Π·Π° ΠΊΠΎΡΠΎΡΠΎΠ΅ ΠΎΠ½ ΡΠΌΠΎΠΆΠ΅Ρ Π΄ΠΎΠ±ΡΠ°ΡΡΡΡ Π΄ΠΎ ΠΊΠ²Π°ΡΡΠΈΡΡ ΠΠ°ΡΠ°ΡΠΈ. Π‘ΡΠΈΡΠ°ΠΉΡΠ΅, ΡΡΠΎ ΠΠ΄Π²Π°ΡΠ΄ ΠΌΠΎΠΆΠ΅Ρ Π²ΡΠΉΡΠΈ ΠΈΠ· ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° ΡΠΎΠ»ΡΠΊΠΎ Ρ ΠΏΠ΅ΡΠ²ΠΎΠ³ΠΎ ΡΡΠ°ΠΆΠ° ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠ΅Π³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° (ΡΡΠΎ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ ΠΌΠ³Π½ΠΎΠ²Π΅Π½Π½ΠΎ). ΠΡΠ»ΠΈ ΠΠ΄Π²Π°ΡΠ΄ ΡΡΠΎΠΈΡ ΠΏΠ΅ΡΠ΅Π΄ Π΄Π²Π΅ΡΡΡ ΠΊΠ°ΠΊΠΎΠ³ΠΎ-ΡΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π°, ΠΎΠ½ ΠΌΠΎΠΆΠ΅Ρ Π·Π°ΠΉΡΠΈ Π² Π½Π΅Π³ΠΎ ΠΈ ΡΡΠ°Π·Ρ ΠΎΠΊΠ°ΠΆΠ΅ΡΡΡ Π½Π° ΠΏΠ΅ΡΠ²ΠΎΠΌ ΡΡΠ°ΠΆΠ΅ ΡΡΠΎΠ³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° (ΡΡΠΎ ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ ΠΌΠ³Π½ΠΎΠ²Π΅Π½Π½ΠΎ). ΠΠ΄Π²Π°ΡΠ΄ ΠΌΠΎΠΆΠ΅Ρ Π²ΡΠ±ΠΈΡΠ°ΡΡ, Π² ΠΊΠ°ΠΊΠΎΠΌ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΈ ΠΈΠ΄ΡΠΈ Π²ΠΎΠΊΡΡΠ³ Π΄ΠΎΠΌΠ°. | Π ΠΏΠ΅ΡΠ²ΠΎΠΉ ΡΡΡΠΎΠΊΠ΅ Π²Ρ
ΠΎΠ΄Π½ΡΡ
Π΄Π°Π½Π½ΡΡ
ΡΠ»Π΅Π΄ΡΡΡ ΡΡΠΈ ΡΠΈΡΠ»Π° *n*, *m*, *k* (1<=β€<=*n*,<=*m*,<=*k*<=β€<=1000)Β β ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄ΠΎΠ² Π² Π΄ΠΎΠΌΠ΅, ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΠ°ΠΆΠ΅ΠΉ Π² ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ ΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΊΠ²Π°ΡΡΠΈΡ Π½Π° ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΡΡΠ°ΠΆΠ΅ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²Π΅Π½Π½ΠΎ.
ΠΠΎ Π²ΡΠΎΡΠΎΠΉ ΡΡΡΠΎΠΊΠ΅ Π²Ρ
ΠΎΠ΄Π½ΡΡ
Π΄Π°Π½Π½ΡΡ
Π·Π°ΠΏΠΈΡΠ°Π½Ρ Π΄Π²Π° ΡΠΈΡΠ»Π° *a* ΠΈ *b* (1<=β€<=*a*,<=*b*<=β€<=*n*Β·*m*Β·*k*)Β β Π½ΠΎΠΌΠ΅ΡΠ° ΠΊΠ²Π°ΡΡΠΈΡ, Π² ΠΊΠΎΡΠΎΡΡΡ
ΠΆΠΈΠ²ΡΡ ΠΠ΄Π²Π°ΡΠ΄ ΠΈ ΠΠ°ΡΠ°ΡΠ°, ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²Π΅Π½Π½ΠΎ. ΠΠ°ΡΠ°Π½ΡΠΈΡΡΠ΅ΡΡΡ, ΡΡΠΎ ΡΡΠΈ Π½ΠΎΠΌΠ΅ΡΠ° ΡΠ°Π·Π»ΠΈΡΠ½Ρ. | ΠΡΠ²Π΅Π΄ΠΈΡΠ΅ Π΅Π΄ΠΈΠ½ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠ΅Π»ΠΎΠ΅ ΡΠΈΡΠ»ΠΎΒ β ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ΅ Π²ΡΠ΅ΠΌΡ (Π² ΡΠ΅ΠΊΡΠ½Π΄Π°Ρ
), Π·Π° ΠΊΠΎΡΠΎΡΠΎΠ΅ ΠΠ΄Π²Π°ΡΠ΄ ΡΠΌΠΎΠΆΠ΅Ρ Π΄ΠΎΠ±ΡΠ°ΡΡΡΡ ΠΎΡ ΡΠ²ΠΎΠ΅ΠΉ ΠΊΠ²Π°ΡΡΠΈΡΡ Π΄ΠΎ ΠΊΠ²Π°ΡΡΠΈΡΡ ΠΠ°ΡΠ°ΡΠΈ. | [
"4 10 5\n200 6\n",
"3 1 5\n7 2\n"
] | [
"39\n",
"15\n"
] | Π ΠΏΠ΅ΡΠ²ΠΎΠΌ ΡΠ΅ΡΡΠΎΠ²ΠΎΠΌ ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΠ΄Π²Π°ΡΠ΄ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π² 4 ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ Π½Π° 10 ΡΡΠ°ΠΆΠ΅, Π° ΠΠ°ΡΠ°ΡΠ° Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π² 1 ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ Π½Π° 2 ΡΡΠ°ΠΆΠ΅. ΠΠΎΡΡΠΎΠΌΡ ΠΠ΄Π²Π°ΡΠ΄Ρ Π²ΡΠ³ΠΎΠ΄Π½ΠΎ ΡΠ½Π°ΡΠ°Π»Π° ΡΠΏΡΡΡΠΈΡΡΡΡ Π½Π° Π»ΠΈΡΡΠ΅ Π½Π° ΠΏΠ΅ΡΠ²ΡΠΉ ΡΡΠ°ΠΆ (Π½Π° ΡΡΠΎ ΠΎΠ½ ΠΏΠΎΡΡΠ°ΡΠΈΡ 19 ΡΠ΅ΠΊΡΠ½Π΄, ΠΈΠ· ΠΊΠΎΡΠΎΡΡΡ
10Β β Π½Π° ΠΎΠΆΠΈΠ΄Π°Π½ΠΈΠ΅ ΠΈ 9Β β Π½Π° ΠΏΠΎΠ΅Π·Π΄ΠΊΡ Π½Π° Π»ΠΈΡΡΠ΅), Π·Π°ΡΠ΅ΠΌ ΠΎΠ±ΠΎΠΉΡΠΈ Π΄ΠΎΠΌ ΠΏΡΠΎΡΠΈΠ² ΡΠ°ΡΠΎΠ²ΠΎΠΉ ΡΡΡΠ΅Π»ΠΊΠΈ Π΄ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° Π½ΠΎΠΌΠ΅Ρ 1 (Π½Π° ΡΡΠΎ ΠΎΠ½ ΠΏΠΎΡΡΠ°ΡΠΈΡ 15 ΡΠ΅ΠΊΡΠ½Π΄), ΠΈ Π½Π°ΠΊΠΎΠ½Π΅Ρ ΠΏΠΎΠ΄Π½ΡΡΡΡΡ ΠΏΠΎ Π»Π΅ΡΡΠ½ΠΈΡΠ΅ Π½Π° ΡΡΠ°ΠΆ Π½ΠΎΠΌΠ΅Ρ 2 (Π½Π° ΡΡΠΎ ΠΎΠ½ ΠΏΠΎΡΡΠ°ΡΠΈΡ 5 ΡΠ΅ΠΊΡΠ½Π΄). Π’Π°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, ΠΎΡΠ²Π΅Ρ ΡΠ°Π²Π΅Π½ 19β+β15β+β5β=β39.
ΠΠΎ Π²ΡΠΎΡΠΎΠΌ ΡΠ΅ΡΡΠΎΠ²ΠΎΠΌ ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΠ΄Π²Π°ΡΠ΄ ΠΆΠΈΠ²ΡΡ Π² ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ 2 Π½Π° ΡΡΠ°ΠΆΠ΅ 1, Π° ΠΠ°ΡΠ°ΡΠ° Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π² ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π΅ 1 Π½Π° ΡΡΠ°ΠΆΠ΅ 1. ΠΠΎΡΡΠΎΠΌΡ ΠΠ΄Π²Π°ΡΠ΄Ρ Π²ΡΠ³ΠΎΠ΄Π½ΠΎ ΠΏΡΠΎΡΡΠΎ ΠΎΠ±ΠΎΠΉΡΠΈ Π΄ΠΎΠΌ ΠΏΠΎ ΡΠ°ΡΠΎΠ²ΠΎΠΉ ΡΡΡΠ΅Π»ΠΊΠ΅ Π΄ΠΎ ΠΏΠΎΠ΄ΡΠ΅Π·Π΄Π° 1, Π½Π° ΡΡΠΎ ΠΎΠ½ ΠΏΠΎΡΡΠ°ΡΠΈΡ 15 ΡΠ΅ΠΊΡΠ½Π΄. | [
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] | 62 | 4,608,000 | -1 | 4,906 |
|
612 | HDD is Outdated Technology | [
"implementation",
"math"
] | null | null | HDD hard drives group data by sectors. All files are split to fragments and each of them are written in some sector of hard drive. Note the fragments can be written in sectors in arbitrary order.
One of the problems of HDD hard drives is the following: the magnetic head should move from one sector to another to read some file.
Find the time need to read file split to *n* fragments. The *i*-th sector contains the *f**i*-th fragment of the file (1<=β€<=*f**i*<=β€<=*n*). Note different sectors contains the different fragments. At the start the magnetic head is in the position that contains the first fragment. The file are reading in the following manner: at first the first fragment is read, then the magnetic head moves to the sector that contains the second fragment, then the second fragment is read and so on until the *n*-th fragment is read. The fragments are read in the order from the first to the *n*-th.
It takes |*a*<=-<=*b*| time units to move the magnetic head from the sector *a* to the sector *b*. Reading a fragment takes no time. | The first line contains a positive integer *n* (1<=β€<=*n*<=β€<=2Β·105) β the number of fragments.
The second line contains *n* different integers *f**i* (1<=β€<=*f**i*<=β€<=*n*) β the number of the fragment written in the *i*-th sector. | Print the only integer β the number of time units needed to read the file. | [
"3\n3 1 2\n",
"5\n1 3 5 4 2\n"
] | [
"3\n",
"10\n"
] | In the second example the head moves in the following way:
- 1->2 means movement from the sector 1 to the sector 5, i.e. it takes 4 time units - 2->3 means movement from the sector 5 to the sector 2, i.e. it takes 3 time units - 3->4 means movement from the sector 2 to the sector 4, i.e. it takes 2 time units - 4->5 means movement from the sector 4 to the sector 3, i.e. it takes 1 time units
So the answer to the second example is 4β+β3β+β2β+β1β=β10. | [
{
"input": "3\n3 1 2",
"output": "3"
},
{
"input": "5\n1 3 5 4 2",
"output": "10"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "1\n1",
"output": "0"
},
{
"input": "10\n8 2 10 3 4 6 1 7 9 5",
"output": "40"
},
{
"input": "10\n1 2 3 4 5 6 7 8 9 10",
"output": "9"
},
{
"input": "10\n1 3 5 7 9 10 8 6 4 2",
"output": "45"
},
{
"input": "100\n11 9 35 34 51 74 16 67 26 21 14 80 84 79 7 61 28 3 53 43 42 5 56 36 69 30 22 88 1 27 65 91 46 31 59 50 17 96 25 18 64 55 78 2 63 24 95 48 93 13 38 76 89 94 15 90 45 81 52 87 83 73 44 49 23 82 85 75 86 33 47 19 58 97 37 20 40 10 92 4 6 68 77 54 71 12 62 60 100 39 41 99 72 29 57 8 70 32 66 98",
"output": "3580"
},
{
"input": "100\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100",
"output": "99"
},
{
"input": "100\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 100 98 96 94 92 90 88 86 84 82 80 78 76 74 72 70 68 66 64 62 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2",
"output": "4950"
}
] | 155 | 57,446,400 | 3 | 4,908 |
|
494 | Treasure | [
"greedy"
] | null | null | Malek has recently found a treasure map. While he was looking for a treasure he found a locked door. There was a string *s* written on the door consisting of characters '(', ')' and '#'. Below there was a manual on how to open the door. After spending a long time Malek managed to decode the manual and found out that the goal is to replace each '#' with one or more ')' characters so that the final string becomes beautiful.
Below there was also written that a string is called beautiful if for each *i* (1<=β€<=*i*<=β€<=|*s*|) there are no more ')' characters than '(' characters among the first *i* characters of *s* and also the total number of '(' characters is equal to the total number of ')' characters.
Help Malek open the door by telling him for each '#' character how many ')' characters he must replace it with. | The first line of the input contains a string *s* (1<=β€<=|*s*|<=β€<=105). Each character of this string is one of the characters '(', ')' or '#'. It is guaranteed that *s* contains at least one '#' character. | If there is no way of replacing '#' characters which leads to a beautiful string print <=-<=1. Otherwise for each character '#' print a separate line containing a positive integer, the number of ')' characters this character must be replaced with.
If there are several possible answers, you may output any of them. | [
"(((#)((#)\n",
"()((#((#(#()\n",
"#\n",
"(#)\n"
] | [
"1\n2\n",
"2\n2\n1",
"-1\n",
"-1\n"
] | |*s*| denotes the length of the string *s*. | [
{
"input": "(((#)((#)",
"output": "1\n2"
},
{
"input": "()((#((#(#()",
"output": "1\n1\n3"
},
{
"input": "#",
"output": "-1"
},
{
"input": "(#)",
"output": "-1"
},
{
"input": "(((((#(#(#(#()",
"output": "1\n1\n1\n5"
},
{
"input": "#))))",
"output": "-1"
},
{
"input": "((#(()#(##",
"output": "1\n1\n1\n1"
},
{
"input": "##((((((()",
"output": "-1"
},
{
"input": "(((((((((((((((((((###################",
"output": "1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1"
},
{
"input": "((#)(",
"output": "-1"
},
{
"input": "((#)((#)((#)((#)((#)((#)((#)((#)((#)((#)((#)((#)((#)((#)((#)((##",
"output": "1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1"
},
{
"input": ")((##((###",
"output": "-1"
},
{
"input": "(#))(#(#)((((#(##((#(#((((#(##((((((#((()(()(())((()#((((#((()((((#(((((#(##)(##()((((()())(((((#(((",
"output": "-1"
},
{
"input": "#(#(#((##((()))(((#)(#()#(((()()(()#(##(((()(((()))#(((((()(((((((()#((#((()(#(((()(()##(()(((()((#(",
"output": "-1"
},
{
"input": "((#(",
"output": "-1"
},
{
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"output": "-1"
},
{
"input": "(())((((#)",
"output": "3"
},
{
"input": "(#(",
"output": "-1"
},
{
"input": "((#)(",
"output": "-1"
},
{
"input": "(((()#(#)(",
"output": "-1"
},
{
"input": "#((#",
"output": "-1"
},
{
"input": "(#((((()",
"output": "-1"
},
{
"input": "(#((",
"output": "-1"
},
{
"input": ")(((())#",
"output": "-1"
}
] | 77 | 307,200 | 0 | 4,922 |
|
741 | Arpaβs overnight party and Mehrdadβs silent entering | [
"constructive algorithms",
"dfs and similar",
"graphs"
] | null | null | Note that girls in Arpaβs land are really attractive.
Arpa loves overnight parties. In the middle of one of these parties Mehrdad suddenly appeared. He saw *n* pairs of friends sitting around a table. *i*-th pair consisted of a boy, sitting on the *a**i*-th chair, and his girlfriend, sitting on the *b**i*-th chair. The chairs were numbered 1 through 2*n* in clockwise direction. There was exactly one person sitting on each chair.
There were two types of food: Kooft and Zahre-mar. Now Mehrdad wonders, was there any way to serve food for the guests such that:
- Each person had exactly one type of food, - No boy had the same type of food as his girlfriend, - Among any three guests sitting on consecutive chairs, there was two of them who had different type of food. Note that chairs 2*n* and 1 are considered consecutive.
Find the answer for the Mehrdad question. If it was possible, find some arrangement of food types that satisfies the conditions. | The first line contains an integer *n* (1<=<=β€<=<=*n*<=<=β€<=<=105)Β β the number of pairs of guests.
The *i*-th of the next *n* lines contains a pair of integers *a**i* and *b**i* (1<=<=β€<=*a**i*,<=*b**i*<=β€<=<=2*n*)Β β the number of chair on which the boy in the *i*-th pair was sitting and the number of chair on which his girlfriend was sitting. It's guaranteed that there was exactly one person sitting on each chair. | If there is no solution, print -1.
Otherwise print *n* lines, the *i*-th of them should contain two integers which represent the type of food for the *i*-th pair. The first integer in the line is the type of food the boy had, and the second integer is the type of food the girl had. If someone had Kooft, print 1, otherwise print 2.
If there are multiple solutions, print any of them. | [
"3\n1 4\n2 5\n3 6\n"
] | [
"1 2\n2 1\n1 2\n"
] | none | [
{
"input": "3\n1 4\n2 5\n3 6",
"output": "1 2\n2 1\n1 2"
},
{
"input": "6\n3 2\n5 11\n7 12\n6 9\n8 4\n1 10",
"output": "1 2\n1 2\n2 1\n2 1\n1 2\n1 2"
},
{
"input": "19\n30 27\n6 38\n10 28\n20 5\n14 18\n32 2\n36 29\n12 1\n31 24\n15 4\n35 11\n3 7\n21 17\n25 19\n16 8\n23 22\n37 33\n13 9\n34 26",
"output": "1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n1 2\n2 1\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1"
},
{
"input": "4\n4 2\n6 8\n5 1\n3 7",
"output": "1 2\n1 2\n2 1\n2 1"
},
{
"input": "17\n11 12\n17 22\n34 7\n3 1\n5 24\n18 20\n27 30\n16 33\n23 21\n19 4\n2 15\n29 28\n9 8\n13 25\n6 10\n32 26\n31 14",
"output": "1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n1 2\n2 1\n1 2"
},
{
"input": "19\n10 7\n9 17\n21 30\n36 8\n14 11\n25 24\n1 23\n38 33\n4 20\n3 37\n27 5\n28 19\n22 2\n6 34\n12 15\n31 32\n35 13\n16 29\n18 26",
"output": "1 2\n2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n1 2\n2 1"
},
{
"input": "17\n17 31\n11 23\n34 22\n24 8\n4 1\n7 14\n20 27\n3 19\n12 26\n32 25\n28 18\n16 29\n21 9\n6 2\n33 30\n5 13\n10 15",
"output": "1 2\n1 2\n2 1\n1 2\n2 1\n1 2\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1"
},
{
"input": "6\n2 7\n5 9\n12 8\n1 4\n3 6\n10 11",
"output": "2 1\n1 2\n1 2\n1 2\n1 2\n1 2"
},
{
"input": "8\n10 3\n2 16\n14 13\n5 15\n1 7\n11 8\n6 4\n12 9",
"output": "1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n1 2"
},
{
"input": "4\n2 8\n3 5\n4 7\n1 6",
"output": "2 1\n2 1\n1 2\n1 2"
},
{
"input": "2\n2 3\n1 4",
"output": "2 1\n1 2"
},
{
"input": "15\n16 22\n4 17\n27 3\n23 24\n18 20\n15 21\n9 7\n2 28\n29 19\n8 30\n14 10\n6 26\n25 11\n12 1\n13 5",
"output": "2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1"
},
{
"input": "10\n19 6\n8 2\n15 18\n17 14\n16 7\n20 10\n5 1\n13 3\n9 12\n11 4",
"output": "2 1\n1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2"
},
{
"input": "9\n12 7\n10 15\n16 14\n2 4\n1 17\n6 9\n8 3\n13 5\n11 18",
"output": "1 2\n2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n2 1\n2 1"
},
{
"input": "7\n3 14\n7 4\n13 10\n11 8\n6 1\n5 9\n2 12",
"output": "2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1"
},
{
"input": "6\n2 11\n7 1\n12 8\n4 10\n3 9\n5 6",
"output": "2 1\n2 1\n2 1\n2 1\n1 2\n1 2"
},
{
"input": "8\n13 6\n10 5\n1 12\n11 15\n7 16\n4 14\n9 2\n8 3",
"output": "1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2"
},
{
"input": "8\n16 5\n10 15\n8 11\n2 14\n6 4\n7 3\n1 13\n9 12",
"output": "1 2\n1 2\n1 2\n2 1\n1 2\n2 1\n1 2\n2 1"
},
{
"input": "7\n10 14\n4 6\n1 11\n7 2\n9 8\n5 13\n3 12",
"output": "2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1"
},
{
"input": "5\n2 5\n10 9\n1 6\n3 8\n4 7",
"output": "2 1\n2 1\n1 2\n1 2\n2 1"
},
{
"input": "8\n14 2\n7 9\n15 6\n13 11\n12 16\n10 5\n8 1\n3 4",
"output": "1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n2 1\n1 2"
},
{
"input": "5\n4 6\n5 1\n2 3\n7 8\n9 10",
"output": "2 1\n2 1\n2 1\n1 2\n1 2"
},
{
"input": "23\n46 21\n17 3\n27 38\n34 43\n7 6\n8 37\n22 4\n16 42\n36 32\n12 9\n10 45\n26 2\n13 24\n23 29\n18 15\n33 30\n31 5\n11 25\n1 14\n44 39\n19 20\n35 28\n41 40",
"output": "2 1\n1 2\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1"
},
{
"input": "26\n8 10\n52 21\n2 33\n18 34\n30 51\n5 19\n22 32\n36 28\n42 16\n13 49\n11 17\n31 39\n43 37\n50 15\n29 20\n35 46\n47 23\n3 1\n44 7\n9 27\n6 48\n40 24\n26 14\n45 4\n12 25\n41 38",
"output": "2 1\n1 2\n2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n2 1\n2 1\n2 1"
},
{
"input": "20\n34 12\n9 6\n5 3\n13 26\n18 15\n16 22\n7 14\n17 37\n38 40\n4 2\n11 23\n21 8\n10 36\n30 33\n28 19\n29 31\n39 20\n35 24\n25 32\n1 27",
"output": "1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2"
},
{
"input": "17\n3 14\n34 22\n24 9\n16 17\n6 30\n33 12\n5 10\n21 8\n32 2\n26 23\n31 27\n19 15\n29 4\n7 18\n25 13\n20 28\n1 11",
"output": "1 2\n1 2\n1 2\n2 1\n1 2\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2"
},
{
"input": "24\n30 4\n41 1\n2 11\n22 42\n29 43\n7 14\n16 6\n40 5\n27 34\n46 33\n17 10\n21 39\n28 31\n19 32\n23 20\n25 48\n12 9\n47 37\n38 3\n44 8\n36 18\n13 26\n24 15\n45 35",
"output": "1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n2 1\n1 2"
},
{
"input": "15\n21 14\n25 5\n7 28\n2 6\n8 27\n29 18\n9 15\n4 26\n12 1\n19 16\n17 20\n24 10\n11 23\n13 22\n30 3",
"output": "1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n1 2"
}
] | 327 | 40,755,200 | -1 | 4,931 |
|
50 | Choosing Symbol Pairs | [
"strings"
] | B. Choosing Symbol Pairs | 2 | 256 | There is a given string *S* consisting of *N* symbols. Your task is to find the number of ordered pairs of integers *i* and *j* such that
1. 1<=β€<=*i*,<=*j*<=β€<=*N*
2. *S*[*i*]<==<=*S*[*j*], that is the *i*-th symbol of string *S* is equal to the *j*-th. | The single input line contains *S*, consisting of lowercase Latin letters and digits. It is guaranteed that string *S* in not empty and its length does not exceed 105. | Print a single number which represents the number of pairs *i* and *j* with the needed property. Pairs (*x*,<=*y*) and (*y*,<=*x*) should be considered different, i.e. the ordered pairs count. | [
"great10\n",
"aaaaaaaaaa\n"
] | [
"7\n",
"100\n"
] | none | [
{
"input": "great10",
"output": "7"
},
{
"input": "aaaaaaaaaa",
"output": "100"
},
{
"input": "great10",
"output": "7"
},
{
"input": "aaaaaaaaaa",
"output": "100"
},
{
"input": "aabb",
"output": "8"
},
{
"input": "w",
"output": "1"
},
{
"input": "129a",
"output": "4"
},
{
"input": "233444",
"output": "14"
},
{
"input": "abacaba",
"output": "21"
},
{
"input": "abcdefghijklmnopqrstuvwxyz0987654321abcdefghijklmnopqrstuvwxyz0987654321abcdefghijklmnopqrstuvwxyz0987654321",
"output": "324"
},
{
"input": "zazaeeeeeeeq34443333444tttttt",
"output": "155"
},
{
"input": "00000000000000000000000",
"output": "529"
},
{
"input": "999000888775646453342311",
"output": "62"
}
] | 2,000 | 2,252,800 | 0 | 4,935 |
818 | Diplomas and Certificates | [
"implementation",
"math"
] | null | null | There are *n* students who have taken part in an olympiad. Now it's time to award the students.
Some of them will receive diplomas, some wiil get certificates, and others won't receive anything. Students with diplomas and certificates are called winners. But there are some rules of counting the number of diplomas and certificates. The number of certificates must be exactly *k* times greater than the number of diplomas. The number of winners must not be greater than half of the number of all students (i.e. not be greater than half of *n*). It's possible that there are no winners.
You have to identify the maximum possible number of winners, according to these rules. Also for this case you have to calculate the number of students with diplomas, the number of students with certificates and the number of students who are not winners. | The first (and the only) line of input contains two integers *n* and *k* (1<=β€<=*n*,<=*k*<=β€<=1012), where *n* is the number of students and *k* is the ratio between the number of certificates and the number of diplomas. | Output three numbers: the number of students with diplomas, the number of students with certificates and the number of students who are not winners in case when the number of winners is maximum possible.
It's possible that there are no winners. | [
"18 2\n",
"9 10\n",
"1000000000000 5\n",
"1000000000000 499999999999\n"
] | [
"3 6 9\n",
"0 0 9\n",
"83333333333 416666666665 500000000002\n",
"1 499999999999 500000000000\n"
] | none | [
{
"input": "18 2",
"output": "3 6 9"
},
{
"input": "9 10",
"output": "0 0 9"
},
{
"input": "1000000000000 5",
"output": "83333333333 416666666665 500000000002"
},
{
"input": "1000000000000 499999999999",
"output": "1 499999999999 500000000000"
},
{
"input": "1 1",
"output": "0 0 1"
},
{
"input": "5 3",
"output": "0 0 5"
},
{
"input": "42 6",
"output": "3 18 21"
},
{
"input": "1000000000000 1000",
"output": "499500499 499500499000 500000000501"
},
{
"input": "999999999999 999999",
"output": "499999 499998500001 500000999999"
},
{
"input": "732577309725 132613",
"output": "2762066 366285858458 366288689201"
},
{
"input": "152326362626 15",
"output": "4760198832 71402982480 76163181314"
},
{
"input": "2 1",
"output": "0 0 2"
},
{
"input": "1000000000000 500000000000",
"output": "0 0 1000000000000"
},
{
"input": "100000000000 50000000011",
"output": "0 0 100000000000"
},
{
"input": "1000000000000 32416187567",
"output": "15 486242813505 513757186480"
},
{
"input": "1000000000000 7777777777",
"output": "64 497777777728 502222222208"
},
{
"input": "1000000000000 77777777777",
"output": "6 466666666662 533333333332"
},
{
"input": "100000000000 578485652",
"output": "86 49749766072 50250233842"
},
{
"input": "999999999999 10000000000",
"output": "49 490000000000 509999999950"
},
{
"input": "7 2",
"output": "1 2 4"
},
{
"input": "420506530901 752346673804",
"output": "0 0 420506530901"
},
{
"input": "960375521135 321688347872",
"output": "1 321688347872 638687173262"
},
{
"input": "1000000000000 1000000000000",
"output": "0 0 1000000000000"
},
{
"input": "99999999999 15253636363",
"output": "3 45760909089 54239090907"
},
{
"input": "19 2",
"output": "3 6 10"
},
{
"input": "999999999999 1000000000000",
"output": "0 0 999999999999"
},
{
"input": "1000000000000 5915587276",
"output": "84 496909331184 503090668732"
},
{
"input": "1000000000000 1000000006",
"output": "499 499000002994 500999996507"
},
{
"input": "549755813888 134217728",
"output": "2047 274743689216 275012122625"
},
{
"input": "99999999999 3333333",
"output": "14999 49996661667 50003323333"
},
{
"input": "9 1",
"output": "2 2 5"
},
{
"input": "1000000000000 250000000001",
"output": "1 250000000001 749999999998"
},
{
"input": "5 1",
"output": "1 1 3"
},
{
"input": "3107038133 596040207",
"output": "2 1192080414 1914957717"
},
{
"input": "1000000000000 73786977",
"output": "6776 499980556152 500019437072"
},
{
"input": "1000000000000 73786976",
"output": "6776 499980549376 500019443848"
},
{
"input": "1000000000000 25000000000",
"output": "19 475000000000 524999999981"
},
{
"input": "216929598879 768233755932",
"output": "0 0 216929598879"
},
{
"input": "1000000000000 250000000000",
"output": "1 250000000000 749999999999"
},
{
"input": "1000000000000 100000000001",
"output": "4 400000000004 599999999992"
},
{
"input": "100000000000 100000000001",
"output": "0 0 100000000000"
},
{
"input": "900000000000 100281800001",
"output": "4 401127200004 498872799992"
},
{
"input": "906028900004 109123020071",
"output": "4 436492080284 469536819716"
},
{
"input": "1000000000000 1",
"output": "250000000000 250000000000 500000000000"
}
] | 155 | 0 | 3 | 4,957 |
|
832 | Petya and Exam | [
"implementation",
"strings"
] | null | null | It's hard times now. Today Petya needs to score 100 points on Informatics exam. The tasks seem easy to Petya, but he thinks he lacks time to finish them all, so he asks you to help with one..
There is a glob pattern in the statements (a string consisting of lowercase English letters, characters "?" and "*"). It is known that character "*" occurs no more than once in the pattern.
Also, *n* query strings are given, it is required to determine for each of them if the pattern matches it or not.
Everything seemed easy to Petya, but then he discovered that the special pattern characters differ from their usual meaning.
A pattern matches a string if it is possible to replace each character "?" with one good lowercase English letter, and the character "*" (if there is one) with any, including empty, string of bad lowercase English letters, so that the resulting string is the same as the given string.
The good letters are given to Petya. All the others are bad. | The first line contains a string with length from 1 to 26 consisting of distinct lowercase English letters. These letters are good letters, all the others are bad.
The second line contains the patternΒ β a string *s* of lowercase English letters, characters "?" and "*" (1<=β€<=|*s*|<=β€<=105). It is guaranteed that character "*" occurs in *s* no more than once.
The third line contains integer *n* (1<=β€<=*n*<=β€<=105)Β β the number of query strings.
*n* lines follow, each of them contains single non-empty string consisting of lowercase English lettersΒ β a query string.
It is guaranteed that the total length of all query strings is not greater than 105. | Print *n* lines: in the *i*-th of them print "YES" if the pattern matches the *i*-th query string, and "NO" otherwise.
You can choose the case (lower or upper) for each letter arbitrary. | [
"ab\na?a\n2\naaa\naab\n",
"abc\na?a?a*\n4\nabacaba\nabaca\napapa\naaaaax\n"
] | [
"YES\nNO\n",
"NO\nYES\nNO\nYES\n"
] | In the first example we can replace "?" with good letters "a" and "b", so we can see that the answer for the first query is "YES", and the answer for the second query is "NO", because we can't match the third letter.
Explanation of the second example.
- The first query: "NO", because character "*" can be replaced with a string of bad letters only, but the only way to match the query string is to replace it with the string "ba", in which both letters are good. - The second query: "YES", because characters "?" can be replaced with corresponding good letters, and character "*" can be replaced with empty string, and the strings will coincide. - The third query: "NO", because characters "?" can't be replaced with bad letters. - The fourth query: "YES", because characters "?" can be replaced with good letters "a", and character "*" can be replaced with a string of bad letters "x". | [
{
"input": "ab\na?a\n2\naaa\naab",
"output": "YES\nNO"
},
{
"input": "abc\na?a?a*\n4\nabacaba\nabaca\napapa\naaaaax",
"output": "NO\nYES\nNO\nYES"
},
{
"input": "s\nc*?cb\n26\nbbaa\nb\ncc\ncbaab\nacacc\nca\na\nc\ncb\nabb\nba\nb\nba\ncac\nccccb\nccb\nbbbc\nabbcb\na\nbc\nc\na\nabb\nca\ncacb\nac",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "o\n*\n28\nbac\nbcc\ncbcb\ncaabc\ncb\nacab\ncbccb\ncbccc\nc\nbbaa\ncaaaa\nbbc\nba\nc\ncacbc\ncbab\naa\nac\nacc\na\nac\nbac\naaac\nba\nabbbb\nbbcc\nbaacb\naabaa",
"output": "YES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES"
},
{
"input": "u\n*b??c\n23\na\nbcbcc\nacb\na\nbacaa\nbb\nb\nbcba\ncbbcc\nb\nabbb\nbcacb\nabcb\ncbca\nb\ncba\ncabcb\nbc\ncc\naaacc\nccac\ncc\nccbcb",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "g\nc?*\n58\nb\ncaac\nbbc\nabb\ncaccc\ncb\naba\nbcaa\ncca\ncbbcb\ncac\nbbaca\nbcba\nbba\nabbab\nccc\nc\nbcb\naac\nbcbbc\nbca\nc\ncbb\nccabb\naaccc\nccaa\nc\nc\nbcca\naa\nccb\ncb\ncbcb\ncc\nab\ncccc\nbbbab\nbab\na\nc\ncbba\nbbacb\naa\nb\nbaab\nacabb\nbcbab\ncbbcb\nbc\ncccba\naa\ncccca\ncacc\naacbb\na\nc\nab\nccca",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "g\nbc*a\n40\nbabac\nccbb\ncacbc\nc\na\naba\nbc\na\nba\nbbcca\nccbac\na\nc\nbabc\ncccbc\nab\nabca\nccb\nacbbb\nb\nbbac\naa\nb\nca\nbc\naaba\nbaaaa\nbcc\nab\na\naba\nb\nc\nba\nbc\nca\nbb\nc\nc\nca",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "g\n*cc?\n93\nac\ncaab\nacaca\ncccc\nbcc\nbab\nbc\nc\nc\nbbaa\nb\ncc\ncb\naa\nabcbb\nbccc\nc\ncbcbc\nac\nca\nbcba\nbb\nbab\nba\nb\nbbba\nbabbc\nbacab\nbc\na\ncbccc\nbbaac\ncbab\ncab\ncc\ncbbcb\nc\nc\ncbaa\nca\nbacab\nc\nbcac\nbbbc\nc\nac\nccab\nccccb\ncccab\nc\nacb\nac\nbccba\nca\nbbbbc\naaca\naa\na\nbabac\nbb\nc\ncac\naca\naacb\naacbb\na\nacaab\ncbb\nbcc\ncb\nbcbaa\ncca\nb\nbaac\nbcca\nc\ncbb\nac\nc\naccc\naac\nbcbc\nabc\nbacab\nb\na\na\nbbacc\ncb\na\nccac\nb\nbbc",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "c\n*\n83\nbbc\ncacb\nbcbc\naca\nba\nc\nccac\nab\nab\nbacba\nbb\nc\nbcc\nc\ncbc\ncbbb\nac\nb\nacbcb\nbccc\ncccb\nb\na\nca\nc\nccaa\naa\ncacb\nccc\na\nccc\nababb\nbab\ncaa\nbaa\na\ncc\ncbbbc\naaaa\nabbab\naabac\nbcbab\nbcb\nacaa\nbcb\na\ncca\na\nbacc\nacacb\nc\nc\ncba\nbcaca\na\ncaac\na\nb\na\nccc\naabca\nbbab\nb\nac\nbabc\nc\nac\nba\nbbcb\nc\naaab\ncab\nacb\nbba\nbbcba\nc\na\naccbb\naaccc\nac\nbaa\nbaabb\nabca",
"output": "NO\nNO\nNO\nNO\nYES\nNO\nNO\nYES\nYES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nYES\nNO\nNO\nYES\nNO\nYES\nYES\nNO\nYES\nYES\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nYES\nYES\nYES\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nYES\nNO\nNO\nYES\nNO\nNO\nYES\nNO\nNO\nNO\nYES\nYES\nNO"
},
{
"input": "s\n*cb\n70\nab\nccb\naaab\nb\nab\ncba\na\nbbaca\nac\nccacb\nbaabb\naaab\nccca\ncb\nba\nbccac\nc\ncc\ncbbbb\ncab\nabbb\ncbb\naabc\ncac\nacb\na\nc\nc\ncbbbb\nbaaca\ncbcc\nbc\naa\nabcb\nacbbc\nbaaa\naa\ncc\ncc\nb\nb\nbcba\ncbacc\nbcb\ncaabc\nacaac\ncb\ncba\ncbaaa\nbcaaa\naccbb\naccac\nca\nacaa\ncc\nc\nb\nbac\nb\nbab\nb\ncca\naacc\nacb\nccc\nbc\nb\naab\naaca\naac",
"output": "NO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "k\n*b\n70\ncbc\nb\ncca\nacbc\nca\nab\nc\nbbb\nbaa\nbbb\nac\nbaacc\nbaabc\naac\na\nba\nb\nc\nc\nba\ncacbb\nabb\nbc\nabcb\nca\na\nbbbbb\ncca\nccacc\ncbaca\nba\ncbcca\ncb\nc\nbbbba\ncca\nabaac\na\nac\nc\nccbc\nbcac\nbcb\na\nc\nabbca\nbaacb\ncc\nacba\nc\nbcc\ncbba\nccba\na\na\ncbb\ncba\nb\naaaac\ncb\nbaacb\nab\nc\ncbbcb\nbab\nac\nca\nc\nac\nb",
"output": "NO\nYES\nNO\nNO\nNO\nYES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nYES\nYES\nNO\nYES\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nYES\nNO\nYES\nYES\nYES\nNO\nYES\nYES\nNO\nNO\nNO\nNO\nYES"
},
{
"input": "l\na*\n40\nacbb\naba\nb\naab\nbb\nbbab\ncaba\naab\naaab\nacac\nacbaa\nbca\nac\nbb\na\nba\naaa\nbc\nbba\ncca\naacab\na\nc\nca\naacaa\nbaac\nbb\nc\nba\nc\nbab\nb\na\ncabaa\nccacc\ncbbab\nbaaca\ncabb\naaccc\nbcbac",
"output": "YES\nYES\nNO\nYES\nNO\nNO\nNO\nYES\nYES\nYES\nYES\nNO\nYES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nYES\nYES\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\nNO"
},
{
"input": "u\ncba*\n26\ncaa\ncccb\nbc\nbacb\nca\nccaaa\nb\naaca\nba\ncacc\ncccac\nabba\nbabc\na\nac\nca\nbbba\na\naa\naaabb\nb\nc\nbba\nbbba\nacaa\nba",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "cba\n?*cbc\n88\ncccca\ncbc\nb\nbcb\naaa\ncaac\nbacb\nacbb\na\nab\ncbcca\nbccc\nabcc\naca\nba\nbbac\nacc\ncba\nbcba\nbc\naa\nab\ncaba\ncccab\ncba\ncbcc\nba\ncacbb\nabcc\na\nc\nbac\nccaba\nb\nac\nbbb\nac\nccaca\na\nba\nacbcc\nbbc\nacbc\nbbabc\nccbb\nb\nacaa\na\nba\nacb\na\nab\naa\nbbbb\naabb\nbcbc\nb\nca\nb\nccab\nab\nc\nb\naabab\nc\ncbbbc\nacbbb\nbacaa\nbcccc\ncbac\nc\nac\nb\nca\ncbb\nccbc\nc\nc\nbcb\nc\nbaaba\nc\nbac\nb\nba\ncb\ncc\nbaaca",
"output": "NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO"
},
{
"input": "a\naa\n1\naaa",
"output": "NO"
},
{
"input": "a\naaa\n1\naaaa",
"output": "NO"
},
{
"input": "a\naa*aa\n1\naaa",
"output": "NO"
},
{
"input": "a\nbb*bb\n1\nbbbbbbbbbbbbbbbb",
"output": "YES"
},
{
"input": "a\na*\n1\nabbbbbbb",
"output": "YES"
},
{
"input": "a\na?a\n1\naaab",
"output": "NO"
},
{
"input": "xy\ncab*aba\n1\ncaba",
"output": "NO"
},
{
"input": "a\n*\n4\nb\na\nab\nba",
"output": "YES\nNO\nNO\nNO"
},
{
"input": "abc\na?a?*a\n3\nababxa\nababca\nababa",
"output": "YES\nNO\nYES"
},
{
"input": "abc\n??a*df?c\n6\nabadfcc\naaaadfac\nbbagthfac\nacadddfac\ndaagdffc\naaaadfcc",
"output": "YES\nNO\nNO\nYES\nNO\nNO"
},
{
"input": "abc\nabc*a\n1\nabckka",
"output": "YES"
},
{
"input": "b\n*a\n1\naba",
"output": "NO"
},
{
"input": "a\nabc*g\n1\nabcdefg",
"output": "YES"
},
{
"input": "a\nab\n1\na",
"output": "NO"
},
{
"input": "abcdefghijklmnopqrstuvwxyz\n*a\n1\na",
"output": "YES"
},
{
"input": "as\naba*aba\n1\naba",
"output": "NO"
},
{
"input": "ab\naweerrtab\n4\naw\naweerrtabwqeqrw\naweerrtabxcvxcbcxbdsfdsfewrewrqweq\naweerrtabaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"output": "NO\nNO\nNO\nNO"
},
{
"input": "a\na\n1\nab",
"output": "NO"
},
{
"input": "a\na*b\n1\nabb",
"output": "YES"
},
{
"input": "a\nb*a\n1\nbbadd",
"output": "NO"
},
{
"input": "a\naaaa\n1\naaa",
"output": "NO"
},
{
"input": "z\n*abcd\n1\nggggggg",
"output": "NO"
},
{
"input": "abc\n*??\n1\nqqqqqqqqab",
"output": "YES"
},
{
"input": "b\naa\n1\na",
"output": "NO"
},
{
"input": "ab\na*pa\n1\nappppa",
"output": "YES"
},
{
"input": "a\nbbb\n1\nbbbbb",
"output": "NO"
},
{
"input": "ab\nabcd?\n1\nabcd",
"output": "NO"
},
{
"input": "c\na\n1\nab",
"output": "NO"
}
] | 374 | 8,806,400 | 0 | 4,966 |
|
209 | Multicolored Marbles | [
"dp",
"math"
] | null | null | Polycarpus plays with red and blue marbles. He put *n* marbles from the left to the right in a row. As it turned out, the marbles form a zebroid.
A non-empty sequence of red and blue marbles is a zebroid, if the colors of the marbles in this sequence alternate. For example, sequences (red; blue; red) and (blue) are zebroids and sequence (red; red) is not a zebroid.
Now Polycarpus wonders, how many ways there are to pick a zebroid subsequence from this sequence. Help him solve the problem, find the number of ways modulo 1000000007 (109<=+<=7). | The first line contains a single integer *n* (1<=β€<=*n*<=β€<=106) β the number of marbles in Polycarpus's sequence. | Print a single number β the answer to the problem modulo 1000000007 (109<=+<=7). | [
"3\n",
"4\n"
] | [
"6\n",
"11\n"
] | Let's consider the first test sample. Let's assume that Polycarpus initially had sequence (red; blue; red), so there are six ways to pick a zebroid:
- pick the first marble; - pick the second marble; - pick the third marble; - pick the first and second marbles; - pick the second and third marbles; - pick the first, second and third marbles.
It can be proven that if Polycarpus picks (blue; red; blue) as the initial sequence, the number of ways won't change. | [
{
"input": "3",
"output": "6"
},
{
"input": "4",
"output": "11"
},
{
"input": "1",
"output": "1"
},
{
"input": "2",
"output": "3"
},
{
"input": "5",
"output": "19"
},
{
"input": "6",
"output": "32"
},
{
"input": "7",
"output": "53"
},
{
"input": "8",
"output": "87"
},
{
"input": "9",
"output": "142"
},
{
"input": "10",
"output": "231"
},
{
"input": "11",
"output": "375"
},
{
"input": "12",
"output": "608"
},
{
"input": "13",
"output": "985"
},
{
"input": "14",
"output": "1595"
},
{
"input": "15",
"output": "2582"
},
{
"input": "16",
"output": "4179"
},
{
"input": "17",
"output": "6763"
},
{
"input": "18",
"output": "10944"
},
{
"input": "19",
"output": "17709"
},
{
"input": "20",
"output": "28655"
},
{
"input": "21",
"output": "46366"
},
{
"input": "22",
"output": "75023"
},
{
"input": "30",
"output": "3524576"
},
{
"input": "40",
"output": "433494435"
},
{
"input": "35",
"output": "39088167"
},
{
"input": "747",
"output": "864986803"
},
{
"input": "811",
"output": "121575679"
},
{
"input": "523",
"output": "810594171"
},
{
"input": "939",
"output": "834252191"
},
{
"input": "7218",
"output": "124017976"
},
{
"input": "6578",
"output": "105202924"
},
{
"input": "4994",
"output": "909729063"
},
{
"input": "3410",
"output": "995527079"
},
{
"input": "9122",
"output": "424682518"
},
{
"input": "11500",
"output": "123418864"
},
{
"input": "37212",
"output": "991850249"
},
{
"input": "95628",
"output": "265542306"
},
{
"input": "21341",
"output": "913329411"
},
{
"input": "63405",
"output": "206564501"
},
{
"input": "670293",
"output": "922731630"
},
{
"input": "12357",
"output": "808648710"
},
{
"input": "838069",
"output": "536545985"
},
{
"input": "696485",
"output": "467961960"
},
{
"input": "1000000",
"output": "986892583"
},
{
"input": "999999",
"output": "452491920"
},
{
"input": "999998",
"output": "534400661"
},
{
"input": "999997",
"output": "918091264"
},
{
"input": "999996",
"output": "616309402"
},
{
"input": "999000",
"output": "47031574"
},
{
"input": "100",
"output": "252403354"
}
] | 2,000 | 13,516,800 | 0 | 4,971 |
|
670 | Cinema | [
"implementation",
"sortings"
] | null | null | Moscow is hosting a major international conference, which is attended by *n* scientists from different countries. Each of the scientists knows exactly one language. For convenience, we enumerate all languages of the world with integers from 1 to 109.
In the evening after the conference, all *n* scientists decided to go to the cinema. There are *m* movies in the cinema they came to. Each of the movies is characterized by two distinct numbersΒ β the index of audio language and the index of subtitles language. The scientist, who came to the movie, will be very pleased if he knows the audio language of the movie, will be almost satisfied if he knows the language of subtitles and will be not satisfied if he does not know neither one nor the other (note that the audio language and the subtitles language for each movie are always different).
Scientists decided to go together to the same movie. You have to help them choose the movie, such that the number of very pleased scientists is maximum possible. If there are several such movies, select among them one that will maximize the number of almost satisfied scientists. | The first line of the input contains a positive integer *n* (1<=β€<=*n*<=β€<=200<=000)Β β the number of scientists.
The second line contains *n* positive integers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=109), where *a**i* is the index of a language, which the *i*-th scientist knows.
The third line contains a positive integer *m* (1<=β€<=*m*<=β€<=200<=000)Β β the number of movies in the cinema.
The fourth line contains *m* positive integers *b*1,<=*b*2,<=...,<=*b**m* (1<=β€<=*b**j*<=β€<=109), where *b**j* is the index of the audio language of the *j*-th movie.
The fifth line contains *m* positive integers *c*1,<=*c*2,<=...,<=*c**m* (1<=β€<=*c**j*<=β€<=109), where *c**j* is the index of subtitles language of the *j*-th movie.
It is guaranteed that audio languages and subtitles language are different for each movie, that is *b**j*<=β <=*c**j*. | Print the single integerΒ β the index of a movie to which scientists should go. After viewing this movie the number of very pleased scientists should be maximum possible. If in the cinema there are several such movies, you need to choose among them one, after viewing which there will be the maximum possible number of almost satisfied scientists.
If there are several possible answers print any of them. | [
"3\n2 3 2\n2\n3 2\n2 3\n",
"6\n6 3 1 1 3 7\n5\n1 2 3 4 5\n2 3 4 5 1\n"
] | [
"2\n",
"1\n"
] | In the first sample, scientists must go to the movie with the index 2, as in such case the 1-th and the 3-rd scientists will be very pleased and the 2-nd scientist will be almost satisfied.
In the second test case scientists can go either to the movie with the index 1 or the index 3. After viewing any of these movies exactly two scientists will be very pleased and all the others will be not satisfied. | [
{
"input": "3\n2 3 2\n2\n3 2\n2 3",
"output": "2"
},
{
"input": "6\n6 3 1 1 3 7\n5\n1 2 3 4 5\n2 3 4 5 1",
"output": "1"
},
{
"input": "1\n10\n1\n10\n3",
"output": "1"
},
{
"input": "2\n1 6\n1\n6\n1",
"output": "1"
},
{
"input": "1\n5\n2\n2 2\n5 5",
"output": "1"
},
{
"input": "2\n4 4\n2\n4 7\n7 5",
"output": "1"
},
{
"input": "10\n3 1 8 8 1 1 5 1 3 5\n2\n1 4\n3 1",
"output": "1"
},
{
"input": "10\n7 6 1 2 7 3 9 7 7 9\n10\n2 9 6 5 9 3 10 3 1 6\n4 6 7 9 7 4 1 9 2 5",
"output": "5"
},
{
"input": "20\n2 2 1 6 6 5 10 2 5 5 4 8 6 8 8 10 2 1 5 6\n20\n1 9 1 1 5 1 9 10 1 10 9 9 8 7 5 1 1 10 2 7\n3 5 9 10 10 8 2 9 6 7 8 8 6 5 3 4 6 3 7 4",
"output": "5"
},
{
"input": "2\n10 8\n10\n8 3 10 8 8 8 3 8 8 8\n10 10 8 3 10 3 8 3 10 10",
"output": "1"
},
{
"input": "5\n9 9 2 4 2\n5\n4 1 1 1 2\n2 4 4 9 7",
"output": "5"
},
{
"input": "1\n320994883\n1\n332200603\n942930950",
"output": "1"
},
{
"input": "3\n1000000000 1 1000000000\n2\n1000000000 1\n1 1000000000",
"output": "1"
},
{
"input": "5\n1 2 3 3 4\n2\n1 2\n3 4",
"output": "1"
},
{
"input": "3\n1 3 2\n2\n1 3\n2 4",
"output": "1"
},
{
"input": "5\n2 2 3 3 4\n3\n5 2 2\n6 3 4",
"output": "2"
},
{
"input": "2\n1 2\n2\n3 3\n4 1",
"output": "2"
},
{
"input": "12\n3 2 1 1 4 4 5 1 6 6 7 7\n4\n3 2 4 7\n2 1 5 6",
"output": "4"
},
{
"input": "14\n1 1 2 2 2 3 3 3 4 5 5 5 6 6\n3\n1 3 5\n2 6 4",
"output": "2"
}
] | 623 | 31,539,200 | 3 | 4,975 |
|
0 | none | [
"none"
] | null | null | Innokenty is a president of a new football league in Byteland. The first task he should do is to assign short names to all clubs to be shown on TV next to the score. Of course, the short names should be distinct, and Innokenty wants that all short names consist of three letters.
Each club's full name consist of two words: the team's name and the hometown's name, for example, "DINAMO BYTECITY". Innokenty doesn't want to assign strange short names, so he wants to choose such short names for each club that:
1. the short name is the same as three first letters of the team's name, for example, for the mentioned club it is "DIN", 1. or, the first two letters of the short name should be the same as the first two letters of the team's name, while the third letter is the same as the first letter in the hometown's name. For the mentioned club it is "DIB".
Apart from this, there is a rule that if for some club *x* the second option of short name is chosen, then there should be no club, for which the first option is chosen which is the same as the first option for the club *x*. For example, if the above mentioned club has short name "DIB", then no club for which the first option is chosen can have short name equal to "DIN". However, it is possible that some club have short name "DIN", where "DI" are the first two letters of the team's name, and "N" is the first letter of hometown's name. Of course, no two teams can have the same short name.
Help Innokenty to choose a short name for each of the teams. If this is impossible, report that. If there are multiple answer, any of them will suit Innokenty. If for some team the two options of short name are equal, then Innokenty will formally think that only one of these options is chosen. | The first line contains a single integer *n* (1<=β€<=*n*<=β€<=1000)Β β the number of clubs in the league.
Each of the next *n* lines contains two wordsΒ β the team's name and the hometown's name for some club. Both team's name and hometown's name consist of uppercase English letters and have length at least 3 and at most 20. | It it is not possible to choose short names and satisfy all constraints, print a single line "NO".
Otherwise, in the first line print "YES". Then print *n* lines, in each line print the chosen short name for the corresponding club. Print the clubs in the same order as they appeared in input.
If there are multiple answers, print any of them. | [
"2\nDINAMO BYTECITY\nFOOTBALL MOSCOW\n",
"2\nDINAMO BYTECITY\nDINAMO BITECITY\n",
"3\nPLAYFOOTBALL MOSCOW\nPLAYVOLLEYBALL SPB\nGOGO TECHNOCUP\n",
"3\nABC DEF\nABC EFG\nABD OOO\n"
] | [
"YES\nDIN\nFOO\n",
"NO\n",
"YES\nPLM\nPLS\nGOG\n",
"YES\nABD\nABE\nABO\n"
] | In the first sample Innokenty can choose first option for both clubs.
In the second example it is not possible to choose short names, because it is not possible that one club has first option, and the other has second option if the first options are equal for both clubs.
In the third example Innokenty can choose the second options for the first two clubs, and the first option for the third club.
In the fourth example note that it is possible that the chosen short name for some club *x* is the same as the first option of another club *y* if the first options of *x* and *y* are different. | [
{
"input": "2\nDINAMO BYTECITY\nFOOTBALL MOSCOW",
"output": "YES\nDIN\nFOO"
},
{
"input": "2\nDINAMO BYTECITY\nDINAMO BITECITY",
"output": "NO"
},
{
"input": "3\nPLAYFOOTBALL MOSCOW\nPLAYVOLLEYBALL SPB\nGOGO TECHNOCUP",
"output": "YES\nPLM\nPLS\nGOG"
},
{
"input": "3\nABC DEF\nABC EFG\nABD OOO",
"output": "YES\nABD\nABE\nABO"
},
{
"input": "3\nABC DEF\nABC EFG\nABC EEEEE",
"output": "NO"
},
{
"input": "3\nABC DEF\nABC EFG\nABD CABA",
"output": "YES\nABD\nABE\nABC"
},
{
"input": "3\nABC DEF\nABC EFG\nABD EABA",
"output": "NO"
},
{
"input": "1\nAAA AAA",
"output": "YES\nAAA"
},
{
"input": "1\nAAAAAAAAAAAAAAAAAAAA ZZZZZZZZZZZZZZZZZZZZ",
"output": "YES\nAAA"
},
{
"input": "5\nADAC BABC\nABB DCB\nABB BCDC\nDBAC BAC\nDBBC DBC",
"output": "YES\nADA\nABD\nABB\nDBA\nDBB"
},
{
"input": "5\nIAH HJIE\nIAH FJK\nIAH BIAA\nIAH AFG\nIAH DEFF",
"output": "YES\nIAH\nIAF\nIAB\nIAA\nIAD"
},
{
"input": "10\nIJGDI KHB\nHBI CKKCG\nFHE GCAA\nEDCGH HHICE\nGFH AIHD\nHED KIK\nDCK BCFIJ\nFFIHE FDB\nJGB AKKI\nIJD CAG",
"output": "YES\nIJG\nHBI\nFHE\nEDC\nGFH\nHED\nDCK\nFFI\nJGB\nIJD"
},
{
"input": "10\nEDBG IGGAC\nEDBG GIKAG\nEDBG IKGEI\nEDBG AJEG\nEDBG HAD\nEDBG ACKK\nEDBG FEDE\nEDBG DAB\nEDBG CCJBD\nEDBG KKGFB",
"output": "NO"
},
{
"input": "10\nADE GBH\nJJDGJ AAF\nJJDGJ BBKG\nADE FKH\nADE CIA\nAIE JCBJ\nAIE BBJB\nEBAK JDB\nJJDGJ IDBG\nCEJE FIG",
"output": "YES\nADG\nJJA\nJJB\nADF\nADC\nAIJ\nAIB\nEBA\nJJI\nCEJ"
},
{
"input": "4\nABA DEF\nABB DEF\nABC DEF\nABE DEF",
"output": "YES\nABA\nABB\nABC\nABE"
},
{
"input": "2\nABC CCC\nABE CCC",
"output": "YES\nABC\nABE"
},
{
"input": "2\nABS SSS\nABD SSD",
"output": "YES\nABS\nABD"
}
] | 62 | 5,120,000 | 0 | 4,978 |
|
444 | DZY Loves Colors | [
"data structures"
] | null | null | DZY loves colors, and he enjoys painting.
On a colorful day, DZY gets a colorful ribbon, which consists of *n* units (they are numbered from 1 to *n* from left to right). The color of the *i*-th unit of the ribbon is *i* at first. It is colorful enough, but we still consider that the colorfulness of each unit is 0 at first.
DZY loves painting, we know. He takes up a paintbrush with color *x* and uses it to draw a line on the ribbon. In such a case some contiguous units are painted. Imagine that the color of unit *i* currently is *y*. When it is painted by this paintbrush, the color of the unit becomes *x*, and the colorfulness of the unit increases by |*x*<=-<=*y*|.
DZY wants to perform *m* operations, each operation can be one of the following:
1. Paint all the units with numbers between *l* and *r* (both inclusive) with color *x*. 1. Ask the sum of colorfulness of the units between *l* and *r* (both inclusive).
Can you help DZY? | The first line contains two space-separated integers *n*,<=*m*Β (1<=β€<=*n*,<=*m*<=β€<=105).
Each of the next *m* lines begins with a integer *type*Β (1<=β€<=*type*<=β€<=2), which represents the type of this operation.
If *type*<==<=1, there will be 3 more integers *l*,<=*r*,<=*x*Β (1<=β€<=*l*<=β€<=*r*<=β€<=*n*;Β 1<=β€<=*x*<=β€<=108) in this line, describing an operation 1.
If *type*<==<=2, there will be 2 more integers *l*,<=*r*Β (1<=β€<=*l*<=β€<=*r*<=β€<=*n*) in this line, describing an operation 2. | For each operation 2, print a line containing the answer β sum of colorfulness. | [
"3 3\n1 1 2 4\n1 2 3 5\n2 1 3\n",
"3 4\n1 1 3 4\n2 1 1\n2 2 2\n2 3 3\n",
"10 6\n1 1 5 3\n1 2 7 9\n1 10 10 11\n1 3 8 12\n1 1 10 3\n2 1 10\n"
] | [
"8\n",
"3\n2\n1\n",
"129\n"
] | In the first sample, the color of each unit is initially [1,β2,β3], and the colorfulness is [0,β0,β0].
After the first operation, colors become [4,β4,β3], colorfulness become [3,β2,β0].
After the second operation, colors become [4,β5,β5], colorfulness become [3,β3,β2].
So the answer to the only operation of type 2 is 8. | [
{
"input": "3 3\n1 1 2 4\n1 2 3 5\n2 1 3",
"output": "8"
},
{
"input": "3 4\n1 1 3 4\n2 1 1\n2 2 2\n2 3 3",
"output": "3\n2\n1"
},
{
"input": "10 6\n1 1 5 3\n1 2 7 9\n1 10 10 11\n1 3 8 12\n1 1 10 3\n2 1 10",
"output": "129"
},
{
"input": "3 3\n1 2 2 31844623\n1 1 2 37662529\n2 2 3",
"output": "37662527"
},
{
"input": "3 3\n2 2 3\n1 1 3 72971211\n2 2 3",
"output": "0\n145942417"
},
{
"input": "10 10\n1 5 9 60144710\n2 3 3\n2 3 4\n2 6 10\n1 8 9 11764737\n1 1 9 38454635\n1 3 10 58013969\n1 2 3 49601991\n1 1 3 73003418\n2 4 6",
"output": "0\n0\n240578810\n260802192"
}
] | 2,000 | 4,403,200 | 0 | 4,979 |
|
662 | International Olympiad | [
"constructive algorithms",
"greedy",
"implementation",
"math"
] | null | null | International Abbreviation Olympiad takes place annually starting from 1989. Each year the competition receives an abbreviation of form IAO'y, where *y* stands for some number of consequent last digits of the current year. Organizers always pick an abbreviation with non-empty string *y* that has never been used before. Among all such valid abbreviations they choose the shortest one and announce it to be the abbreviation of this year's competition.
For example, the first three Olympiads (years 1989, 1990 and 1991, respectively) received the abbreviations IAO'9, IAO'0 and IAO'1, while the competition in 2015 received an abbreviation IAO'15, as IAO'5 has been already used in 1995.
You are given a list of abbreviations. For each of them determine the year it stands for. | The first line of the input contains a single integer *n* (1<=β€<=*n*<=β€<=1000)Β β the number of abbreviations to process.
Then *n* lines follow, each containing a single abbreviation. It's guaranteed that each abbreviation contains at most nine digits. | For each abbreviation given in the input, find the year of the corresponding Olympiad. | [
"5\nIAO'15\nIAO'2015\nIAO'1\nIAO'9\nIAO'0\n",
"4\nIAO'9\nIAO'99\nIAO'999\nIAO'9999\n"
] | [
"2015\n12015\n1991\n1989\n1990\n",
"1989\n1999\n2999\n9999\n"
] | none | [
{
"input": "5\nIAO'15\nIAO'2015\nIAO'1\nIAO'9\nIAO'0",
"output": "2015\n12015\n1991\n1989\n1990"
},
{
"input": "4\nIAO'9\nIAO'99\nIAO'999\nIAO'9999",
"output": "1989\n1999\n2999\n9999"
},
{
"input": "1\nIAO'111110",
"output": "1111110"
},
{
"input": "2\nIAO'0\nIAO'00",
"output": "1990\n2000"
},
{
"input": "1\nIAO'111111",
"output": "1111111"
},
{
"input": "1\nIAO'111111111",
"output": "1111111111"
},
{
"input": "1\nIAO'001",
"output": "3001"
},
{
"input": "1\nIAO'2000",
"output": "12000"
},
{
"input": "1\nIAO'11109999",
"output": "111109999"
},
{
"input": "1\nIAO'11111",
"output": "111111"
},
{
"input": "1\nIAO'100000",
"output": "1100000"
},
{
"input": "1\nIAO'18999990",
"output": "18999990"
},
{
"input": "1\nIAO'113098",
"output": "1113098"
},
{
"input": "1\nIAO'111122",
"output": "1111122"
},
{
"input": "1\nIAO'1110222",
"output": "11110222"
},
{
"input": "1\nIAO'11133333",
"output": "11133333"
},
{
"input": "1\nIAO'000000000",
"output": "1000000000"
},
{
"input": "4\nIAO'3098\nIAO'99\nIAO'999\nIAO'9999",
"output": "13098\n1999\n2999\n9999"
},
{
"input": "1\nIAO'11100000",
"output": "111100000"
},
{
"input": "2\nIAO'15\nIAO'15",
"output": "2015\n2015"
},
{
"input": "1\nIAO'999999999",
"output": "999999999"
},
{
"input": "1\nIAO'1112121",
"output": "11112121"
},
{
"input": "1\nIAO'111113098",
"output": "1111113098"
},
{
"input": "1\nIAO'10005000",
"output": "110005000"
},
{
"input": "1\nIAO'111378",
"output": "1111378"
},
{
"input": "1\nIAO'112222",
"output": "1112222"
},
{
"input": "1\nIAO'021113099",
"output": "1021113099"
},
{
"input": "1\nIAO'123456789",
"output": "123456789"
},
{
"input": "1\nIAO'000000001",
"output": "1000000001"
},
{
"input": "1\nIAO'089",
"output": "3089"
},
{
"input": "9\nIAO'0\nIAO'00\nIAO'000\nIAO'0000\nIAO'00000\nIAO'000000\nIAO'0000000\nIAO'00000000\nIAO'000000000",
"output": "1990\n2000\n3000\n10000\n100000\n1000000\n10000000\n100000000\n1000000000"
},
{
"input": "2\nIAO'999999999\nIAO'999999999",
"output": "999999999\n999999999"
},
{
"input": "1\nIAO'2015",
"output": "12015"
},
{
"input": "1\nIAO'113097",
"output": "1113097"
},
{
"input": "1\nIAO'11378",
"output": "111378"
}
] | 46 | 0 | 3 | 4,984 |
|
222 | Reducing Fractions | [
"implementation",
"math",
"number theory",
"sortings"
] | null | null | To confuse the opponents, the Galactic Empire represents fractions in an unusual format. The fractions are represented as two sets of integers. The product of numbers from the first set gives the fraction numerator, the product of numbers from the second set gives the fraction denominator. However, it turned out that the programs that work with fractions in this representations aren't complete, they lack supporting the operation of reducing fractions. Implement this operation and the Empire won't forget you. | The first input line contains two space-separated integers *n*, *m* (1<=β€<=*n*,<=*m*<=β€<=105) that show how many numbers the first set (the numerator) and the second set (the denominator) contain, correspondingly.
The second line contains *n* space-separated integers: *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=107) β the numbers that are multiplied to produce the numerator.
The third line contains *m* space-separated integers: *b*1,<=*b*2,<=...,<=*b**m* (1<=β€<=*b**i*<=β€<=107) β the numbers that are multiplied to produce the denominator. | Print the answer to the problem in the form, similar to the form of the input data. The number of values in the sets you print *n**out*,<=*m**out* must satisfy the inequality 1<=β€<=*n**out*,<=*m**out*<=β€<=105, and the actual values in the sets *a**out*,<=*i* and *b**out*,<=*i* must satisfy the inequality 1<=β€<=*a**out*,<=*i*,<=*b**out*,<=*i*<=β€<=107.
Separate the values in the lines by spaces. The printed fraction must be reduced, that is, there mustn't be such integer *x* (*x*<=><=1), that the numerator and the denominator of the printed fraction are divisible by *x*. If there are several matching answers, print any of them. | [
"3 2\n100 5 2\n50 10\n",
"4 3\n2 5 10 20\n100 1 3\n"
] | [
"2 3\n2 1\n1 1 1\n",
"1 1\n20\n3\n"
] | In the first test sample the numerator equals 1000, the denominator equals 500. If we reduce fraction 1000/500 by the greatest common divisor of the numerator and the denominator (by 500), we obtain fraction 2/1.
In the second test sample the numerator equals 2000, the denominator equals 300. If we reduce fraction 2000/300 by the greatest common divisor of the numerator and the denominator (by 100), we obtain fraction 20/3. | [
{
"input": "3 2\n100 5 2\n50 10",
"output": "2 3\n2 1\n1 1 1"
},
{
"input": "4 3\n2 5 10 20\n100 1 3",
"output": "1 1\n20\n3"
},
{
"input": "2 3\n50 10\n100 5 2",
"output": "2 3\n1 1 \n2 1 1 "
},
{
"input": "1 1\n1\n1",
"output": "1 1\n1 \n1 "
},
{
"input": "3 2\n100 5 2\n10 100",
"output": "3 2\n1 1 1 \n1 1 "
},
{
"input": "5 3\n16 24 36 54 81\n4 6 9",
"output": "5 3\n16 24 9 27 3 \n1 1 1 "
},
{
"input": "10 10\n2 5 11 17 23 31 41 47 59 67\n3 7 13 19 29 37 43 53 61 71",
"output": "10 10\n2 5 11 17 23 31 41 47 59 67 \n3 7 13 19 29 37 43 53 61 71 "
},
{
"input": "5 5\n2 9 8 3 5\n5 7 8 1 1",
"output": "5 5\n2 9 1 3 1 \n1 7 1 1 1 "
},
{
"input": "10 11\n7 43 39 13 25 23 33 40 5 2\n42 22 39 1 23 37 12 48 46 2 2",
"output": "10 11\n1 43 13 1 25 1 1 5 5 1 \n6 2 3 1 23 37 4 8 1 1 1 "
},
{
"input": "1 5\n99\n3 55 18 1 19",
"output": "1 5\n1 \n3 5 2 1 19 "
}
] | 904 | 135,577,600 | 0 | 4,988 |
|
359 | Prime Number | [
"math",
"number theory"
] | null | null | Simon has a prime number *x* and an array of non-negative integers *a*1,<=*a*2,<=...,<=*a**n*.
Simon loves fractions very much. Today he wrote out number on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: , where number *t* equals *x**a*1<=+<=*a*2<=+<=...<=+<=*a**n*. Now Simon wants to reduce the resulting fraction.
Help him, find the greatest common divisor of numbers *s* and *t*. As GCD can be rather large, print it as a remainder after dividing it by number 1000000007 (109<=+<=7). | The first line contains two positive integers *n* and *x* (1<=β€<=*n*<=β€<=105, 2<=β€<=*x*<=β€<=109) β the size of the array and the prime number.
The second line contains *n* space-separated integers *a*1,<=*a*2,<=...,<=*a**n* (0<=β€<=*a*1<=β€<=*a*2<=β€<=...<=β€<=*a**n*<=β€<=109). | Print a single number β the answer to the problem modulo 1000000007 (109<=+<=7). | [
"2 2\n2 2\n",
"3 3\n1 2 3\n",
"2 2\n29 29\n",
"4 5\n0 0 0 0\n"
] | [
"8\n",
"27\n",
"73741817\n",
"1\n"
] | In the first sample <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/7745f7cc87c6c5f753e3414fad9baa3b1e3fea48.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Thus, the answer to the problem is 8.
In the second sample, <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/acb3d7990f024100be499bcb59828fa6e23a867d.png" style="max-width: 100.0%;max-height: 100.0%;"/>. The answer to the problem is 27, as 351β=β13Β·27, 729β=β27Β·27.
In the third sample the answer to the problem is 1073741824Β *mod*Β 1000000007β=β73741817.
In the fourth sample <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/05a5fca3fb4690369838ff6dfeda521c959aa937.png" style="max-width: 100.0%;max-height: 100.0%;"/>. Thus, the answer to the problem is 1. | [
{
"input": "2 2\n2 2",
"output": "8"
},
{
"input": "3 3\n1 2 3",
"output": "27"
},
{
"input": "2 2\n29 29",
"output": "73741817"
},
{
"input": "4 5\n0 0 0 0",
"output": "1"
},
{
"input": "1 2\n1000000000",
"output": "1"
},
{
"input": "26 2\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2",
"output": "8"
},
{
"input": "26 7\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2",
"output": "49"
},
{
"input": "3 2\n0 1 1",
"output": "4"
},
{
"input": "1 127\n1000000000",
"output": "1"
},
{
"input": "1 800000011\n800000011",
"output": "1"
},
{
"input": "1 800000011\n999999999",
"output": "1"
},
{
"input": "3 3\n1 1 1",
"output": "27"
}
] | 234 | 31,129,600 | 0 | 4,993 |
|
22 | Scheme | [
"dfs and similar",
"graphs",
"trees"
] | E. Scheme | 2 | 256 | To learn as soon as possible the latest news about their favourite fundamentally new operating system, BolgenOS community from Nizhni Tagil decided to develop a scheme. According to this scheme a community member, who is the first to learn the news, calls some other member, the latter, in his turn, calls some third member, and so on; i.e. a person with index *i* got a person with index *f**i*, to whom he has to call, if he learns the news. With time BolgenOS community members understood that their scheme doesn't work sometimes β there were cases when some members didn't learn the news at all. Now they want to supplement the scheme: they add into the scheme some instructions of type (*x**i*,<=*y**i*), which mean that person *x**i* has to call person *y**i* as well. What is the minimum amount of instructions that they need to add so, that at the end everyone learns the news, no matter who is the first to learn it? | The first input line contains number *n* (2<=β€<=*n*<=β€<=105) β amount of BolgenOS community members. The second line contains *n* space-separated integer numbers *f**i* (1<=β€<=*f**i*<=β€<=*n*,<=*i*<=β <=*f**i*) β index of a person, to whom calls a person with index *i*. | In the first line output one number β the minimum amount of instructions to add. Then output one of the possible variants to add these instructions into the scheme, one instruction in each line. If the solution is not unique, output any. | [
"3\n3 3 2\n",
"7\n2 3 1 3 4 4 1\n"
] | [
"1\n3 1\n",
"3\n2 5\n2 6\n3 7\n"
] | none | [
{
"input": "3\n3 3 2",
"output": "1\n3 1"
},
{
"input": "7\n2 3 1 3 4 4 1",
"output": "3\n1 5\n1 6\n1 7"
},
{
"input": "2\n2 1",
"output": "0"
},
{
"input": "3\n2 3 1",
"output": "0"
},
{
"input": "4\n2 4 4 3",
"output": "1\n4 1"
},
{
"input": "5\n5 3 5 2 3",
"output": "2\n5 1\n5 4"
},
{
"input": "9\n2 5 6 7 4 1 9 6 8",
"output": "1\n1 3"
},
{
"input": "20\n20 10 16 14 9 20 6 20 14 19 17 13 16 13 14 8 8 8 8 19",
"output": "10\n20 1\n20 2\n20 3\n20 4\n20 5\n20 7\n20 11\n20 12\n20 15\n20 18"
},
{
"input": "100\n13 71 16 92 25 53 97 63 70 83 51 16 51 84 5 10 54 89 18 95 48 29 82 27 84 68 7 4 65 99 95 37 26 24 24 39 3 28 74 7 75 32 27 24 73 48 72 15 46 66 91 94 19 44 77 23 94 88 51 84 72 95 75 55 80 47 58 13 87 88 25 2 89 81 71 36 7 42 16 59 32 43 58 61 44 96 36 48 88 49 53 91 13 1 37 87 90 47 61 87",
"output": "36\n25 6\n25 8\n25 9\n25 11\n25 12\n25 14\n25 17\n25 20\n25 21\n25 22\n25 30\n25 31\n25 33\n25 34\n25 35\n25 38\n25 40\n25 41\n25 45\n25 50\n25 52\n25 56\n25 57\n25 60\n25 62\n25 64\n25 67\n25 69\n25 76\n25 78\n25 79\n25 85\n25 86\n25 93\n25 98\n25 100"
},
{
"input": "7\n3 1 2 5 6 7 4",
"output": "2\n1 4\n4 1"
}
] | 248 | 56,934,400 | -1 | 4,994 |
722 | Generating Sets | [
"binary search",
"data structures",
"dfs and similar",
"greedy",
"strings",
"trees"
] | null | null | You are given a set *Y* of *n* distinct positive integers *y*1,<=*y*2,<=...,<=*y**n*.
Set *X* of *n* distinct positive integers *x*1,<=*x*2,<=...,<=*x**n* is said to generate set *Y* if one can transform *X* to *Y* by applying some number of the following two operation to integers in *X*:
1. Take any integer *x**i* and multiply it by two, i.e. replace *x**i* with 2Β·*x**i*. 1. Take any integer *x**i*, multiply it by two and add one, i.e. replace *x**i* with 2Β·*x**i*<=+<=1.
Note that integers in *X* are not required to be distinct after each operation.
Two sets of distinct integers *X* and *Y* are equal if they are equal as sets. In other words, if we write elements of the sets in the array in the increasing order, these arrays would be equal.
Note, that any set of integers (or its permutation) generates itself.
You are given a set *Y* and have to find a set *X* that generates *Y* and the maximum element of *X* is mininum possible. | The first line of the input contains a single integer *n* (1<=β€<=*n*<=β€<=50<=000)Β β the number of elements in *Y*.
The second line contains *n* integers *y*1,<=...,<=*y**n* (1<=β€<=*y**i*<=β€<=109), that are guaranteed to be distinct. | Print *n* integersΒ β set of distinct integers that generate *Y* and the maximum element of which is minimum possible. If there are several such sets, print any of them. | [
"5\n1 2 3 4 5\n",
"6\n15 14 3 13 1 12\n",
"6\n9 7 13 17 5 11\n"
] | [
"4 5 2 3 1 \n",
"12 13 14 7 3 1 \n",
"4 5 2 6 3 1 \n"
] | none | [
{
"input": "5\n1 2 3 4 5",
"output": "4 5 2 3 1 "
},
{
"input": "6\n15 14 3 13 1 12",
"output": "12 13 14 7 3 1 "
},
{
"input": "6\n9 7 13 17 5 11",
"output": "4 5 2 6 3 1 "
},
{
"input": "10\n18 14 19 17 11 7 20 10 4 12",
"output": "8 9 4 10 5 2 6 7 3 1 "
},
{
"input": "100\n713 716 230 416 3 2 597 216 779 839 13 156 723 793 168 368 232 316 98 257 170 27 746 9 616 147 792 890 796 362 852 117 993 556 885 73 131 475 121 753 508 158 473 931 527 282 541 325 606 321 159 17 682 290 586 685 529 11 645 224 821 53 152 966 269 754 672 523 386 347 719 525 92 315 832 393 893 83 956 725 258 851 112 38 601 782 324 210 642 818 56 485 679 10 922 469 36 990 14 742",
"output": "128 129 130 131 65 32 132 134 135 139 141 17 145 146 147 73 36 149 150 151 152 154 38 156 157 158 159 79 9 160 161 80 162 81 83 168 84 85 42 86 21 10 89 44 90 45 22 92 93 46 94 47 23 11 5 2 96 97 48 98 99 49 24 102 51 12 104 105 52 106 53 26 108 110 111 55 27 13 6 112 56 115 57 28 116 117 58 118 119 59 29 14 120 121 60 123 124 127 3 1 "
},
{
"input": "100\n41 173 40 30 165 155 92 180 193 24 187 189 65 4 200 80 152 174 20 81 170 72 104 8 13 7 117 176 191 34 90 46 17 188 63 134 76 60 116 42 183 45 1 103 15 119 142 70 148 136 73 68 86 94 32 190 112 166 141 78 6 102 66 97 93 106 47 22 132 129 139 177 62 105 100 77 88 54 3 167 120 145 197 195 64 11 38 2 28 140 87 109 185 23 31 153 39 18 57 122",
"output": "129 64 65 32 132 66 134 136 68 139 34 140 141 70 142 17 8 145 72 73 148 18 152 153 76 155 77 38 78 39 4 80 81 40 165 166 167 41 20 170 42 173 86 174 87 176 177 88 180 90 183 45 22 185 92 187 93 46 188 189 94 95 47 23 11 5 2 96 97 48 98 24 100 50 102 103 104 105 106 109 54 13 6 112 57 28 116 117 119 120 60 122 30 62 63 31 15 7 3 1 "
},
{
"input": "10\n10 1 6 7 9 8 4 3 5 2",
"output": "8 9 4 10 5 2 6 7 3 1 "
},
{
"input": "100\n70 54 10 72 81 84 56 15 27 19 43 100 49 44 52 33 63 40 95 17 58 2 51 39 22 18 82 1 16 99 32 29 24 94 9 98 5 37 47 14 42 73 41 31 79 64 12 6 53 26 68 67 89 13 90 4 21 93 46 74 75 88 66 57 23 7 25 48 92 62 30 8 50 61 38 87 71 34 97 28 80 11 60 91 3 35 86 96 36 20 59 65 83 45 76 77 78 69 85 55",
"output": "64 65 32 66 67 33 16 68 69 34 70 71 35 17 8 72 73 36 74 75 37 18 76 77 38 78 79 39 19 9 4 80 81 40 82 83 41 20 84 85 42 86 87 43 21 10 88 89 44 90 91 45 22 92 93 46 94 95 47 23 11 5 2 96 97 48 98 99 49 24 100 50 51 25 12 52 53 26 54 55 27 13 6 56 57 28 58 59 29 14 60 61 30 62 63 31 15 7 3 1 "
},
{
"input": "1\n32",
"output": "1 "
},
{
"input": "30\n1000000000 500000000 250000000 125000000 62500000 31250000 15625000 7812500 3906250 1953125 976562 488281 244140 122070 61035 30517 15258 7629 3814 1907 953 476 238 119 59 29 14 7 3 1",
"output": "1000000000 500000000 250000000 125000000 62500000 31250000 15625000 7812500 3906250 1953125 976562 488281 244140 122070 61035 30517 15258 7629 3814 1907 953 476 238 119 59 29 14 7 3 1 "
}
] | 733 | 27,136,000 | 3 | 5,005 |
|
253 | Text Editor | [
"data structures",
"dfs and similar",
"graphs",
"greedy",
"shortest paths"
] | null | null | Vasya is pressing the keys on the keyboard reluctantly, squeezing out his ideas on the classical epos depicted in Homer's Odysseus... How can he explain to his literature teacher that he isn't going to become a writer? In fact, he is going to become a programmer. So, he would take great pleasure in writing a program, but none β in writing a composition.
As Vasya was fishing for a sentence in the dark pond of his imagination, he suddenly wondered: what is the least number of times he should push a key to shift the cursor from one position to another one?
Let's describe his question more formally: to type a text, Vasya is using the text editor. He has already written *n* lines, the *i*-th line contains *a**i* characters (including spaces). If some line contains *k* characters, then this line overall contains (*k*<=+<=1) positions where the cursor can stand: before some character or after all characters (at the end of the line). Thus, the cursor's position is determined by a pair of integers (*r*,<=*c*), where *r* is the number of the line and *c* is the cursor's position in the line (the positions are indexed starting from one from the beginning of the line).
Vasya doesn't use the mouse to move the cursor. He uses keys "Up", "Down", "Right" and "Left". When he pushes each of these keys, the cursor shifts in the needed direction. Let's assume that before the corresponding key is pressed, the cursor was located in the position (*r*,<=*c*), then Vasya pushed key:
- "Up": if the cursor was located in the first line (*r*<==<=1), then it does not move. Otherwise, it moves to the previous line (with number *r*<=-<=1), to the same position. At that, if the previous line was short, that is, the cursor couldn't occupy position *c* there, the cursor moves to the last position of the line with number *r*<=-<=1;- "Down": if the cursor was located in the last line (*r*<==<=*n*), then it does not move. Otherwise, it moves to the next line (with number *r*<=+<=1), to the same position. At that, if the next line was short, that is, the cursor couldn't occupy position *c* there, the cursor moves to the last position of the line with number *r*<=+<=1;- "Right": if the cursor can move to the right in this line (*c*<=<<=*a**r*<=+<=1), then it moves to the right (to position *c*<=+<=1). Otherwise, it is located at the end of the line and doesn't move anywhere when Vasya presses the "Right" key;- "Left": if the cursor can move to the left in this line (*c*<=><=1), then it moves to the left (to position *c*<=-<=1). Otherwise, it is located at the beginning of the line and doesn't move anywhere when Vasya presses the "Left" key.
You've got the number of lines in the text file and the number of characters, written in each line of this file. Find the least number of times Vasya should push the keys, described above, to shift the cursor from position (*r*1,<=*c*1) to position (*r*2,<=*c*2). | The first line of the input contains an integer *n* (1<=β€<=*n*<=β€<=100) β the number of lines in the file. The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=β€<=*a**i*<=β€<=105), separated by single spaces. The third line contains four integers *r*1,<=*c*1,<=*r*2,<=*c*2 (1<=β€<=*r*1,<=*r*2<=β€<=*n*,<=1<=β€<=*c*1<=β€<=*a**r*1<=+<=1,<=1<=β€<=*c*2<=β€<=*a**r*2<=+<=1). | Print a single integer β the minimum number of times Vasya should push a key to move the cursor from position (*r*1,<=*c*1) to position (*r*2,<=*c*2). | [
"4\n2 1 6 4\n3 4 4 2\n",
"4\n10 5 6 4\n1 11 4 2\n",
"3\n10 1 10\n1 10 1 1\n"
] | [
"3\n",
"6\n",
"3\n"
] | In the first sample the editor contains four lines. Let's represent the cursor's possible positions in the line as numbers. Letter *s* represents the cursor's initial position, letter *t* represents the last one. Then all possible positions of the cursor in the text editor are described by the following table.
123
12
123s567
1t345
One of the possible answers in the given sample is: "Left", "Down", "Left". | [
{
"input": "4\n2 1 6 4\n3 4 4 2",
"output": "3"
},
{
"input": "4\n10 5 6 4\n1 11 4 2",
"output": "6"
},
{
"input": "3\n10 1 10\n1 10 1 1",
"output": "3"
},
{
"input": "4\n2 1 6 4\n4 2 3 5",
"output": "4"
},
{
"input": "3\n20 3 20\n1 20 1 1",
"output": "5"
},
{
"input": "2\n10 1\n1 3 2 1",
"output": "2"
},
{
"input": "20\n3 1 9 9 6 1 3 4 5 6 7 3 1 9 9 1 9 1 5 7\n17 7 19 5",
"output": "5"
},
{
"input": "20\n81 90 11 68 23 18 78 75 45 86 58 37 21 15 98 40 53 100 10 70\n11 55 8 19",
"output": "7"
},
{
"input": "25\n55 47 5 63 55 11 8 32 0 62 41 7 17 70 33 6 41 68 37 82 33 64 28 33 12\n6 11 14 12",
"output": "19"
},
{
"input": "30\n77 38 82 87 88 1 90 3 79 69 64 36 85 12 1 19 80 89 75 56 49 28 10 31 37 65 27 84 10 72\n26 65 19 3",
"output": "15"
},
{
"input": "100\n119 384 220 357 394 123 371 57 6 221 219 79 305 292 71 113 428 326 166 235 120 404 77 223 2 171 81 1 119 307 200 323 89 294 178 421 125 197 89 154 335 46 210 311 216 182 246 262 195 99 175 153 310 302 417 167 222 349 63 325 175 345 6 78 9 147 126 308 229 295 175 368 230 116 95 254 443 15 299 265 322 171 179 184 435 115 384 324 213 359 414 159 322 49 209 296 376 173 369 302\n8 47 23 65",
"output": "73"
},
{
"input": "100\n120 336 161 474 285 126 321 63 82 303 421 110 143 279 505 231 40 413 20 421 271 30 465 186 495 156 225 445 530 156 516 305 360 261 123 5 50 377 124 8 115 529 395 408 271 166 121 240 336 348 352 359 487 471 171 379 381 182 109 425 252 434 131 430 461 386 33 189 481 461 163 89 374 505 525 526 132 468 80 88 90 538 280 281 552 415 194 41 333 296 297 205 40 79 22 219 108 213 158 410\n58 119 82 196",
"output": "186"
},
{
"input": "100\n9 8 5 2 10 6 10 10 1 9 8 5 0 9 1 6 6 2 3 9 9 3 2 7 2 7 8 10 6 6 2 8 5 0 0 8 7 3 0 4 7 5 9 0 3 6 9 6 5 0 4 9 4 7 7 1 5 8 2 4 10 3 9 8 10 6 10 7 4 9 0 1 3 6 6 2 1 1 5 7 0 9 6 0 4 6 8 4 7 6 1 9 4 3 10 9 7 0 0 7\n72 2 87 2",
"output": "16"
},
{
"input": "100\n9 72 46 37 26 94 80 1 43 85 26 53 58 18 24 19 67 2 100 52 61 81 48 15 73 41 97 93 45 1 73 54 75 51 28 79 0 14 41 42 24 50 70 18 96 100 67 1 68 48 44 39 63 77 78 18 10 51 32 53 26 60 1 13 66 39 55 27 23 71 75 0 27 88 73 31 16 95 87 84 86 71 37 40 66 70 65 83 19 4 81 99 26 51 67 63 80 54 23 44\n6 76 89 15",
"output": "97"
},
{
"input": "100\n176 194 157 24 27 153 31 159 196 85 127 114 142 39 133 4 44 36 141 96 80 40 120 16 88 29 157 136 158 98 145 152 19 40 106 116 19 195 184 70 72 95 78 146 199 1 103 3 120 71 52 77 160 148 24 156 108 64 86 124 103 97 108 66 107 126 29 172 23 106 29 69 64 90 9 171 59 85 1 63 79 50 136 21 115 164 30 115 86 26 25 6 128 48 122 14 198 88 182 117\n71 4 85 80",
"output": "92"
},
{
"input": "100\n1622 320 1261 282 1604 57 1427 1382 904 911 1719 1682 984 1727 1301 1799 1110 1057 248 764 1642 1325 1172 1677 182 32 665 397 1146 73 412 554 973 874 774 1948 1676 1959 518 280 1467 568 613 760 594 252 224 1359 876 253 760 1566 929 1614 940 1079 288 245 1432 1647 1534 1768 1947 733 225 495 1239 644 124 522 1859 1856 1464 485 1962 131 1693 1622 242 1119 1290 538 998 1342 791 711 809 1407 1369 414 124 758 1104 1142 355 324 665 1155 551 1611\n36 1383 51 21",
"output": "47"
},
{
"input": "50\n966 151 777 841 507 884 487 813 29 230 966 819 390 482 137 365 391 693 56 756 327 500 895 22 361 619 8 516 21 770 572 53 497 682 162 32 308 309 110 470 699 318 947 658 720 679 435 645 481 42\n45 510 25 48",
"output": "59"
},
{
"input": "50\n4143 2907 2028 539 3037 1198 6597 3658 972 9809 854 4931 642 3170 9777 2992 7121 8094 6634 684 5580 4684 3397 7909 3908 3822 2137 8299 8146 2105 7578 4338 7363 8237 530 301 4566 1153 4795 5342 3257 6953 4401 8311 9977 9260 7019 7705 5416 6754\n21 3413 23 218",
"output": "112"
},
{
"input": "50\n8974 13208 81051 72024 84908 49874 22875 64935 27340 38682 28512 43441 78752 83458 63344 5723 83425 54009 61980 7824 59956 43184 49274 3896 44079 67313 68565 9138 55087 68458 43009 3685 22879 85032 84273 93643 64957 73428 57016 33405 85961 47708 90325 1352 1551 20935 76821 75406 59309 40757\n14 45232 2 6810",
"output": "1102"
},
{
"input": "100\n34 80 42 99 7 49 109 61 20 7 92 2 62 96 65 77 70 5 16 83 99 39 88 66 106 1 80 68 71 74 28 75 19 97 38 100 30 1 55 86 3 13 61 82 72 50 68 18 77 89 96 27 26 35 46 13 83 77 40 31 85 108 15 5 40 80 1 108 44 18 66 26 46 7 36 80 34 76 17 9 23 57 109 90 88 1 54 66 71 94 6 89 50 22 93 82 32 74 41 74\n91 7 56 3",
"output": "36"
},
{
"input": "100\n156 150 75 72 205 133 139 99 212 82 58 104 133 88 46 157 49 179 32 72 159 188 42 47 36 58 127 215 125 115 209 118 109 11 62 159 110 151 92 202 203 25 44 209 153 8 199 168 126 34 21 106 31 40 48 212 106 0 131 166 2 126 13 126 103 44 2 66 33 25 194 41 37 198 199 6 22 1 161 16 95 11 198 198 166 145 214 159 143 2 181 130 159 118 176 165 192 178 42 168\n49 12 66 23",
"output": "39"
},
{
"input": "100\n289 16 321 129 0 121 61 86 93 5 63 276 259 144 275 236 309 257 244 138 107 18 158 14 295 162 7 113 58 101 142 196 181 329 115 109 62 237 110 87 19 205 68 257 252 0 166 45 310 244 140 251 262 315 213 206 290 128 287 230 198 83 135 40 8 273 319 295 288 274 34 260 288 252 172 129 201 110 294 111 95 180 34 98 16 188 170 40 274 153 11 159 245 51 328 290 112 11 105 182\n99 53 21 77",
"output": "154"
},
{
"input": "10\n11284 10942 14160 10062 1858 6457 1336 13842 5498 4236\n1 7123 5 664",
"output": "681"
},
{
"input": "53\n29496 9630 10781 25744 28508 15670 8252 14284 25995 20215 24251 14240 1370 15724 28268 30377 4839 16791 33515 23776 24252 1045 15245 12839 17531 28591 13091 27339 23361 10997 30438 26977 26789 18402 32938 2106 26599 10733 29549 9760 31507 33572 16934 7273 26477 15040 23704 19905 1941 3861 5950 1265 34\n11 6571 1 3145",
"output": "1788"
},
{
"input": "31\n14324 29226 58374 19956 61695 71586 13261 11436 58443 34879 12689 62786 68194 34303 99201 67616 51364 67539 56799 60130 22021 64546 28331 75746 45036 43950 2150 61718 33030 37781 34319\n24 57393 7 6152",
"output": "4024"
},
{
"input": "23\n5397 13279 11741 20182 18311 20961 16720 11864 2486 14081 15637 16216 3736 437 16346 12449 20205 10949 14237 2213 15281 15271 19138\n5 11479 13 68",
"output": "380"
},
{
"input": "40\n41997 20736 34699 73866 45509 41964 36050 16673 10454 21166 28306 69335 6172 65943 78569 16794 10439 68061 40392 52510 78248 63851 45294 49929 22580 5574 40993 18334 73897 59148 47727 76645 4280 23651 58772 64500 13704 60366 37099 20336\n14 29991 16 11904",
"output": "1468"
},
{
"input": "16\n922 7593 4748 4103 7672 6001 1573 3973 8524 8265 4747 3202 4796 2637 889 9359\n12 2165 12 1654",
"output": "90"
},
{
"input": "18\n22746 9084 3942 1120 25391 25307 7409 1189 23473 26175 10964 13584 5541 500 24338 12272 15824 27656\n3 1395 12 90",
"output": "424"
},
{
"input": "45\n2286 4425 14666 34959 10792 3723 30132 34266 18100 22813 28627 23310 33911 27285 1211 993 15526 4751 13611 21400 25712 24437 27435 34808 33950 18373 33685 23487 5444 10249 21415 16368 35398 7889 30918 19940 1552 12164 34292 13922 10011 31377 24102 34539 11992\n20 21252 28 2058",
"output": "531"
},
{
"input": "29\n56328 80183 27682 79083 60680 12286 34299 8015 51808 50756 82133 45930 43695 65863 25178 70825 2288 15111 39667 39637 11453 62821 81484 84216 54524 53749 8396 67712 76146\n13 10739 9 3622",
"output": "1345"
},
{
"input": "46\n67864 68218 3593 30646 66413 65542 65322 26801 28984 61330 15247 16522 39142 14013 49272 41585 56739 6881 44227 7101 57657 21121 51857 39351 13500 71528 8488 66118 14756 43923 21284 20018 49049 60198 6181 62460 44141 55828 42636 14623 59758 68321 12192 29978 24745 16467\n27 5545 4 3766",
"output": "197"
},
{
"input": "70\n53691 15034 17444 13375 23285 29211 24567 21643 45514 10290 70111 24541 25072 5365 12162 34564 27535 48253 39581 13468 33718 35105 30468 50214 53365 74800 16749 33935 36346 54230 73796 26826 27866 41887 67566 40813 32267 58821 56828 26439 23708 32335 69515 33825 6092 20510 50174 11129 4592 74116 21498 77951 48056 28554 43904 21885 5967 40253 4990 70029 34374 41201 25399 6101 10354 61833 43646 20534 371 11111\n21 3911 45 1755",
"output": "1455"
},
{
"input": "10\n8121 10681 10179 10221 9410 5214 19040 17893 7862 4611\n7 7780 7 3369",
"output": "1249"
},
{
"input": "2\n1 2\n1 1 1 1",
"output": "0"
},
{
"input": "3\n1 10 20\n2 10 3 1",
"output": "4"
}
] | 122 | 2,867,200 | -1 | 5,007 |
|
819 | Mister B and Flight to the Moon | [
"constructive algorithms",
"graphs"
] | null | null | In order to fly to the Moon Mister B just needs to solve the following problem.
There is a complete indirected graph with *n* vertices. You need to cover it with several simple cycles of length 3 and 4 so that each edge is in exactly 2 cycles.
We are sure that Mister B will solve the problem soon and will fly to the Moon. Will you? | The only line contains single integer *n* (3<=β€<=*n*<=β€<=300). | If there is no answer, print -1.
Otherwise, in the first line print *k* (1<=β€<=*k*<=β€<=*n*2)Β β the number of cycles in your solution.
In each of the next *k* lines print description of one cycle in the following format: first print integer *m* (3<=β€<=*m*<=β€<=4)Β β the length of the cycle, then print *m* integers *v*1,<=*v*2,<=...,<=*v**m* (1<=β€<=*v**i*<=β€<=*n*)Β β the vertices in the cycle in the traverse order. Each edge should be in exactly two cycles. | [
"3\n",
"5\n"
] | [
"2\n3 1 2 3\n3 1 2 3\n",
"6\n3 5 4 2\n3 3 1 5\n4 4 5 2 3\n4 4 3 2 1\n3 4 2 1\n3 3 1 5\n"
] | none | [
{
"input": "3",
"output": "2\n3 1 2 3\n3 1 2 3"
},
{
"input": "5",
"output": "6\n3 1 2 3\n3 2 3 4\n3 3 4 5\n3 4 5 1\n4 2 1 3 5\n4 5 1 4 2"
},
{
"input": "299",
"output": "22350\n4 2 3 1 4\n4 1 4 299 5\n4 299 5 298 6\n4 298 6 297 7\n4 297 7 296 8\n4 296 8 295 9\n4 295 9 294 10\n4 294 10 293 11\n4 293 11 292 12\n4 292 12 291 13\n4 291 13 290 14\n4 290 14 289 15\n4 289 15 288 16\n4 288 16 287 17\n4 287 17 286 18\n4 286 18 285 19\n4 285 19 284 20\n4 284 20 283 21\n4 283 21 282 22\n4 282 22 281 23\n4 281 23 280 24\n4 280 24 279 25\n4 279 25 278 26\n4 278 26 277 27\n4 277 27 276 28\n4 276 28 275 29\n4 275 29 274 30\n4 274 30 273 31\n4 273 31 272 32\n4 272 32 271 33\n4 271 33 270 ..."
},
{
"input": "300",
"output": "22500\n3 300 1 2\n4 300 2 299 3\n4 299 3 298 4\n4 298 4 297 5\n4 297 5 296 6\n4 296 6 295 7\n4 295 7 294 8\n4 294 8 293 9\n4 293 9 292 10\n4 292 10 291 11\n4 291 11 290 12\n4 290 12 289 13\n4 289 13 288 14\n4 288 14 287 15\n4 287 15 286 16\n4 286 16 285 17\n4 285 17 284 18\n4 284 18 283 19\n4 283 19 282 20\n4 282 20 281 21\n4 281 21 280 22\n4 280 22 279 23\n4 279 23 278 24\n4 278 24 277 25\n4 277 25 276 26\n4 276 26 275 27\n4 275 27 274 28\n4 274 28 273 29\n4 273 29 272 30\n4 272 30 271 31\n4 271 31 270 32..."
},
{
"input": "4",
"output": "4\n3 4 1 2\n3 2 3 4\n3 1 2 3\n3 3 4 1"
},
{
"input": "5",
"output": "6\n3 1 2 3\n3 2 3 4\n3 3 4 5\n3 4 5 1\n4 2 1 3 5\n4 5 1 4 2"
},
{
"input": "6",
"output": "9\n3 6 1 2\n4 6 2 5 3\n3 3 4 5\n3 1 2 3\n4 1 3 6 4\n3 4 5 6\n3 2 3 4\n4 2 4 1 5\n3 5 6 1"
},
{
"input": "7",
"output": "12\n4 2 3 1 4\n4 3 4 2 5\n4 4 5 3 6\n4 5 6 4 7\n4 6 7 5 1\n4 7 1 6 2\n3 2 5 6\n3 1 5 4\n3 3 6 7\n3 7 4 3\n3 3 2 1\n3 7 1 2"
},
{
"input": "8",
"output": "16\n3 8 1 2\n4 8 2 7 3\n4 7 3 6 4\n3 4 5 6\n3 1 2 3\n4 1 3 8 4\n4 8 4 7 5\n3 5 6 7\n3 2 3 4\n4 2 4 1 5\n4 1 5 8 6\n3 6 7 8\n3 3 4 5\n4 3 5 2 6\n4 2 6 1 7\n3 7 8 1"
},
{
"input": "9",
"output": "20\n3 1 2 3\n4 1 3 9 4\n3 2 3 4\n4 2 4 1 5\n3 3 4 5\n4 3 5 2 6\n3 4 5 6\n4 4 6 3 7\n3 5 6 7\n4 5 7 4 8\n3 6 7 8\n4 6 8 5 9\n3 7 8 9\n4 7 9 6 1\n3 8 9 1\n4 8 1 7 2\n4 2 1 5 9\n4 9 1 6 2\n4 3 9 4 8\n4 8 2 7 3"
},
{
"input": "10",
"output": "25\n3 10 1 2\n4 10 2 9 3\n4 9 3 8 4\n4 8 4 7 5\n3 5 6 7\n3 1 2 3\n4 1 3 10 4\n4 10 4 9 5\n4 9 5 8 6\n3 6 7 8\n3 2 3 4\n4 2 4 1 5\n4 1 5 10 6\n4 10 6 9 7\n3 7 8 9\n3 3 4 5\n4 3 5 2 6\n4 2 6 1 7\n4 1 7 10 8\n3 8 9 10\n3 4 5 6\n4 4 6 3 7\n4 3 7 2 8\n4 2 8 1 9\n3 9 10 1"
},
{
"input": "298",
"output": "22201\n3 298 1 2\n4 298 2 297 3\n4 297 3 296 4\n4 296 4 295 5\n4 295 5 294 6\n4 294 6 293 7\n4 293 7 292 8\n4 292 8 291 9\n4 291 9 290 10\n4 290 10 289 11\n4 289 11 288 12\n4 288 12 287 13\n4 287 13 286 14\n4 286 14 285 15\n4 285 15 284 16\n4 284 16 283 17\n4 283 17 282 18\n4 282 18 281 19\n4 281 19 280 20\n4 280 20 279 21\n4 279 21 278 22\n4 278 22 277 23\n4 277 23 276 24\n4 276 24 275 25\n4 275 25 274 26\n4 274 26 273 27\n4 273 27 272 28\n4 272 28 271 29\n4 271 29 270 30\n4 270 30 269 31\n4 269 31 268 32..."
},
{
"input": "297",
"output": "22052\n3 1 2 3\n4 1 3 297 4\n4 297 4 296 5\n4 296 5 295 6\n4 295 6 294 7\n4 294 7 293 8\n4 293 8 292 9\n4 292 9 291 10\n4 291 10 290 11\n4 290 11 289 12\n4 289 12 288 13\n4 288 13 287 14\n4 287 14 286 15\n4 286 15 285 16\n4 285 16 284 17\n4 284 17 283 18\n4 283 18 282 19\n4 282 19 281 20\n4 281 20 280 21\n4 280 21 279 22\n4 279 22 278 23\n4 278 23 277 24\n4 277 24 276 25\n4 276 25 275 26\n4 275 26 274 27\n4 274 27 273 28\n4 273 28 272 29\n4 272 29 271 30\n4 271 30 270 31\n4 270 31 269 32\n4 269 32 268 33\n..."
},
{
"input": "11",
"output": "30\n4 2 3 1 4\n4 1 4 11 5\n4 3 4 2 5\n4 2 5 1 6\n4 4 5 3 6\n4 3 6 2 7\n4 5 6 4 7\n4 4 7 3 8\n4 6 7 5 8\n4 5 8 4 9\n4 7 8 6 9\n4 6 9 5 10\n4 8 9 7 10\n4 7 10 6 11\n4 9 10 8 11\n4 8 11 7 1\n4 10 11 9 1\n4 9 1 8 2\n4 11 1 10 2\n4 10 2 9 3\n3 2 7 8\n3 1 7 6\n3 3 8 9\n3 11 6 5\n3 4 9 10\n3 10 5 4\n3 3 2 1\n3 11 1 2\n3 4 3 11\n3 10 11 3"
},
{
"input": "14",
"output": "49\n3 14 1 2\n4 14 2 13 3\n4 13 3 12 4\n4 12 4 11 5\n4 11 5 10 6\n4 10 6 9 7\n3 7 8 9\n3 1 2 3\n4 1 3 14 4\n4 14 4 13 5\n4 13 5 12 6\n4 12 6 11 7\n4 11 7 10 8\n3 8 9 10\n3 2 3 4\n4 2 4 1 5\n4 1 5 14 6\n4 14 6 13 7\n4 13 7 12 8\n4 12 8 11 9\n3 9 10 11\n3 3 4 5\n4 3 5 2 6\n4 2 6 1 7\n4 1 7 14 8\n4 14 8 13 9\n4 13 9 12 10\n3 10 11 12\n3 4 5 6\n4 4 6 3 7\n4 3 7 2 8\n4 2 8 1 9\n4 1 9 14 10\n4 14 10 13 11\n3 11 12 13\n3 5 6 7\n4 5 7 4 8\n4 4 8 3 9\n4 3 9 2 10\n4 2 10 1 11\n4 1 11 14 12\n3 12 13 14\n3 6 7 8\n4 6 ..."
},
{
"input": "21",
"output": "110\n3 1 2 3\n4 1 3 21 4\n4 21 4 20 5\n4 20 5 19 6\n4 19 6 18 7\n3 2 3 4\n4 2 4 1 5\n4 1 5 21 6\n4 21 6 20 7\n4 20 7 19 8\n3 3 4 5\n4 3 5 2 6\n4 2 6 1 7\n4 1 7 21 8\n4 21 8 20 9\n3 4 5 6\n4 4 6 3 7\n4 3 7 2 8\n4 2 8 1 9\n4 1 9 21 10\n3 5 6 7\n4 5 7 4 8\n4 4 8 3 9\n4 3 9 2 10\n4 2 10 1 11\n3 6 7 8\n4 6 8 5 9\n4 5 9 4 10\n4 4 10 3 11\n4 3 11 2 12\n3 7 8 9\n4 7 9 6 10\n4 6 10 5 11\n4 5 11 4 12\n4 4 12 3 13\n3 8 9 10\n4 8 10 7 11\n4 7 11 6 12\n4 6 12 5 13\n4 5 13 4 14\n3 9 10 11\n4 9 11 8 12\n4 8 12 7 13\n4 7 ..."
},
{
"input": "28",
"output": "196\n3 28 1 2\n4 28 2 27 3\n4 27 3 26 4\n4 26 4 25 5\n4 25 5 24 6\n4 24 6 23 7\n4 23 7 22 8\n4 22 8 21 9\n4 21 9 20 10\n4 20 10 19 11\n4 19 11 18 12\n4 18 12 17 13\n4 17 13 16 14\n3 14 15 16\n3 1 2 3\n4 1 3 28 4\n4 28 4 27 5\n4 27 5 26 6\n4 26 6 25 7\n4 25 7 24 8\n4 24 8 23 9\n4 23 9 22 10\n4 22 10 21 11\n4 21 11 20 12\n4 20 12 19 13\n4 19 13 18 14\n4 18 14 17 15\n3 15 16 17\n3 2 3 4\n4 2 4 1 5\n4 1 5 28 6\n4 28 6 27 7\n4 27 7 26 8\n4 26 8 25 9\n4 25 9 24 10\n4 24 10 23 11\n4 23 11 22 12\n4 22 12 21 13\n4 ..."
},
{
"input": "35",
"output": "306\n4 2 3 1 4\n4 1 4 35 5\n4 35 5 34 6\n4 34 6 33 7\n4 33 7 32 8\n4 32 8 31 9\n4 31 9 30 10\n4 30 10 29 11\n4 3 4 2 5\n4 2 5 1 6\n4 1 6 35 7\n4 35 7 34 8\n4 34 8 33 9\n4 33 9 32 10\n4 32 10 31 11\n4 31 11 30 12\n4 4 5 3 6\n4 3 6 2 7\n4 2 7 1 8\n4 1 8 35 9\n4 35 9 34 10\n4 34 10 33 11\n4 33 11 32 12\n4 32 12 31 13\n4 5 6 4 7\n4 4 7 3 8\n4 3 8 2 9\n4 2 9 1 10\n4 1 10 35 11\n4 35 11 34 12\n4 34 12 33 13\n4 33 13 32 14\n4 6 7 5 8\n4 5 8 4 9\n4 4 9 3 10\n4 3 10 2 11\n4 2 11 1 12\n4 1 12 35 13\n4 35 13 34 14\n4..."
},
{
"input": "42",
"output": "441\n3 42 1 2\n4 42 2 41 3\n4 41 3 40 4\n4 40 4 39 5\n4 39 5 38 6\n4 38 6 37 7\n4 37 7 36 8\n4 36 8 35 9\n4 35 9 34 10\n4 34 10 33 11\n4 33 11 32 12\n4 32 12 31 13\n4 31 13 30 14\n4 30 14 29 15\n4 29 15 28 16\n4 28 16 27 17\n4 27 17 26 18\n4 26 18 25 19\n4 25 19 24 20\n4 24 20 23 21\n3 21 22 23\n3 1 2 3\n4 1 3 42 4\n4 42 4 41 5\n4 41 5 40 6\n4 40 6 39 7\n4 39 7 38 8\n4 38 8 37 9\n4 37 9 36 10\n4 36 10 35 11\n4 35 11 34 12\n4 34 12 33 13\n4 33 13 32 14\n4 32 14 31 15\n4 31 15 30 16\n4 30 16 29 17\n4 29 17 2..."
},
{
"input": "49",
"output": "600\n3 1 2 3\n4 1 3 49 4\n4 49 4 48 5\n4 48 5 47 6\n4 47 6 46 7\n4 46 7 45 8\n4 45 8 44 9\n4 44 9 43 10\n4 43 10 42 11\n4 42 11 41 12\n4 41 12 40 13\n4 40 13 39 14\n3 2 3 4\n4 2 4 1 5\n4 1 5 49 6\n4 49 6 48 7\n4 48 7 47 8\n4 47 8 46 9\n4 46 9 45 10\n4 45 10 44 11\n4 44 11 43 12\n4 43 12 42 13\n4 42 13 41 14\n4 41 14 40 15\n3 3 4 5\n4 3 5 2 6\n4 2 6 1 7\n4 1 7 49 8\n4 49 8 48 9\n4 48 9 47 10\n4 47 10 46 11\n4 46 11 45 12\n4 45 12 44 13\n4 44 13 43 14\n4 43 14 42 15\n4 42 15 41 16\n3 4 5 6\n4 4 6 3 7\n4 3 7 ..."
},
{
"input": "56",
"output": "784\n3 56 1 2\n4 56 2 55 3\n4 55 3 54 4\n4 54 4 53 5\n4 53 5 52 6\n4 52 6 51 7\n4 51 7 50 8\n4 50 8 49 9\n4 49 9 48 10\n4 48 10 47 11\n4 47 11 46 12\n4 46 12 45 13\n4 45 13 44 14\n4 44 14 43 15\n4 43 15 42 16\n4 42 16 41 17\n4 41 17 40 18\n4 40 18 39 19\n4 39 19 38 20\n4 38 20 37 21\n4 37 21 36 22\n4 36 22 35 23\n4 35 23 34 24\n4 34 24 33 25\n4 33 25 32 26\n4 32 26 31 27\n4 31 27 30 28\n3 28 29 30\n3 1 2 3\n4 1 3 56 4\n4 56 4 55 5\n4 55 5 54 6\n4 54 6 53 7\n4 53 7 52 8\n4 52 8 51 9\n4 51 9 50 10\n4 50 10 4..."
},
{
"input": "63",
"output": "992\n4 2 3 1 4\n4 1 4 63 5\n4 63 5 62 6\n4 62 6 61 7\n4 61 7 60 8\n4 60 8 59 9\n4 59 9 58 10\n4 58 10 57 11\n4 57 11 56 12\n4 56 12 55 13\n4 55 13 54 14\n4 54 14 53 15\n4 53 15 52 16\n4 52 16 51 17\n4 51 17 50 18\n4 3 4 2 5\n4 2 5 1 6\n4 1 6 63 7\n4 63 7 62 8\n4 62 8 61 9\n4 61 9 60 10\n4 60 10 59 11\n4 59 11 58 12\n4 58 12 57 13\n4 57 13 56 14\n4 56 14 55 15\n4 55 15 54 16\n4 54 16 53 17\n4 53 17 52 18\n4 52 18 51 19\n4 4 5 3 6\n4 3 6 2 7\n4 2 7 1 8\n4 1 8 63 9\n4 63 9 62 10\n4 62 10 61 11\n4 61 11 60 12\n..."
},
{
"input": "70",
"output": "1225\n3 70 1 2\n4 70 2 69 3\n4 69 3 68 4\n4 68 4 67 5\n4 67 5 66 6\n4 66 6 65 7\n4 65 7 64 8\n4 64 8 63 9\n4 63 9 62 10\n4 62 10 61 11\n4 61 11 60 12\n4 60 12 59 13\n4 59 13 58 14\n4 58 14 57 15\n4 57 15 56 16\n4 56 16 55 17\n4 55 17 54 18\n4 54 18 53 19\n4 53 19 52 20\n4 52 20 51 21\n4 51 21 50 22\n4 50 22 49 23\n4 49 23 48 24\n4 48 24 47 25\n4 47 25 46 26\n4 46 26 45 27\n4 45 27 44 28\n4 44 28 43 29\n4 43 29 42 30\n4 42 30 41 31\n4 41 31 40 32\n4 40 32 39 33\n4 39 33 38 34\n4 38 34 37 35\n3 35 36 37\n3 1..."
},
{
"input": "77",
"output": "1482\n3 1 2 3\n4 1 3 77 4\n4 77 4 76 5\n4 76 5 75 6\n4 75 6 74 7\n4 74 7 73 8\n4 73 8 72 9\n4 72 9 71 10\n4 71 10 70 11\n4 70 11 69 12\n4 69 12 68 13\n4 68 13 67 14\n4 67 14 66 15\n4 66 15 65 16\n4 65 16 64 17\n4 64 17 63 18\n4 63 18 62 19\n4 62 19 61 20\n4 61 20 60 21\n3 2 3 4\n4 2 4 1 5\n4 1 5 77 6\n4 77 6 76 7\n4 76 7 75 8\n4 75 8 74 9\n4 74 9 73 10\n4 73 10 72 11\n4 72 11 71 12\n4 71 12 70 13\n4 70 13 69 14\n4 69 14 68 15\n4 68 15 67 16\n4 67 16 66 17\n4 66 17 65 18\n4 65 18 64 19\n4 64 19 63 20\n4 63 ..."
},
{
"input": "84",
"output": "1764\n3 84 1 2\n4 84 2 83 3\n4 83 3 82 4\n4 82 4 81 5\n4 81 5 80 6\n4 80 6 79 7\n4 79 7 78 8\n4 78 8 77 9\n4 77 9 76 10\n4 76 10 75 11\n4 75 11 74 12\n4 74 12 73 13\n4 73 13 72 14\n4 72 14 71 15\n4 71 15 70 16\n4 70 16 69 17\n4 69 17 68 18\n4 68 18 67 19\n4 67 19 66 20\n4 66 20 65 21\n4 65 21 64 22\n4 64 22 63 23\n4 63 23 62 24\n4 62 24 61 25\n4 61 25 60 26\n4 60 26 59 27\n4 59 27 58 28\n4 58 28 57 29\n4 57 29 56 30\n4 56 30 55 31\n4 55 31 54 32\n4 54 32 53 33\n4 53 33 52 34\n4 52 34 51 35\n4 51 35 50 36\n..."
},
{
"input": "91",
"output": "2070\n4 2 3 1 4\n4 1 4 91 5\n4 91 5 90 6\n4 90 6 89 7\n4 89 7 88 8\n4 88 8 87 9\n4 87 9 86 10\n4 86 10 85 11\n4 85 11 84 12\n4 84 12 83 13\n4 83 13 82 14\n4 82 14 81 15\n4 81 15 80 16\n4 80 16 79 17\n4 79 17 78 18\n4 78 18 77 19\n4 77 19 76 20\n4 76 20 75 21\n4 75 21 74 22\n4 74 22 73 23\n4 73 23 72 24\n4 72 24 71 25\n4 3 4 2 5\n4 2 5 1 6\n4 1 6 91 7\n4 91 7 90 8\n4 90 8 89 9\n4 89 9 88 10\n4 88 10 87 11\n4 87 11 86 12\n4 86 12 85 13\n4 85 13 84 14\n4 84 14 83 15\n4 83 15 82 16\n4 82 16 81 17\n4 81 17 80 1..."
},
{
"input": "98",
"output": "2401\n3 98 1 2\n4 98 2 97 3\n4 97 3 96 4\n4 96 4 95 5\n4 95 5 94 6\n4 94 6 93 7\n4 93 7 92 8\n4 92 8 91 9\n4 91 9 90 10\n4 90 10 89 11\n4 89 11 88 12\n4 88 12 87 13\n4 87 13 86 14\n4 86 14 85 15\n4 85 15 84 16\n4 84 16 83 17\n4 83 17 82 18\n4 82 18 81 19\n4 81 19 80 20\n4 80 20 79 21\n4 79 21 78 22\n4 78 22 77 23\n4 77 23 76 24\n4 76 24 75 25\n4 75 25 74 26\n4 74 26 73 27\n4 73 27 72 28\n4 72 28 71 29\n4 71 29 70 30\n4 70 30 69 31\n4 69 31 68 32\n4 68 32 67 33\n4 67 33 66 34\n4 66 34 65 35\n4 65 35 64 36\n..."
},
{
"input": "105",
"output": "2756\n3 1 2 3\n4 1 3 105 4\n4 105 4 104 5\n4 104 5 103 6\n4 103 6 102 7\n4 102 7 101 8\n4 101 8 100 9\n4 100 9 99 10\n4 99 10 98 11\n4 98 11 97 12\n4 97 12 96 13\n4 96 13 95 14\n4 95 14 94 15\n4 94 15 93 16\n4 93 16 92 17\n4 92 17 91 18\n4 91 18 90 19\n4 90 19 89 20\n4 89 20 88 21\n4 88 21 87 22\n4 87 22 86 23\n4 86 23 85 24\n4 85 24 84 25\n4 84 25 83 26\n4 83 26 82 27\n4 82 27 81 28\n3 2 3 4\n4 2 4 1 5\n4 1 5 105 6\n4 105 6 104 7\n4 104 7 103 8\n4 103 8 102 9\n4 102 9 101 10\n4 101 10 100 11\n4 100 11 99 ..."
},
{
"input": "112",
"output": "3136\n3 112 1 2\n4 112 2 111 3\n4 111 3 110 4\n4 110 4 109 5\n4 109 5 108 6\n4 108 6 107 7\n4 107 7 106 8\n4 106 8 105 9\n4 105 9 104 10\n4 104 10 103 11\n4 103 11 102 12\n4 102 12 101 13\n4 101 13 100 14\n4 100 14 99 15\n4 99 15 98 16\n4 98 16 97 17\n4 97 17 96 18\n4 96 18 95 19\n4 95 19 94 20\n4 94 20 93 21\n4 93 21 92 22\n4 92 22 91 23\n4 91 23 90 24\n4 90 24 89 25\n4 89 25 88 26\n4 88 26 87 27\n4 87 27 86 28\n4 86 28 85 29\n4 85 29 84 30\n4 84 30 83 31\n4 83 31 82 32\n4 82 32 81 33\n4 81 33 80 34\n4 80..."
},
{
"input": "119",
"output": "3540\n4 2 3 1 4\n4 1 4 119 5\n4 119 5 118 6\n4 118 6 117 7\n4 117 7 116 8\n4 116 8 115 9\n4 115 9 114 10\n4 114 10 113 11\n4 113 11 112 12\n4 112 12 111 13\n4 111 13 110 14\n4 110 14 109 15\n4 109 15 108 16\n4 108 16 107 17\n4 107 17 106 18\n4 106 18 105 19\n4 105 19 104 20\n4 104 20 103 21\n4 103 21 102 22\n4 102 22 101 23\n4 101 23 100 24\n4 100 24 99 25\n4 99 25 98 26\n4 98 26 97 27\n4 97 27 96 28\n4 96 28 95 29\n4 95 29 94 30\n4 94 30 93 31\n4 93 31 92 32\n4 3 4 2 5\n4 2 5 1 6\n4 1 6 119 7\n4 119 7 118..."
},
{
"input": "126",
"output": "3969\n3 126 1 2\n4 126 2 125 3\n4 125 3 124 4\n4 124 4 123 5\n4 123 5 122 6\n4 122 6 121 7\n4 121 7 120 8\n4 120 8 119 9\n4 119 9 118 10\n4 118 10 117 11\n4 117 11 116 12\n4 116 12 115 13\n4 115 13 114 14\n4 114 14 113 15\n4 113 15 112 16\n4 112 16 111 17\n4 111 17 110 18\n4 110 18 109 19\n4 109 19 108 20\n4 108 20 107 21\n4 107 21 106 22\n4 106 22 105 23\n4 105 23 104 24\n4 104 24 103 25\n4 103 25 102 26\n4 102 26 101 27\n4 101 27 100 28\n4 100 28 99 29\n4 99 29 98 30\n4 98 30 97 31\n4 97 31 96 32\n4 96 3..."
},
{
"input": "133",
"output": "4422\n3 1 2 3\n4 1 3 133 4\n4 133 4 132 5\n4 132 5 131 6\n4 131 6 130 7\n4 130 7 129 8\n4 129 8 128 9\n4 128 9 127 10\n4 127 10 126 11\n4 126 11 125 12\n4 125 12 124 13\n4 124 13 123 14\n4 123 14 122 15\n4 122 15 121 16\n4 121 16 120 17\n4 120 17 119 18\n4 119 18 118 19\n4 118 19 117 20\n4 117 20 116 21\n4 116 21 115 22\n4 115 22 114 23\n4 114 23 113 24\n4 113 24 112 25\n4 112 25 111 26\n4 111 26 110 27\n4 110 27 109 28\n4 109 28 108 29\n4 108 29 107 30\n4 107 30 106 31\n4 106 31 105 32\n4 105 32 104 33\n4..."
},
{
"input": "140",
"output": "4900\n3 140 1 2\n4 140 2 139 3\n4 139 3 138 4\n4 138 4 137 5\n4 137 5 136 6\n4 136 6 135 7\n4 135 7 134 8\n4 134 8 133 9\n4 133 9 132 10\n4 132 10 131 11\n4 131 11 130 12\n4 130 12 129 13\n4 129 13 128 14\n4 128 14 127 15\n4 127 15 126 16\n4 126 16 125 17\n4 125 17 124 18\n4 124 18 123 19\n4 123 19 122 20\n4 122 20 121 21\n4 121 21 120 22\n4 120 22 119 23\n4 119 23 118 24\n4 118 24 117 25\n4 117 25 116 26\n4 116 26 115 27\n4 115 27 114 28\n4 114 28 113 29\n4 113 29 112 30\n4 112 30 111 31\n4 111 31 110 32\n..."
},
{
"input": "147",
"output": "5402\n4 2 3 1 4\n4 1 4 147 5\n4 147 5 146 6\n4 146 6 145 7\n4 145 7 144 8\n4 144 8 143 9\n4 143 9 142 10\n4 142 10 141 11\n4 141 11 140 12\n4 140 12 139 13\n4 139 13 138 14\n4 138 14 137 15\n4 137 15 136 16\n4 136 16 135 17\n4 135 17 134 18\n4 134 18 133 19\n4 133 19 132 20\n4 132 20 131 21\n4 131 21 130 22\n4 130 22 129 23\n4 129 23 128 24\n4 128 24 127 25\n4 127 25 126 26\n4 126 26 125 27\n4 125 27 124 28\n4 124 28 123 29\n4 123 29 122 30\n4 122 30 121 31\n4 121 31 120 32\n4 120 32 119 33\n4 119 33 118 3..."
},
{
"input": "154",
"output": "5929\n3 154 1 2\n4 154 2 153 3\n4 153 3 152 4\n4 152 4 151 5\n4 151 5 150 6\n4 150 6 149 7\n4 149 7 148 8\n4 148 8 147 9\n4 147 9 146 10\n4 146 10 145 11\n4 145 11 144 12\n4 144 12 143 13\n4 143 13 142 14\n4 142 14 141 15\n4 141 15 140 16\n4 140 16 139 17\n4 139 17 138 18\n4 138 18 137 19\n4 137 19 136 20\n4 136 20 135 21\n4 135 21 134 22\n4 134 22 133 23\n4 133 23 132 24\n4 132 24 131 25\n4 131 25 130 26\n4 130 26 129 27\n4 129 27 128 28\n4 128 28 127 29\n4 127 29 126 30\n4 126 30 125 31\n4 125 31 124 32\n..."
},
{
"input": "161",
"output": "6480\n3 1 2 3\n4 1 3 161 4\n4 161 4 160 5\n4 160 5 159 6\n4 159 6 158 7\n4 158 7 157 8\n4 157 8 156 9\n4 156 9 155 10\n4 155 10 154 11\n4 154 11 153 12\n4 153 12 152 13\n4 152 13 151 14\n4 151 14 150 15\n4 150 15 149 16\n4 149 16 148 17\n4 148 17 147 18\n4 147 18 146 19\n4 146 19 145 20\n4 145 20 144 21\n4 144 21 143 22\n4 143 22 142 23\n4 142 23 141 24\n4 141 24 140 25\n4 140 25 139 26\n4 139 26 138 27\n4 138 27 137 28\n4 137 28 136 29\n4 136 29 135 30\n4 135 30 134 31\n4 134 31 133 32\n4 133 32 132 33\n4..."
},
{
"input": "168",
"output": "7056\n3 168 1 2\n4 168 2 167 3\n4 167 3 166 4\n4 166 4 165 5\n4 165 5 164 6\n4 164 6 163 7\n4 163 7 162 8\n4 162 8 161 9\n4 161 9 160 10\n4 160 10 159 11\n4 159 11 158 12\n4 158 12 157 13\n4 157 13 156 14\n4 156 14 155 15\n4 155 15 154 16\n4 154 16 153 17\n4 153 17 152 18\n4 152 18 151 19\n4 151 19 150 20\n4 150 20 149 21\n4 149 21 148 22\n4 148 22 147 23\n4 147 23 146 24\n4 146 24 145 25\n4 145 25 144 26\n4 144 26 143 27\n4 143 27 142 28\n4 142 28 141 29\n4 141 29 140 30\n4 140 30 139 31\n4 139 31 138 32\n..."
},
{
"input": "175",
"output": "7656\n4 2 3 1 4\n4 1 4 175 5\n4 175 5 174 6\n4 174 6 173 7\n4 173 7 172 8\n4 172 8 171 9\n4 171 9 170 10\n4 170 10 169 11\n4 169 11 168 12\n4 168 12 167 13\n4 167 13 166 14\n4 166 14 165 15\n4 165 15 164 16\n4 164 16 163 17\n4 163 17 162 18\n4 162 18 161 19\n4 161 19 160 20\n4 160 20 159 21\n4 159 21 158 22\n4 158 22 157 23\n4 157 23 156 24\n4 156 24 155 25\n4 155 25 154 26\n4 154 26 153 27\n4 153 27 152 28\n4 152 28 151 29\n4 151 29 150 30\n4 150 30 149 31\n4 149 31 148 32\n4 148 32 147 33\n4 147 33 146 3..."
},
{
"input": "182",
"output": "8281\n3 182 1 2\n4 182 2 181 3\n4 181 3 180 4\n4 180 4 179 5\n4 179 5 178 6\n4 178 6 177 7\n4 177 7 176 8\n4 176 8 175 9\n4 175 9 174 10\n4 174 10 173 11\n4 173 11 172 12\n4 172 12 171 13\n4 171 13 170 14\n4 170 14 169 15\n4 169 15 168 16\n4 168 16 167 17\n4 167 17 166 18\n4 166 18 165 19\n4 165 19 164 20\n4 164 20 163 21\n4 163 21 162 22\n4 162 22 161 23\n4 161 23 160 24\n4 160 24 159 25\n4 159 25 158 26\n4 158 26 157 27\n4 157 27 156 28\n4 156 28 155 29\n4 155 29 154 30\n4 154 30 153 31\n4 153 31 152 32\n..."
},
{
"input": "189",
"output": "8930\n3 1 2 3\n4 1 3 189 4\n4 189 4 188 5\n4 188 5 187 6\n4 187 6 186 7\n4 186 7 185 8\n4 185 8 184 9\n4 184 9 183 10\n4 183 10 182 11\n4 182 11 181 12\n4 181 12 180 13\n4 180 13 179 14\n4 179 14 178 15\n4 178 15 177 16\n4 177 16 176 17\n4 176 17 175 18\n4 175 18 174 19\n4 174 19 173 20\n4 173 20 172 21\n4 172 21 171 22\n4 171 22 170 23\n4 170 23 169 24\n4 169 24 168 25\n4 168 25 167 26\n4 167 26 166 27\n4 166 27 165 28\n4 165 28 164 29\n4 164 29 163 30\n4 163 30 162 31\n4 162 31 161 32\n4 161 32 160 33\n4..."
},
{
"input": "196",
"output": "9604\n3 196 1 2\n4 196 2 195 3\n4 195 3 194 4\n4 194 4 193 5\n4 193 5 192 6\n4 192 6 191 7\n4 191 7 190 8\n4 190 8 189 9\n4 189 9 188 10\n4 188 10 187 11\n4 187 11 186 12\n4 186 12 185 13\n4 185 13 184 14\n4 184 14 183 15\n4 183 15 182 16\n4 182 16 181 17\n4 181 17 180 18\n4 180 18 179 19\n4 179 19 178 20\n4 178 20 177 21\n4 177 21 176 22\n4 176 22 175 23\n4 175 23 174 24\n4 174 24 173 25\n4 173 25 172 26\n4 172 26 171 27\n4 171 27 170 28\n4 170 28 169 29\n4 169 29 168 30\n4 168 30 167 31\n4 167 31 166 32\n..."
},
{
"input": "203",
"output": "10302\n4 2 3 1 4\n4 1 4 203 5\n4 203 5 202 6\n4 202 6 201 7\n4 201 7 200 8\n4 200 8 199 9\n4 199 9 198 10\n4 198 10 197 11\n4 197 11 196 12\n4 196 12 195 13\n4 195 13 194 14\n4 194 14 193 15\n4 193 15 192 16\n4 192 16 191 17\n4 191 17 190 18\n4 190 18 189 19\n4 189 19 188 20\n4 188 20 187 21\n4 187 21 186 22\n4 186 22 185 23\n4 185 23 184 24\n4 184 24 183 25\n4 183 25 182 26\n4 182 26 181 27\n4 181 27 180 28\n4 180 28 179 29\n4 179 29 178 30\n4 178 30 177 31\n4 177 31 176 32\n4 176 32 175 33\n4 175 33 174 ..."
},
{
"input": "210",
"output": "11025\n3 210 1 2\n4 210 2 209 3\n4 209 3 208 4\n4 208 4 207 5\n4 207 5 206 6\n4 206 6 205 7\n4 205 7 204 8\n4 204 8 203 9\n4 203 9 202 10\n4 202 10 201 11\n4 201 11 200 12\n4 200 12 199 13\n4 199 13 198 14\n4 198 14 197 15\n4 197 15 196 16\n4 196 16 195 17\n4 195 17 194 18\n4 194 18 193 19\n4 193 19 192 20\n4 192 20 191 21\n4 191 21 190 22\n4 190 22 189 23\n4 189 23 188 24\n4 188 24 187 25\n4 187 25 186 26\n4 186 26 185 27\n4 185 27 184 28\n4 184 28 183 29\n4 183 29 182 30\n4 182 30 181 31\n4 181 31 180 32..."
},
{
"input": "217",
"output": "11772\n3 1 2 3\n4 1 3 217 4\n4 217 4 216 5\n4 216 5 215 6\n4 215 6 214 7\n4 214 7 213 8\n4 213 8 212 9\n4 212 9 211 10\n4 211 10 210 11\n4 210 11 209 12\n4 209 12 208 13\n4 208 13 207 14\n4 207 14 206 15\n4 206 15 205 16\n4 205 16 204 17\n4 204 17 203 18\n4 203 18 202 19\n4 202 19 201 20\n4 201 20 200 21\n4 200 21 199 22\n4 199 22 198 23\n4 198 23 197 24\n4 197 24 196 25\n4 196 25 195 26\n4 195 26 194 27\n4 194 27 193 28\n4 193 28 192 29\n4 192 29 191 30\n4 191 30 190 31\n4 190 31 189 32\n4 189 32 188 33\n..."
},
{
"input": "224",
"output": "12544\n3 224 1 2\n4 224 2 223 3\n4 223 3 222 4\n4 222 4 221 5\n4 221 5 220 6\n4 220 6 219 7\n4 219 7 218 8\n4 218 8 217 9\n4 217 9 216 10\n4 216 10 215 11\n4 215 11 214 12\n4 214 12 213 13\n4 213 13 212 14\n4 212 14 211 15\n4 211 15 210 16\n4 210 16 209 17\n4 209 17 208 18\n4 208 18 207 19\n4 207 19 206 20\n4 206 20 205 21\n4 205 21 204 22\n4 204 22 203 23\n4 203 23 202 24\n4 202 24 201 25\n4 201 25 200 26\n4 200 26 199 27\n4 199 27 198 28\n4 198 28 197 29\n4 197 29 196 30\n4 196 30 195 31\n4 195 31 194 32..."
},
{
"input": "231",
"output": "13340\n4 2 3 1 4\n4 1 4 231 5\n4 231 5 230 6\n4 230 6 229 7\n4 229 7 228 8\n4 228 8 227 9\n4 227 9 226 10\n4 226 10 225 11\n4 225 11 224 12\n4 224 12 223 13\n4 223 13 222 14\n4 222 14 221 15\n4 221 15 220 16\n4 220 16 219 17\n4 219 17 218 18\n4 218 18 217 19\n4 217 19 216 20\n4 216 20 215 21\n4 215 21 214 22\n4 214 22 213 23\n4 213 23 212 24\n4 212 24 211 25\n4 211 25 210 26\n4 210 26 209 27\n4 209 27 208 28\n4 208 28 207 29\n4 207 29 206 30\n4 206 30 205 31\n4 205 31 204 32\n4 204 32 203 33\n4 203 33 202 ..."
},
{
"input": "238",
"output": "14161\n3 238 1 2\n4 238 2 237 3\n4 237 3 236 4\n4 236 4 235 5\n4 235 5 234 6\n4 234 6 233 7\n4 233 7 232 8\n4 232 8 231 9\n4 231 9 230 10\n4 230 10 229 11\n4 229 11 228 12\n4 228 12 227 13\n4 227 13 226 14\n4 226 14 225 15\n4 225 15 224 16\n4 224 16 223 17\n4 223 17 222 18\n4 222 18 221 19\n4 221 19 220 20\n4 220 20 219 21\n4 219 21 218 22\n4 218 22 217 23\n4 217 23 216 24\n4 216 24 215 25\n4 215 25 214 26\n4 214 26 213 27\n4 213 27 212 28\n4 212 28 211 29\n4 211 29 210 30\n4 210 30 209 31\n4 209 31 208 32..."
},
{
"input": "245",
"output": "15006\n3 1 2 3\n4 1 3 245 4\n4 245 4 244 5\n4 244 5 243 6\n4 243 6 242 7\n4 242 7 241 8\n4 241 8 240 9\n4 240 9 239 10\n4 239 10 238 11\n4 238 11 237 12\n4 237 12 236 13\n4 236 13 235 14\n4 235 14 234 15\n4 234 15 233 16\n4 233 16 232 17\n4 232 17 231 18\n4 231 18 230 19\n4 230 19 229 20\n4 229 20 228 21\n4 228 21 227 22\n4 227 22 226 23\n4 226 23 225 24\n4 225 24 224 25\n4 224 25 223 26\n4 223 26 222 27\n4 222 27 221 28\n4 221 28 220 29\n4 220 29 219 30\n4 219 30 218 31\n4 218 31 217 32\n4 217 32 216 33\n..."
},
{
"input": "252",
"output": "15876\n3 252 1 2\n4 252 2 251 3\n4 251 3 250 4\n4 250 4 249 5\n4 249 5 248 6\n4 248 6 247 7\n4 247 7 246 8\n4 246 8 245 9\n4 245 9 244 10\n4 244 10 243 11\n4 243 11 242 12\n4 242 12 241 13\n4 241 13 240 14\n4 240 14 239 15\n4 239 15 238 16\n4 238 16 237 17\n4 237 17 236 18\n4 236 18 235 19\n4 235 19 234 20\n4 234 20 233 21\n4 233 21 232 22\n4 232 22 231 23\n4 231 23 230 24\n4 230 24 229 25\n4 229 25 228 26\n4 228 26 227 27\n4 227 27 226 28\n4 226 28 225 29\n4 225 29 224 30\n4 224 30 223 31\n4 223 31 222 32..."
},
{
"input": "259",
"output": "16770\n4 2 3 1 4\n4 1 4 259 5\n4 259 5 258 6\n4 258 6 257 7\n4 257 7 256 8\n4 256 8 255 9\n4 255 9 254 10\n4 254 10 253 11\n4 253 11 252 12\n4 252 12 251 13\n4 251 13 250 14\n4 250 14 249 15\n4 249 15 248 16\n4 248 16 247 17\n4 247 17 246 18\n4 246 18 245 19\n4 245 19 244 20\n4 244 20 243 21\n4 243 21 242 22\n4 242 22 241 23\n4 241 23 240 24\n4 240 24 239 25\n4 239 25 238 26\n4 238 26 237 27\n4 237 27 236 28\n4 236 28 235 29\n4 235 29 234 30\n4 234 30 233 31\n4 233 31 232 32\n4 232 32 231 33\n4 231 33 230 ..."
},
{
"input": "266",
"output": "17689\n3 266 1 2\n4 266 2 265 3\n4 265 3 264 4\n4 264 4 263 5\n4 263 5 262 6\n4 262 6 261 7\n4 261 7 260 8\n4 260 8 259 9\n4 259 9 258 10\n4 258 10 257 11\n4 257 11 256 12\n4 256 12 255 13\n4 255 13 254 14\n4 254 14 253 15\n4 253 15 252 16\n4 252 16 251 17\n4 251 17 250 18\n4 250 18 249 19\n4 249 19 248 20\n4 248 20 247 21\n4 247 21 246 22\n4 246 22 245 23\n4 245 23 244 24\n4 244 24 243 25\n4 243 25 242 26\n4 242 26 241 27\n4 241 27 240 28\n4 240 28 239 29\n4 239 29 238 30\n4 238 30 237 31\n4 237 31 236 32..."
},
{
"input": "273",
"output": "18632\n3 1 2 3\n4 1 3 273 4\n4 273 4 272 5\n4 272 5 271 6\n4 271 6 270 7\n4 270 7 269 8\n4 269 8 268 9\n4 268 9 267 10\n4 267 10 266 11\n4 266 11 265 12\n4 265 12 264 13\n4 264 13 263 14\n4 263 14 262 15\n4 262 15 261 16\n4 261 16 260 17\n4 260 17 259 18\n4 259 18 258 19\n4 258 19 257 20\n4 257 20 256 21\n4 256 21 255 22\n4 255 22 254 23\n4 254 23 253 24\n4 253 24 252 25\n4 252 25 251 26\n4 251 26 250 27\n4 250 27 249 28\n4 249 28 248 29\n4 248 29 247 30\n4 247 30 246 31\n4 246 31 245 32\n4 245 32 244 33\n..."
},
{
"input": "280",
"output": "19600\n3 280 1 2\n4 280 2 279 3\n4 279 3 278 4\n4 278 4 277 5\n4 277 5 276 6\n4 276 6 275 7\n4 275 7 274 8\n4 274 8 273 9\n4 273 9 272 10\n4 272 10 271 11\n4 271 11 270 12\n4 270 12 269 13\n4 269 13 268 14\n4 268 14 267 15\n4 267 15 266 16\n4 266 16 265 17\n4 265 17 264 18\n4 264 18 263 19\n4 263 19 262 20\n4 262 20 261 21\n4 261 21 260 22\n4 260 22 259 23\n4 259 23 258 24\n4 258 24 257 25\n4 257 25 256 26\n4 256 26 255 27\n4 255 27 254 28\n4 254 28 253 29\n4 253 29 252 30\n4 252 30 251 31\n4 251 31 250 32..."
},
{
"input": "287",
"output": "20592\n4 2 3 1 4\n4 1 4 287 5\n4 287 5 286 6\n4 286 6 285 7\n4 285 7 284 8\n4 284 8 283 9\n4 283 9 282 10\n4 282 10 281 11\n4 281 11 280 12\n4 280 12 279 13\n4 279 13 278 14\n4 278 14 277 15\n4 277 15 276 16\n4 276 16 275 17\n4 275 17 274 18\n4 274 18 273 19\n4 273 19 272 20\n4 272 20 271 21\n4 271 21 270 22\n4 270 22 269 23\n4 269 23 268 24\n4 268 24 267 25\n4 267 25 266 26\n4 266 26 265 27\n4 265 27 264 28\n4 264 28 263 29\n4 263 29 262 30\n4 262 30 261 31\n4 261 31 260 32\n4 260 32 259 33\n4 259 33 258 ..."
},
{
"input": "294",
"output": "21609\n3 294 1 2\n4 294 2 293 3\n4 293 3 292 4\n4 292 4 291 5\n4 291 5 290 6\n4 290 6 289 7\n4 289 7 288 8\n4 288 8 287 9\n4 287 9 286 10\n4 286 10 285 11\n4 285 11 284 12\n4 284 12 283 13\n4 283 13 282 14\n4 282 14 281 15\n4 281 15 280 16\n4 280 16 279 17\n4 279 17 278 18\n4 278 18 277 19\n4 277 19 276 20\n4 276 20 275 21\n4 275 21 274 22\n4 274 22 273 23\n4 273 23 272 24\n4 272 24 271 25\n4 271 25 270 26\n4 270 26 269 27\n4 269 27 268 28\n4 268 28 267 29\n4 267 29 266 30\n4 266 30 265 31\n4 265 31 264 32..."
}
] | 46 | 0 | 0 | 5,013 |
|
525 | Pasha and String | [
"constructive algorithms",
"greedy",
"math",
"strings"
] | null | null | Pasha got a very beautiful string *s* for his birthday, the string consists of lowercase Latin letters. The letters in the string are numbered from 1 to |*s*| from left to right, where |*s*| is the length of the given string.
Pasha didn't like his present very much so he decided to change it. After his birthday Pasha spent *m* days performing the following transformations on his stringΒ βΒ each day he chose integer *a**i* and reversed a piece of string (a segment) from position *a**i* to position |*s*|<=-<=*a**i*<=+<=1. It is guaranteed that 2Β·*a**i*<=β€<=|*s*|.
You face the following task: determine what Pasha's string will look like after *m* days. | The first line of the input contains Pasha's string *s* of length from 2 to 2Β·105 characters, consisting of lowercase Latin letters.
The second line contains a single integer *m* (1<=β€<=*m*<=β€<=105)Β βΒ the number of days when Pasha changed his string.
The third line contains *m* space-separated elements *a**i* (1<=β€<=*a**i*; 2Β·*a**i*<=β€<=|*s*|)Β βΒ the position from which Pasha started transforming the string on the *i*-th day. | In the first line of the output print what Pasha's string *s* will look like after *m* days. | [
"abcdef\n1\n2\n",
"vwxyz\n2\n2 2\n",
"abcdef\n3\n1 2 3\n"
] | [
"aedcbf\n",
"vwxyz\n",
"fbdcea\n"
] | none | [
{
"input": "abcdef\n1\n2",
"output": "aedcbf"
},
{
"input": "vwxyz\n2\n2 2",
"output": "vwxyz"
},
{
"input": "abcdef\n3\n1 2 3",
"output": "fbdcea"
},
{
"input": "jc\n5\n1 1 1 1 1",
"output": "cj"
},
{
"input": "wljqgdlxyc\n13\n3 4 3 3 5 4 4 2 4 4 5 3 3",
"output": "wyjldgqxlc"
},
{
"input": "keicnqmuqinhsmtudqcilocxkbqgzhbkitmqwttdyoyvcbxincwjryzknubpacsngorexaldfurondbednowemnnlphhboycfavs\n2\n5 12",
"output": "keiccyobhhphsmtudqcilocxkbqgzhbkitmqwttdyoyvcbxincwjryzknubpacsngorexaldfurondbednowemnnlniqumqnfavs"
},
{
"input": "xwcxggxvfqbdklewbxkjzibmufnaywuxsqvwakefxbbkfandvigasbhbatsxyqxicrosatfsfybedklsaztyyiuurfbrzmwumujy\n100\n14 43 30 13 8 19 33 7 8 14 15 35 5 18 44 1 35 1 18 7 50 47 9 49 28 29 39 37 27 17 19 12 5 24 37 42 37 23 35 31 10 26 5 38 40 34 42 47 2 40 43 34 16 25 14 45 35 38 46 48 49 27 49 38 10 49 5 7 3 3 41 25 24 34 37 33 17 50 48 11 40 43 48 10 9 50 18 39 32 13 26 40 37 16 45 50 27 3 7 31",
"output": "xjcxggxvfbbruliyyxkjzikdebnfyftxsorcaxqyxbtkfhbdvigasnababsxfekiwvqsauwsayfumblsaztbweukdfqrzmwumuwy"
}
] | 2,000 | 7,372,800 | 0 | 5,022 |
|
183 | Zoo | [
"brute force",
"geometry"
] | null | null | The Zoo in the Grid Kingdom is represented by an infinite grid. The Zoo has *n* observation binoculars located at the *OX* axis. For each *i* between 1 and *n*, inclusive, there exists a single binocular located at the point with coordinates (*i*,<=0). There are *m* flamingos in the Zoo, located at points with positive coordinates. The flamingos are currently sleeping and you can assume that they don't move.
In order to get a good view over the flamingos, each of the binoculars can be independently rotated to face any angle (not necessarily integer). Then, the binocular can be used to observe all flamingos that is located at the straight line passing through the binocular at the angle it is set. In other words, you can assign each binocular a direction corresponding to any straight line passing through the binocular, and the binocular will be able to see all flamingos located on that line.
Today, some kids from the prestigious Codeforces kindergarten went on a Field Study to the Zoo. Their teacher would like to set each binocular an angle to maximize the number of flamingos that can be seen by the binocular. The teacher is very interested in the sum of these values over all binoculars. Please help him find this sum. | The first line contains two space-separated integers *n* and *m* (1<=β€<=*n*<=β€<=106,<=1<=β€<=*m*<=β€<=250), denoting the number of binoculars and the number of flamingos, respectively.
Then *m* lines follow, the *i*-th line will contain two space-separated integers *x**i* and *y**i* (1<=β€<=*x**i*,<=*y**i*<=β€<=109), which means that the *i*-th flamingo is located at point (*x**i*,<=*y**i*).
All flamingos will be located at distinct points. | Print a single integer denoting the maximum total number of flamingos that can be seen by all the binoculars. | [
"5 5\n2 1\n4 1\n3 2\n4 3\n4 4\n"
] | [
"11\n"
] | This picture shows the answer to the example test case. | [
{
"input": "5 5\n2 1\n4 1\n3 2\n4 3\n4 4",
"output": "11"
},
{
"input": "3 3\n1 1\n2 10\n3 100",
"output": "3"
},
{
"input": "1 2\n450000001 500000000\n900000001 1000000000",
"output": "2"
},
{
"input": "3 6\n1 1\n1 2\n1 3\n2 1\n2 2\n3 1",
"output": "7"
},
{
"input": "3 3\n227495634 254204506\n454991267 508409012\n715803819 799841973",
"output": "4"
},
{
"input": "3 3\n96684705 23204141\n193369409 46408282\n217792636 52269809",
"output": "4"
},
{
"input": "1000000 2\n136395332 110293751\n568110113 459392523",
"output": "1000000"
},
{
"input": "3 3\n227495634 254204506\n454991267 508409012\n217792637 799841973",
"output": "4"
},
{
"input": "3 3\n333333334 1\n666666667 2\n1000000000 3",
"output": "5"
},
{
"input": "3 3\n333333334 1\n666666667 2\n999999999 3",
"output": "5"
},
{
"input": "3 3\n2 333333333\n3 666666666\n4 999999999",
"output": "5"
},
{
"input": "3 3\n2 333333333\n3 666666666\n4 1000000000",
"output": "4"
},
{
"input": "3 3\n2 333333333\n3 666666666\n4 999999998",
"output": "4"
},
{
"input": "1000000 2\n136395332 110293751\n568110113 459392523",
"output": "1000000"
},
{
"input": "1000000 2\n881456674 979172365\n878302062 975668042",
"output": "1000000"
},
{
"input": "3 10\n1000000000 1000000000\n1000000000 999999999\n1000000000 999999998\n1000000000 999999997\n1000000000 999999996\n1000000000 999999995\n1000000000 999999994\n1000000000 999999993\n1000000000 999999992\n1000000000 999999991",
"output": "3"
},
{
"input": "1000000 2\n194305 1024\n4388610 1023",
"output": "1000000"
},
{
"input": "4 5\n1 3\n2 2\n3 1\n4 2\n4 3",
"output": "7"
},
{
"input": "5 5\n2 1\n1 1\n3 1\n4 1\n4 4",
"output": "6"
}
] | 2,000 | 253,132,800 | 0 | 5,030 |
|
17 | Palisection | [
"strings"
] | E. Palisection | 2 | 128 | In an English class Nick had nothing to do at all, and remembered about wonderful strings called palindromes. We should remind you that a string is called a palindrome if it can be read the same way both from left to right and from right to left. Here are examples of such strings: Β«eyeΒ», Β«popΒ», Β«levelΒ», Β«abaΒ», Β«deedΒ», Β«racecarΒ», Β«rotorΒ», Β«madamΒ».
Nick started to look carefully for all palindromes in the text that they were reading in the class. For each occurrence of each palindrome in the text he wrote a pair β the position of the beginning and the position of the ending of this occurrence in the text. Nick called each occurrence of each palindrome he found in the text subpalindrome. When he found all the subpalindromes, he decided to find out how many different pairs among these subpalindromes cross. Two subpalindromes cross if they cover common positions in the text. No palindrome can cross itself.
Let's look at the actions, performed by Nick, by the example of text Β«babbΒ». At first he wrote out all subpalindromes:
Then Nick counted the amount of different pairs among these subpalindromes that cross. These pairs were six:
Since it's very exhausting to perform all the described actions manually, Nick asked you to help him and write a program that can find out the amount of different subpalindrome pairs that cross. Two subpalindrome pairs are regarded as different if one of the pairs contains a subpalindrome that the other does not. | The first input line contains integer *n* (1<=β€<=*n*<=β€<=2Β·106) β length of the text. The following line contains *n* lower-case Latin letters (from a to z). | In the only line output the amount of different pairs of two subpalindromes that cross each other. Output the answer modulo 51123987. | [
"4\nbabb\n",
"2\naa\n"
] | [
"6\n",
"2\n"
] | none | [] | 60 | 0 | 0 | 5,033 |
55 | Pie or die | [
"games"
] | C. Pie or die | 2 | 256 | Volodya and Vlad play the following game. There are *k* pies at the cells of *n*<=<=Γ<=<=*m* board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy. | First line contains 3 integers, separated by space: 1<=β€<=*n*,<=*m*<=β€<=100 β dimensions of the board and 0<=β€<=*k*<=β€<=100 β the number of pies. Each of the next *k* lines contains 2 integers, separated by space: 1<=β€<=*x*<=β€<=*n*, 1<=β€<=*y*<=β€<=*m* β coordinates of the corresponding pie. There could be more than one pie at a cell. | Output only one word: "YES" β if Volodya wins, "NO" β otherwise. | [
"2 2 1\n1 2\n",
"3 4 0\n",
"100 50 2\n50 25\n50 25\n"
] | [
"YES",
"NO",
"NO"
] | none | [
{
"input": "2 2 1\n1 2",
"output": "YES"
},
{
"input": "3 4 0",
"output": "NO"
},
{
"input": "100 50 2\n50 25\n50 25",
"output": "NO"
},
{
"input": "20 20 4\n10 10\n10 10\n10 10\n10 10",
"output": "NO"
},
{
"input": "15 15 1\n8 8",
"output": "NO"
},
{
"input": "8 8 2\n4 4\n5 5",
"output": "YES"
},
{
"input": "100 100 2\n50 96\n51 96",
"output": "YES"
},
{
"input": "100 100 2\n50 95\n51 95",
"output": "NO"
},
{
"input": "20 20 1\n16 10",
"output": "YES"
},
{
"input": "20 20 4\n15 9\n15 10\n15 11\n15 12",
"output": "NO"
},
{
"input": "11 11 1\n6 6",
"output": "NO"
},
{
"input": "11 11 1\n6 5",
"output": "YES"
},
{
"input": "35 13 20\n13 8\n19 8\n24 7\n20 6\n23 7\n23 6\n30 7\n29 7\n7 7\n6 8\n9 8\n29 6\n20 7\n25 6\n19 6\n23 8\n26 6\n12 6\n15 7\n6 8",
"output": "NO"
},
{
"input": "50 17 27\n17 8\n19 6\n25 8\n30 10\n22 10\n30 9\n25 8\n27 6\n19 7\n29 11\n39 8\n31 8\n39 8\n40 7\n11 8\n30 11\n32 8\n31 11\n36 12\n10 11\n32 8\n8 7\n7 12\n17 11\n27 7\n8 8\n23 12",
"output": "NO"
},
{
"input": "24 29 22\n16 6\n14 22\n7 15\n11 17\n12 22\n10 13\n12 22\n12 13\n6 16\n12 21\n11 11\n9 13\n18 22\n7 20\n13 6\n6 14\n17 10\n9 13\n7 23\n14 11\n7 22\n8 12",
"output": "NO"
},
{
"input": "32 45 3\n12 30\n27 9\n14 27",
"output": "NO"
},
{
"input": "35 15 63\n6 6\n14 9\n7 6\n25 6\n25 8\n13 9\n18 7\n20 8\n30 10\n25 10\n7 7\n18 8\n11 10\n12 6\n8 8\n6 9\n21 9\n27 10\n28 8\n28 9\n7 9\n28 9\n10 10\n29 10\n25 8\n28 7\n22 6\n13 9\n14 7\n23 9\n20 8\n28 10\n22 7\n12 8\n13 7\n27 9\n17 8\n10 8\n19 10\n6 10\n26 6\n19 8\n28 9\n15 9\n14 7\n25 10\n17 8\n21 8\n29 6\n7 6\n16 10\n7 10\n25 7\n9 9\n30 9\n23 8\n28 8\n7 10\n12 6\n20 9\n24 8\n6 6\n26 7",
"output": "NO"
},
{
"input": "41 50 37\n21 24\n20 32\n10 12\n35 7\n8 19\n30 22\n21 11\n35 12\n7 8\n16 10\n13 39\n6 43\n31 12\n16 14\n25 32\n27 21\n6 34\n22 26\n7 41\n18 13\n24 19\n9 44\n36 21\n17 16\n36 24\n6 31\n19 20\n12 19\n27 36\n6 31\n11 13\n19 9\n20 12\n25 25\n18 27\n17 36\n8 16",
"output": "NO"
},
{
"input": "96 95 31\n14 23\n70 47\n11 77\n53 66\n63 87\n3 14\n57 44\n65 69\n80 74\n49 6\n57 86\n75 8\n2 32\n75 21\n14 51\n56 46\n77 6\n17 89\n87 3\n21 18\n70 67\n47 64\n13 47\n61 33\n56 30\n28 2\n65 18\n17 90\n44 77\n54 26\n32 70",
"output": "YES"
},
{
"input": "80 51 47\n67 41\n74 7\n68 41\n6 2\n19 38\n37 28\n65 4\n6 25\n39 11\n19 34\n47 36\n62 26\n27 44\n70 45\n24 33\n41 2\n13 10\n3 17\n78 35\n53 46\n62 47\n33 17\n17 49\n2 3\n47 38\n72 35\n4 8\n32 21\n52 43\n67 12\n28 22\n53 34\n36 11\n45 45\n32 12\n5 11\n6 3\n55 21\n73 4\n55 21\n36 13\n48 18\n19 8\n70 24\n43 45\n59 50\n58 7",
"output": "YES"
},
{
"input": "25 92 38\n21 36\n20 18\n9 29\n18 77\n10 58\n10 39\n5 3\n21 51\n11 78\n16 32\n24 71\n15 17\n23 23\n25 59\n18 57\n11 2\n16 35\n1 47\n20 59\n19 54\n11 55\n4 33\n15 41\n17 18\n16 67\n4 15\n5 23\n3 24\n20 70\n5 87\n11 1\n23 66\n21 83\n2 32\n17 22\n2 26\n16 42\n24 15",
"output": "YES"
},
{
"input": "67 41 68\n35 16\n66 14\n1 15\n43 6\n26 17\n30 13\n42 11\n32 20\n66 14\n15 35\n35 6\n12 11\n25 9\n39 37\n31 14\n52 11\n4 32\n17 14\n32 1\n58 31\n30 20\n7 23\n13 3\n27 25\n60 27\n56 39\n60 39\n11 5\n33 14\n29 12\n13 34\n30 16\n25 16\n64 25\n47 6\n33 36\n14 40\n19 38\n57 34\n67 8\n10 13\n7 36\n22 24\n6 33\n23 40\n13 19\n65 6\n14 37\n37 21\n27 12\n41 36\n60 15\n27 11\n23 33\n67 40\n45 39\n1 41\n50 21\n28 38\n20 24\n41 34\n43 35\n51 5\n59 37\n27 4\n28 17\n63 20\n1 9",
"output": "YES"
},
{
"input": "14 95 49\n11 48\n9 12\n1 18\n7 54\n11 20\n9 82\n12 1\n12 84\n1 13\n2 13\n12 57\n13 15\n12 18\n9 47\n13 14\n10 14\n13 94\n7 46\n14 14\n6 46\n7 95\n9 29\n13 15\n6 76\n8 60\n6 27\n9 63\n5 39\n5 70\n10 59\n5 75\n3 19\n9 32\n13 59\n5 13\n4 5\n13 80\n10 62\n13 65\n5 25\n4 81\n7 12\n10 94\n8 55\n7 61\n11 58\n7 77\n12 14\n12 47",
"output": "YES"
},
{
"input": "15 96 22\n4 7\n7 40\n13 30\n8 53\n6 78\n5 9\n15 35\n3 13\n5 31\n2 9\n13 50\n11 17\n4 2\n10 91\n11 74\n14 49\n8 30\n10 66\n12 44\n6 19\n9 62\n15 50",
"output": "YES"
},
{
"input": "19 19 50\n11 16\n4 11\n5 12\n19 19\n7 16\n15 10\n8 17\n8 1\n11 10\n5 19\n5 14\n17 6\n12 15\n18 17\n17 14\n10 5\n15 11\n8 8\n5 8\n18 18\n7 11\n8 4\n11 9\n6 16\n1 15\n19 13\n5 12\n10 10\n4 19\n12 4\n8 14\n19 9\n7 1\n19 11\n15 8\n4 19\n19 9\n6 7\n15 7\n2 16\n12 9\n3 18\n17 10\n3 5\n11 7\n12 6\n4 15\n19 4\n17 15\n3 10",
"output": "YES"
},
{
"input": "93 40 43\n14 15\n58 9\n72 15\n40 40\n46 20\n17 26\n31 26\n91 36\n24 28\n32 27\n51 10\n2 35\n73 7\n6 33\n59 21\n59 39\n33 8\n22 21\n77 20\n30 38\n76 35\n40 6\n48 31\n67 29\n30 24\n6 16\n39 27\n24 29\n14 16\n5 25\n76 14\n61 25\n85 13\n60 9\n80 7\n49 19\n35 20\n90 31\n57 40\n67 27\n3 27\n21 16\n21 38",
"output": "YES"
},
{
"input": "70 50 62\n31 22\n41 21\n31 47\n2 46\n22 8\n6 4\n45 32\n40 29\n10 11\n62 40\n70 26\n48 25\n13 44\n53 22\n3 8\n41 19\n13 8\n21 41\n66 20\n34 34\n41 48\n9 35\n23 26\n29 30\n39 27\n58 11\n35 2\n67 3\n59 23\n41 10\n54 9\n10 18\n23 44\n5 2\n37 30\n31 24\n2 21\n2 36\n34 5\n59 44\n7 4\n23 22\n47 27\n14 50\n54 50\n6 4\n64 1\n29 5\n5 37\n60 50\n58 45\n70 4\n4 46\n68 43\n62 34\n15 12\n16 2\n70 21\n59 8\n13 27\n25 41\n13 20",
"output": "YES"
},
{
"input": "61 96 15\n27 36\n19 64\n27 53\n59 63\n48 56\n55 30\n10 23\n6 79\n32 74\n7 51\n29 65\n60 16\n43 74\n40 80\n14 31",
"output": "YES"
},
{
"input": "87 50 62\n34 31\n42 21\n2 23\n20 25\n57 39\n46 26\n59 46\n29 33\n32 35\n79 41\n54 19\n65 7\n41 6\n40 23\n8 41\n2 31\n56 5\n37 33\n63 23\n79 4\n85 27\n53 38\n58 21\n16 11\n15 46\n33 39\n38 6\n27 41\n6 15\n25 47\n58 16\n28 50\n43 38\n48 20\n5 48\n31 6\n8 18\n40 10\n32 29\n44 20\n42 46\n63 21\n18 10\n28 49\n66 26\n64 28\n73 23\n16 29\n48 12\n23 21\n84 14\n10 45\n75 37\n80 3\n75 24\n31 25\n8 42\n67 22\n80 45\n8 31\n16 28\n49 34",
"output": "YES"
},
{
"input": "23 100 53\n16 63\n16 31\n8 31\n4 86\n8 43\n8 27\n21 6\n13 49\n11 54\n5 86\n1 41\n19 14\n2 98\n15 76\n6 25\n6 57\n2 45\n6 98\n10 27\n16 74\n22 72\n22 13\n22 20\n15 63\n18 17\n14 32\n14 32\n2 28\n7 46\n23 16\n20 64\n18 17\n3 69\n22 77\n2 98\n11 20\n22 17\n21 8\n19 77\n19 13\n18 25\n9 24\n18 83\n19 27\n7 37\n16 19\n9 60\n11 70\n3 30\n4 84\n9 54\n22 33\n3 22",
"output": "YES"
},
{
"input": "36 89 27\n21 66\n3 60\n11 32\n10 81\n30 31\n27 62\n11 81\n24 41\n30 6\n13 45\n34 86\n26 46\n9 62\n8 86\n17 56\n4 86\n25 36\n23 72\n18 55\n18 87\n22 67\n18 12\n19 75\n21 60\n16 49\n33 63\n26 12",
"output": "YES"
},
{
"input": "93 93 50\n7 5\n73 91\n66 55\n12 24\n82 46\n38 49\n86 72\n51 69\n17 73\n9 85\n86 69\n65 2\n40 88\n92 26\n45 80\n74 45\n4 55\n57 93\n80 70\n49 69\n29 46\n67 38\n46 12\n16 87\n62 3\n79 62\n29 45\n58 30\n48 4\n76 73\n14 68\n31 8\n49 85\n73 78\n18 7\n87 56\n82 54\n52 73\n29 71\n87 74\n75 84\n45 28\n47 57\n44 53\n21 5\n86 5\n57 51\n45 9\n93 8\n82 43",
"output": "YES"
},
{
"input": "11 38 21\n2 21\n2 28\n7 19\n9 18\n7 25\n8 4\n3 23\n2 32\n5 34\n10 36\n8 21\n4 6\n6 6\n4 35\n8 34\n10 18\n11 4\n10 2\n10 13\n4 37\n2 29",
"output": "YES"
},
{
"input": "26 11 59\n13 6\n18 6\n12 6\n18 6\n21 6\n19 6\n12 6\n7 6\n6 6\n16 6\n7 6\n9 6\n19 6\n19 6\n15 6\n16 6\n16 6\n18 6\n17 6\n8 6\n13 6\n18 6\n11 6\n21 6\n9 6\n19 6\n20 6\n8 6\n20 6\n14 6\n11 6\n18 6\n7 6\n16 6\n19 6\n6 6\n6 6\n7 6\n13 6\n9 6\n16 6\n9 6\n15 6\n12 6\n17 6\n16 6\n9 6\n11 6\n10 6\n16 6\n14 6\n15 6\n7 6\n20 6\n7 6\n8 6\n17 6\n14 6\n14 6",
"output": "NO"
},
{
"input": "30 84 35\n20 60\n23 21\n14 24\n24 72\n13 76\n25 35\n11 64\n15 57\n9 55\n14 66\n10 24\n13 68\n11 8\n19 43\n11 14\n16 26\n11 22\n10 26\n15 66\n17 65\n21 34\n7 61\n24 64\n18 16\n22 18\n12 9\n10 40\n8 24\n16 52\n10 9\n7 17\n21 78\n18 75\n10 45\n16 29",
"output": "NO"
},
{
"input": "100 77 53\n62 72\n23 51\n42 8\n66 33\n62 16\n28 53\n72 54\n71 34\n30 26\n91 28\n27 37\n81 47\n22 40\n42 23\n92 46\n36 37\n86 70\n62 22\n20 9\n46 36\n86 67\n46 61\n33 30\n68 49\n44 57\n34 7\n89 36\n48 39\n47 62\n76 56\n22 41\n7 52\n16 8\n70 50\n52 27\n27 17\n44 30\n66 44\n62 10\n95 37\n94 39\n91 68\n12 49\n85 55\n63 28\n64 15\n75 31\n93 26\n53 51\n53 55\n66 65\n38 36\n40 15",
"output": "NO"
},
{
"input": "66 94 26\n11 75\n46 72\n55 74\n34 10\n33 84\n25 11\n13 23\n27 73\n45 22\n54 34\n53 63\n28 8\n57 46\n26 78\n52 46\n32 38\n22 55\n17 71\n56 18\n9 60\n31 54\n6 84\n59 57\n60 81\n51 49\n41 77",
"output": "NO"
},
{
"input": "68 100 18\n17 85\n10 77\n59 55\n29 46\n25 74\n55 11\n37 16\n57 61\n26 11\n11 88\n19 18\n28 38\n32 12\n36 49\n32 6\n57 45\n30 6\n59 95",
"output": "NO"
},
{
"input": "28 61 4\n12 18\n21 31\n14 52\n6 36",
"output": "NO"
},
{
"input": "11 73 1\n4 67",
"output": "YES"
},
{
"input": "11 79 0",
"output": "NO"
},
{
"input": "11 23 1\n11 9",
"output": "YES"
},
{
"input": "25 11 0",
"output": "NO"
},
{
"input": "39 11 1\n18 3",
"output": "YES"
},
{
"input": "69 11 0",
"output": "NO"
},
{
"input": "18 15 45\n6 7\n7 14\n12 3\n17 1\n15 3\n7 11\n9 3\n7 11\n15 4\n8 1\n12 2\n17 7\n14 15\n2 9\n12 4\n14 9\n18 8\n2 2\n17 1\n7 9\n2 4\n16 1\n12 7\n17 10\n4 1\n18 13\n10 13\n9 12\n14 1\n1 6\n3 10\n6 2\n15 3\n4 8\n14 6\n5 14\n8 11\n8 13\n6 7\n16 9\n2 7\n17 14\n17 11\n7 9\n15 8",
"output": "YES"
},
{
"input": "16 18 70\n14 17\n16 8\n14 1\n7 1\n5 3\n7 5\n15 15\n15 2\n8 17\n12 12\n8 7\n10 16\n16 6\n14 7\n2 7\n12 4\n1 9\n6 9\n1 10\n10 13\n7 11\n2 2\n9 5\n3 10\n14 7\n4 5\n2 7\n7 16\n5 7\n7 14\n14 6\n10 16\n8 1\n4 14\n3 15\n8 11\n3 16\n12 1\n10 12\n13 3\n14 17\n5 5\n6 8\n13 10\n11 13\n3 5\n15 7\n10 3\n6 12\n13 15\n7 5\n3 8\n7 18\n6 7\n15 1\n9 6\n6 17\n11 2\n2 17\n7 16\n6 6\n2 18\n2 10\n5 16\n7 17\n3 8\n15 2\n11 11\n5 13\n16 1",
"output": "YES"
},
{
"input": "14 20 68\n6 7\n2 15\n4 6\n10 18\n6 9\n14 14\n5 18\n9 15\n5 15\n2 9\n9 13\n10 17\n4 2\n12 12\n6 19\n7 13\n10 11\n1 1\n3 16\n7 6\n8 16\n10 17\n1 13\n12 11\n13 13\n2 20\n14 12\n11 18\n10 8\n12 4\n13 7\n13 11\n1 1\n10 6\n14 17\n1 2\n11 5\n6 12\n13 2\n4 3\n8 19\n12 8\n8 7\n5 1\n2 10\n11 10\n12 19\n2 10\n8 4\n12 13\n3 15\n8 8\n5 9\n14 15\n5 19\n7 7\n1 16\n6 12\n11 18\n5 13\n1 12\n10 14\n4 5\n2 8\n3 20\n14 7\n6 3\n4 18",
"output": "YES"
},
{
"input": "19 13 83\n5 2\n12 11\n5 6\n3 11\n17 8\n10 8\n3 10\n9 10\n16 3\n15 12\n14 2\n11 8\n18 6\n15 10\n11 12\n2 1\n15 3\n16 3\n1 7\n15 7\n2 9\n11 13\n18 9\n4 7\n13 4\n7 4\n3 1\n14 8\n4 5\n5 7\n8 3\n17 2\n18 2\n16 3\n10 12\n6 2\n3 6\n5 2\n10 3\n18 9\n14 3\n3 6\n6 5\n12 8\n7 12\n2 11\n6 6\n18 6\n14 4\n3 10\n3 2\n13 3\n12 9\n2 10\n15 6\n1 5\n9 12\n6 12\n4 6\n18 3\n7 2\n9 13\n3 10\n19 13\n6 7\n5 1\n4 10\n12 13\n8 12\n15 1\n4 3\n3 8\n4 8\n3 7\n4 13\n8 7\n7 13\n2 8\n14 6\n12 1\n16 8\n9 4\n5 8",
"output": "YES"
},
{
"input": "13 19 1\n6 10",
"output": "NO"
},
{
"input": "14 17 0",
"output": "NO"
},
{
"input": "20 19 5\n7 14\n14 12\n7 12\n15 9\n12 6",
"output": "NO"
},
{
"input": "17 15 3\n10 7\n12 6\n8 6",
"output": "NO"
},
{
"input": "14 17 4\n9 9\n8 7\n8 12\n7 9",
"output": "NO"
},
{
"input": "15 11 0",
"output": "NO"
},
{
"input": "14 16 4\n6 11\n6 8\n8 6\n6 7",
"output": "NO"
},
{
"input": "16 16 0",
"output": "NO"
},
{
"input": "19 20 2\n10 14\n8 11",
"output": "NO"
},
{
"input": "13 15 1\n7 10",
"output": "NO"
},
{
"input": "11 100 4\n6 10\n6 20\n6 30\n6 80",
"output": "NO"
},
{
"input": "100 11 2\n40 6\n70 6",
"output": "NO"
},
{
"input": "100 11 5\n20 6\n30 6\n43 7\n78 6\n89 6",
"output": "YES"
},
{
"input": "20 20 5\n10 6\n6 8\n16 11\n11 11\n7 15",
"output": "YES"
},
{
"input": "30 30 5\n7 15\n24 11\n15 15\n8 24\n9 6",
"output": "NO"
}
] | 124 | 0 | 0 | 5,048 |
711 | Coloring Trees | [
"dp"
] | null | null | ZS the Coder and Chris the Baboon has arrived at Udayland! They walked in the park where *n* trees grow. They decided to be naughty and color the trees in the park. The trees are numbered with integers from 1 to *n* from left to right.
Initially, tree *i* has color *c**i*. ZS the Coder and Chris the Baboon recognizes only *m* different colors, so 0<=β€<=*c**i*<=β€<=*m*, where *c**i*<==<=0 means that tree *i* is uncolored.
ZS the Coder and Chris the Baboon decides to color only the uncolored trees, i.e. the trees with *c**i*<==<=0. They can color each of them them in any of the *m* colors from 1 to *m*. Coloring the *i*-th tree with color *j* requires exactly *p**i*,<=*j* litres of paint.
The two friends define the beauty of a coloring of the trees as the minimum number of contiguous groups (each group contains some subsegment of trees) you can split all the *n* trees into so that each group contains trees of the same color. For example, if the colors of the trees from left to right are 2,<=1,<=1,<=1,<=3,<=2,<=2,<=3,<=1,<=3, the beauty of the coloring is 7, since we can partition the trees into 7 contiguous groups of the same color : {2},<={1,<=1,<=1},<={3},<={2,<=2},<={3},<={1},<={3}.
ZS the Coder and Chris the Baboon wants to color all uncolored trees so that the beauty of the coloring is exactly *k*. They need your help to determine the minimum amount of paint (in litres) needed to finish the job.
Please note that the friends can't color the trees that are already colored. | The first line contains three integers, *n*, *m* and *k* (1<=β€<=*k*<=β€<=*n*<=β€<=100, 1<=β€<=*m*<=β€<=100)Β β the number of trees, number of colors and beauty of the resulting coloring respectively.
The second line contains *n* integers *c*1,<=*c*2,<=...,<=*c**n* (0<=β€<=*c**i*<=β€<=*m*), the initial colors of the trees. *c**i* equals to 0 if the tree number *i* is uncolored, otherwise the *i*-th tree has color *c**i*.
Then *n* lines follow. Each of them contains *m* integers. The *j*-th number on the *i*-th of them line denotes *p**i*,<=*j* (1<=β€<=*p**i*,<=*j*<=β€<=109)Β β the amount of litres the friends need to color *i*-th tree with color *j*. *p**i*,<=*j*'s are specified even for the initially colored trees, but such trees still can't be colored. | Print a single integer, the minimum amount of paint needed to color the trees. If there are no valid tree colorings of beauty *k*, print <=-<=1. | [
"3 2 2\n0 0 0\n1 2\n3 4\n5 6\n",
"3 2 2\n2 1 2\n1 3\n2 4\n3 5\n",
"3 2 2\n2 0 0\n1 3\n2 4\n3 5\n",
"3 2 3\n2 1 2\n1 3\n2 4\n3 5\n"
] | [
"10",
"-1",
"5",
"0"
] | In the first sample case, coloring the trees with colors 2,β1,β1 minimizes the amount of paint used, which equals to 2β+β3β+β5β=β10. Note that 1,β1,β1 would not be valid because the beauty of such coloring equals to 1 ({1,β1,β1} is a way to group the trees into a single group of the same color).
In the second sample case, all the trees are colored, but the beauty of the coloring is 3, so there is no valid coloring, and the answer is β-β1.
In the last sample case, all the trees are colored and the beauty of the coloring matches *k*, so no paint is used and the answer is 0. | [
{
"input": "3 2 2\n0 0 0\n1 2\n3 4\n5 6",
"output": "10"
},
{
"input": "3 2 2\n2 1 2\n1 3\n2 4\n3 5",
"output": "-1"
},
{
"input": "3 2 2\n2 0 0\n1 3\n2 4\n3 5",
"output": "5"
},
{
"input": "3 2 3\n2 1 2\n1 3\n2 4\n3 5",
"output": "0"
},
{
"input": "3 2 3\n0 0 0\n10 30000\n20000 1000000000\n1000000000 50000",
"output": "100000"
},
{
"input": "4 2 1\n0 0 0 0\n10 30000\n20000 1000000000\n1000000000 50000\n55 55",
"output": "1000020065"
},
{
"input": "4 2 1\n0 0 0 2\n10 30000\n20000 1000000000\n1000000000 50000\n55 55",
"output": "1000080000"
},
{
"input": "1 1 1\n0\n5",
"output": "5"
},
{
"input": "1 10 1\n0\n1 2 20 1000000000 41 23 39 55 44 1234567",
"output": "1"
},
{
"input": "1 1 1\n1\n5",
"output": "0"
},
{
"input": "8 6 6\n0 0 0 0 0 0 0 0\n709812879 751993522 552838834 932579085 381597201 889756688\n77223016 35398130 932703875 852137134 124534767 472656085\n828677108 158247840 540181954 573979204 389860841 490718346\n666733838 404533406 50010075 311518758 460372535 69832342\n591244215 400838850 867732307 113910196 445904988 184328895\n564004525 89903316 756707872 628355859 689211716 85839524\n272478028 286740424 178709321 86780970 947181211 809721979\n813772965 663391037 731882431 804451037 31893872 744734983",
"output": "1014096507"
},
{
"input": "4 4 3\n4 3 2 1\n608531991 110838465 78523745 621397088\n923748933 697335134 350140891 422577481\n907779022 895436439 216021587 50630582\n120114007 984106338 70847223 755445813",
"output": "-1"
},
{
"input": "1 3 1\n0\n3 2 1",
"output": "1"
}
] | 2,000 | 37,478,400 | 0 | 5,052 |
|
883 | Automatic Door | [
"implementation"
] | null | null | There is an automatic door at the entrance of a factory. The door works in the following way:
- when one or several people come to the door and it is closed, the door immediately opens automatically and all people immediately come inside, - when one or several people come to the door and it is open, all people immediately come inside, - opened door immediately closes in *d* seconds after its opening, - if the door is closing and one or several people are coming to the door at the same moment, then all of them will have enough time to enter and only after that the door will close.
For example, if *d*<==<=3 and four people are coming at four different moments of time *t*1<==<=4, *t*2<==<=7, *t*3<==<=9 and *t*4<==<=13 then the door will open three times: at moments 4, 9 and 13. It will close at moments 7 and 12.
It is known that *n* employees will enter at moments *a*,<=2Β·*a*,<=3Β·*a*,<=...,<=*n*Β·*a* (the value *a* is positive integer). Also *m* clients will enter at moments *t*1,<=*t*2,<=...,<=*t**m*.
Write program to find the number of times the automatic door will open. Assume that the door is initially closed. | The first line contains four integers *n*, *m*, *a* and *d* (1<=β€<=*n*,<=*a*<=β€<=109, 1<=β€<=*m*<=β€<=105, 1<=β€<=*d*<=β€<=1018) β the number of the employees, the number of the clients, the moment of time when the first employee will come and the period of time in which the door closes.
The second line contains integer sequence *t*1,<=*t*2,<=...,<=*t**m* (1<=β€<=*t**i*<=β€<=1018) β moments of time when clients will come. The values *t**i* are given in non-decreasing order. | Print the number of times the door will open. | [
"1 1 3 4\n7\n",
"4 3 4 2\n7 9 11\n"
] | [
"1\n",
"4\n"
] | In the first example the only employee will come at moment 3. At this moment the door will open and will stay open until the moment 7. At the same moment of time the client will come, so at first he will enter and only after it the door will close. Thus the door will open one time. | [
{
"input": "1 1 3 4\n7",
"output": "1"
},
{
"input": "4 3 4 2\n7 9 11",
"output": "4"
},
{
"input": "10 10 51 69\n154 170 170 183 251 337 412 426 445 452",
"output": "6"
},
{
"input": "70 10 26 17\n361 371 579 585 629 872 944 1017 1048 1541",
"output": "70"
},
{
"input": "100 20 49 52\n224 380 690 1585 1830 1973 2490 2592 3240 3341 3406 3429 3549 3560 3895 3944 4344 4390 4649 4800",
"output": "55"
},
{
"input": "100 30 36 47\n44 155 275 390 464 532 1186 1205 1345 1349 1432 1469 1482 1775 1832 1856 1869 2049 2079 2095 2374 2427 2577 2655 2792 2976 3020 3317 3482 3582",
"output": "51"
},
{
"input": "97 60 1 1\n5 6 6 7 9 10 10 11 11 11 12 13 13 13 13 14 14 15 16 18 20 23 23 24 25 26 29 31 32 35 38 41 43 43 46 47 48 48 49 52 53 54 55 56 58 59 68 70 72 74 78 81 81 82 91 92 96 96 97 98",
"output": "49"
},
{
"input": "1000000000 1 157 468\n57575875712",
"output": "333333334"
},
{
"input": "1000000000 1 1000000000 1000000000000000000\n1000000000000000000",
"output": "1"
}
] | 61 | 5,529,600 | 0 | 5,054 |
|
572 | Order Book | [
"data structures",
"greedy",
"implementation",
"sortings"
] | null | null | In this task you need to process a set of stock exchange orders and use them to create order book.
An order is an instruction of some participant to buy or sell stocks on stock exchange. The order number *i* has price *p**i*, direction *d**i* β buy or sell, and integer *q**i*. This means that the participant is ready to buy or sell *q**i* stocks at price *p**i* for one stock. A value *q**i* is also known as a volume of an order.
All orders with the same price *p* and direction *d* are merged into one aggregated order with price *p* and direction *d*. The volume of such order is a sum of volumes of the initial orders.
An order book is a list of aggregated orders, the first part of which contains sell orders sorted by price in descending order, the second contains buy orders also sorted by price in descending order.
An order book of depth *s* contains *s* best aggregated orders for each direction. A buy order is better if it has higher price and a sell order is better if it has lower price. If there are less than *s* aggregated orders for some direction then all of them will be in the final order book.
You are given *n* stock exhange orders. Your task is to print order book of depth *s* for these orders. | The input starts with two positive integers *n* and *s* (1<=β€<=*n*<=β€<=1000,<=1<=β€<=*s*<=β€<=50), the number of orders and the book depth.
Next *n* lines contains a letter *d**i* (either 'B' or 'S'), an integer *p**i* (0<=β€<=*p**i*<=β€<=105) and an integer *q**i* (1<=β€<=*q**i*<=β€<=104) β direction, price and volume respectively. The letter 'B' means buy, 'S' means sell. The price of any sell order is higher than the price of any buy order. | Print no more than 2*s* lines with aggregated orders from order book of depth *s*. The output format for orders should be the same as in input. | [
"6 2\nB 10 3\nS 50 2\nS 40 1\nS 50 6\nB 20 4\nB 25 10\n"
] | [
"S 50 8\nS 40 1\nB 25 10\nB 20 4\n"
] | Denote (x, y) an order with price *x* and volume *y*. There are 3 aggregated buy orders (10, 3), (20, 4), (25, 10) and two sell orders (50, 8), (40, 1) in the sample.
You need to print no more than two best orders for each direction, so you shouldn't print the order (10 3) having the worst price among buy orders. | [
{
"input": "6 2\nB 10 3\nS 50 2\nS 40 1\nS 50 6\nB 20 4\nB 25 10",
"output": "S 50 8\nS 40 1\nB 25 10\nB 20 4"
},
{
"input": "2 1\nB 7523 5589\nS 69799 1711",
"output": "S 69799 1711\nB 7523 5589"
},
{
"input": "1 1\nB 48259 991",
"output": "B 48259 991"
},
{
"input": "1 50\nB 47828 7726",
"output": "B 47828 7726"
},
{
"input": "1 1\nS 95992 7257",
"output": "S 95992 7257"
},
{
"input": "1 50\nS 72218 8095",
"output": "S 72218 8095"
},
{
"input": "2 50\nB 758 9290\nS 86168 3367",
"output": "S 86168 3367\nB 758 9290"
},
{
"input": "3 3\nB 5878 1568\nS 60238 4895\nS 76276 1905",
"output": "S 76276 1905\nS 60238 4895\nB 5878 1568"
},
{
"input": "6 2\nB 0 1\nS 1 1\nS 1 1\nS 1 1\nB 0 1\nB 0 1",
"output": "S 1 3\nB 0 3"
},
{
"input": "2 2\nS 1 1\nB 0 2",
"output": "S 1 1\nB 0 2"
},
{
"input": "2 1\nS 10 1\nB 0 1",
"output": "S 10 1\nB 0 1"
},
{
"input": "2 10\nB 0 1\nS 100000 1",
"output": "S 100000 1\nB 0 1"
},
{
"input": "2 1\nS 1 1\nB 0 1",
"output": "S 1 1\nB 0 1"
},
{
"input": "2 1\nB 0 100\nS 1 100",
"output": "S 1 100\nB 0 100"
},
{
"input": "2 2\nB 0 3\nS 10 3",
"output": "S 10 3\nB 0 3"
},
{
"input": "2 10\nB 0 1\nS 1 1",
"output": "S 1 1\nB 0 1"
},
{
"input": "2 50\nB 2 5\nB 0 1",
"output": "B 2 5\nB 0 1"
}
] | 61 | 307,200 | 0 | 5,058 |
|
300 | Coach | [
"brute force",
"dfs and similar",
"graphs"
] | null | null | A programming coach has *n* students to teach. We know that *n* is divisible by 3. Let's assume that all students are numbered from 1 to *n*, inclusive.
Before the university programming championship the coach wants to split all students into groups of three. For some pairs of students we know that they want to be on the same team. Besides, if the *i*-th student wants to be on the same team with the *j*-th one, then the *j*-th student wants to be on the same team with the *i*-th one. The coach wants the teams to show good results, so he wants the following condition to hold: if the *i*-th student wants to be on the same team with the *j*-th, then the *i*-th and the *j*-th students must be on the same team. Also, it is obvious that each student must be on exactly one team.
Help the coach and divide the teams the way he wants. | The first line of the input contains integers *n* and *m* (3<=β€<=*n*<=β€<=48, . Then follow *m* lines, each contains a pair of integers *a**i*,<=*b**i* (1<=β€<=*a**i*<=<<=*b**i*<=β€<=*n*) β the pair *a**i*,<=*b**i* means that students with numbers *a**i* and *b**i* want to be on the same team.
It is guaranteed that *n* is divisible by 3. It is guaranteed that each pair *a**i*,<=*b**i* occurs in the input at most once. | If the required division into teams doesn't exist, print number -1. Otherwise, print lines. In each line print three integers *x**i*, *y**i*, *z**i* (1<=β€<=*x**i*,<=*y**i*,<=*z**i*<=β€<=*n*) β the *i*-th team.
If there are multiple answers, you are allowed to print any of them. | [
"3 0\n",
"6 4\n1 2\n2 3\n3 4\n5 6\n",
"3 3\n1 2\n2 3\n1 3\n"
] | [
"3 2 1 \n",
"-1\n",
"3 2 1 \n"
] | none | [
{
"input": "3 0",
"output": "3 2 1 "
},
{
"input": "6 4\n1 2\n2 3\n3 4\n5 6",
"output": "-1"
},
{
"input": "3 3\n1 2\n2 3\n1 3",
"output": "3 2 1 "
},
{
"input": "6 3\n1 2\n3 4\n5 6",
"output": "-1"
},
{
"input": "15 9\n1 4\n1 6\n2 7\n2 11\n4 6\n5 12\n7 11\n9 14\n13 15",
"output": "6 4 1 \n11 7 2 \n12 5 3 \n14 9 8 \n15 13 10 "
},
{
"input": "3 1\n1 3",
"output": "3 2 1 "
},
{
"input": "15 13\n1 9\n1 11\n2 7\n2 12\n3 8\n3 15\n4 10\n5 6\n5 14\n6 14\n7 12\n8 15\n9 11",
"output": "11 9 1 \n12 7 2 \n14 6 5 \n15 8 3 \n13 10 4 "
},
{
"input": "36 27\n1 34\n2 18\n2 20\n3 9\n3 21\n4 5\n4 25\n5 25\n6 13\n6 22\n8 23\n8 31\n9 21\n10 14\n11 17\n11 19\n13 22\n15 24\n15 26\n17 19\n18 20\n23 31\n24 26\n28 29\n28 33\n29 33\n32 36",
"output": "19 17 11 \n20 18 2 \n21 9 3 \n22 13 6 \n25 5 4 \n26 24 15 \n31 23 8 \n33 29 28 \n14 10 7 \n34 12 1 \n36 32 16 \n35 30 27 "
},
{
"input": "18 12\n1 10\n2 4\n2 8\n3 15\n3 18\n4 8\n5 6\n9 13\n12 14\n12 16\n14 16\n15 18",
"output": "8 4 2 \n16 14 12 \n18 15 3 \n7 6 5 \n11 10 1 \n17 13 9 "
},
{
"input": "39 27\n1 2\n1 25\n2 25\n4 16\n5 22\n5 28\n6 7\n6 26\n7 26\n8 24\n10 31\n10 38\n11 17\n11 21\n12 35\n12 37\n13 34\n17 21\n18 23\n19 39\n22 28\n27 29\n27 36\n29 36\n31 38\n32 33\n35 37",
"output": "21 17 11 \n25 2 1 \n26 7 6 \n28 22 5 \n36 29 27 \n37 35 12 \n38 31 10 \n16 4 3 \n23 18 9 \n24 14 8 \n33 32 15 \n34 20 13 \n39 30 19 "
},
{
"input": "12 7\n1 2\n4 5\n6 12\n7 8\n9 10\n9 11\n10 11",
"output": "-1"
},
{
"input": "33 22\n3 9\n3 28\n4 12\n5 11\n5 31\n6 18\n8 15\n8 29\n9 28\n10 22\n11 31\n13 14\n15 29\n16 23\n16 27\n17 25\n17 32\n19 21\n20 30\n23 27\n24 33\n25 32",
"output": "-1"
},
{
"input": "18 8\n1 14\n2 16\n4 7\n5 11\n8 9\n8 12\n9 12\n10 18",
"output": "12 9 8 \n7 4 3 \n11 6 5 \n14 13 1 \n16 15 2 \n18 17 10 "
},
{
"input": "27 21\n1 3\n2 9\n2 11\n5 16\n5 25\n7 26\n8 14\n8 22\n9 11\n10 17\n10 27\n12 21\n13 20\n13 23\n14 22\n15 18\n15 19\n16 25\n17 27\n18 19\n20 23",
"output": "11 9 2 \n19 18 15 \n22 14 8 \n23 20 13 \n25 16 5 \n27 17 10 \n4 3 1 \n21 12 6 \n26 24 7 "
},
{
"input": "24 21\n1 14\n2 6\n3 4\n3 19\n4 19\n5 7\n5 21\n7 21\n8 18\n8 23\n9 15\n9 16\n10 12\n10 17\n11 22\n12 17\n13 20\n13 24\n15 16\n18 23\n20 24",
"output": "-1"
},
{
"input": "45 31\n1 5\n2 45\n3 29\n3 30\n4 16\n4 32\n6 40\n7 13\n7 25\n8 42\n10 31\n11 20\n11 26\n12 27\n12 34\n13 25\n14 24\n14 43\n15 36\n15 37\n16 32\n18 19\n18 33\n19 33\n20 26\n23 41\n24 43\n27 34\n28 39\n29 30\n36 37",
"output": "25 13 7 \n26 20 11 \n30 29 3 \n32 16 4 \n33 19 18 \n34 27 12 \n37 36 15 \n43 24 14 \n9 5 1 \n31 17 10 \n39 28 21 \n40 22 6 \n41 35 23 \n42 38 8 \n45 44 2 "
},
{
"input": "18 9\n1 16\n2 17\n4 6\n5 18\n7 8\n7 15\n8 15\n9 11\n10 13",
"output": "-1"
},
{
"input": "6 6\n1 6\n1 3\n3 6\n2 4\n4 5\n2 5",
"output": "5 4 2 \n6 3 1 "
},
{
"input": "48 48\n7 39\n39 45\n7 45\n25 26\n26 31\n25 31\n4 11\n11 19\n4 19\n8 16\n16 37\n8 37\n14 22\n22 33\n14 33\n6 12\n12 46\n6 46\n29 44\n44 48\n29 48\n15 27\n27 41\n15 41\n3 24\n24 34\n3 34\n13 20\n20 47\n13 47\n5 9\n9 36\n5 36\n21 40\n40 43\n21 43\n2 35\n35 38\n2 38\n23 28\n28 42\n23 42\n1 10\n10 32\n1 32\n17 18\n18 30\n17 30",
"output": "19 11 4 \n30 18 17 \n31 26 25 \n32 10 1 \n33 22 14 \n34 24 3 \n36 9 5 \n37 16 8 \n38 35 2 \n41 27 15 \n42 28 23 \n43 40 21 \n45 39 7 \n46 12 6 \n47 20 13 \n48 44 29 "
},
{
"input": "12 9\n1 2\n2 4\n1 3\n5 6\n6 8\n5 7\n9 10\n10 12\n9 11",
"output": "-1"
},
{
"input": "9 7\n1 2\n3 4\n5 6\n7 8\n2 3\n2 5\n2 7",
"output": "-1"
},
{
"input": "9 3\n4 5\n6 7\n8 9",
"output": "5 4 1 \n7 6 2 \n9 8 3 "
},
{
"input": "6 2\n3 4\n5 6",
"output": "4 3 1 \n6 5 2 "
},
{
"input": "9 7\n1 2\n2 3\n1 3\n4 5\n4 6\n4 7\n4 8",
"output": "-1"
},
{
"input": "6 1\n1 2",
"output": "3 2 1 \n6 5 4 "
},
{
"input": "48 1\n1 2",
"output": "3 2 1 \n6 5 4 \n9 8 7 \n12 11 10 \n15 14 13 \n18 17 16 \n21 20 19 \n24 23 22 \n27 26 25 \n30 29 28 \n33 32 31 \n36 35 34 \n39 38 37 \n42 41 40 \n45 44 43 \n48 47 46 "
}
] | 218 | 7,065,600 | 0 | 5,068 |
|
88 | Keyboard | [
"implementation"
] | B. Keyboard | 1 | 256 | Vasya learns to type. He has an unusual keyboard at his disposal: it is rectangular and it has *n* rows of keys containing *m* keys in each row. Besides, the keys are of two types. Some of the keys have lowercase Latin letters on them and some of the keys work like the "Shift" key on standard keyboards, that is, they make lowercase letters uppercase.
Vasya can press one or two keys with one hand. However, he can only press two keys if the Euclidean distance between the centers of the keys does not exceed *x*. The keys are considered as squares with a side equal to 1. There are no empty spaces between neighbouring keys.
Vasya is a very lazy boy, that's why he tries to type with one hand as he eats chips with his other one. However, it is possible that some symbol can't be typed with one hand only, because the distance between it and the closest "Shift" key is strictly larger than *x*. In this case he will have to use his other hand. Having typed the symbol, Vasya returns other hand back to the chips.
You are given Vasya's keyboard and the text. Count the minimum number of times Vasya will have to use the other hand. | The first line contains three integers *n*, *m*, *x* (1<=β€<=*n*,<=*m*<=β€<=30,<=1<=β€<=*x*<=β€<=50).
Next *n* lines contain descriptions of all the keyboard keys. Each line contains the descriptions of exactly *m* keys, without spaces. The letter keys are marked with the corresponding lowercase letters. The "Shift" keys are marked with the "S" symbol.
Then follow the length of the text *q* (1<=β€<=*q*<=β€<=5Β·105). The last line contains the text *T*, which consists of *q* symbols, which are uppercase and lowercase Latin letters. | If Vasya can type the text, then print the minimum number of times he will have to use his other hand. Otherwise, print "-1" (without the quotes). | [
"2 2 1\nab\ncd\n1\nA\n",
"2 2 1\nab\ncd\n1\ne\n",
"2 2 1\nab\ncS\n5\nabcBA\n",
"3 9 4\nqwertyuio\nasdfghjkl\nSzxcvbnmS\n35\nTheQuIcKbRoWnFOXjummsovertHeLazYDOG\n"
] | [
"-1\n",
"-1\n",
"1\n",
"2\n"
] | In the first sample the symbol "A" is impossible to print as there's no "Shift" key on the keyboard.
In the second sample the symbol "e" is impossible to print as there's no such key on the keyboard.
In the fourth sample the symbols "T", "G" are impossible to print with one hand. The other letters that are on the keyboard can be printed. Those symbols come up in the text twice, thus, the answer is 2. | [
{
"input": "2 2 1\nab\ncd\n1\nA",
"output": "-1"
},
{
"input": "2 2 1\nab\ncd\n1\ne",
"output": "-1"
},
{
"input": "2 2 1\nab\ncS\n5\nabcBA",
"output": "1"
},
{
"input": "3 9 4\nqwertyuio\nasdfghjkl\nSzxcvbnmS\n35\nTheQuIcKbRoWnFOXjummsovertHeLazYDOG",
"output": "2"
},
{
"input": "10 9 3\noboxlgpey\nyxcuwkkmp\njuqeflhwq\nsfnxqtjqS\nkkudcnyjl\nhgjlcrkjq\njnofqksxn\nqbhsnuguv\nlvahnifao\nebwnnlrwe\n35\nCodeforcesBetaRoundproblemAtestfive",
"output": "4"
},
{
"input": "2 7 4\niuqtieo\nysxcgmS\n2\nsQ",
"output": "1"
},
{
"input": "1 2 4\nbS\n8\nbBbbbBbb",
"output": "0"
},
{
"input": "7 8 5\nfqiubjpm\nqbshcsyk\ncjbxpbef\nptwpmapx\nryazscbm\nqnvsgzrf\nhtardzkz\n9\nuxrmwkayy",
"output": "0"
},
{
"input": "8 6 4\nefvmov\nkeofnw\npwajpe\nknptky\nSibruu\nrgdukk\nbsxosd\nhovgSe\n10\nECreruXmsC",
"output": "-1"
},
{
"input": "10 3 2\nukk\neqt\nfex\nqSh\ntvz\nfjn\niol\nehd\nnte\ngyx\n5\ncgQxI",
"output": "-1"
},
{
"input": "10 10 19\nowqjcaSpqn\nvgrhboqahn\nbzziocjmbu\npurqsmiSop\nxcsifctjhy\nycyytwoamk\nrnjfxsxowl\nnkgcywcdff\nbazljrisqv\nkcakigSekq\n100\nzewpATtssQVicNrlRrcoifTutTAfFMUEfDFKoNyQbSrSYxTGMadNkRpmJvoEqUsqPYgAdQreaUrwDKMNFWiwdRRCcJBPorfMVMoK",
"output": "0"
},
{
"input": "10 10 26\nwxmssptheb\nzpxbxsyxsy\nqbjkpaywqp\nfwhnuzjcgq\nycgaanzedz\njrycrbzqfs\ngswwakybus\nfhtxhljedz\noSepmyjosv\ndwviycevdn\n100\nyapwUfnyPzgZyFvAHGKWVbXQHkuhJDoUTvCAtdMMCQmKchxKkilUTECOqYJFUSHPqKiRKhDXZgHxwApDWlShdwakmVCgaeKCLOMX",
"output": "0"
},
{
"input": "10 10 3\nrvouufmnqu\nbyukrnmnhr\nzjggwxgvkz\ntcagkSitiw\nhryajgtpwc\njragfhqoks\nkgroxxkuvp\nbpgrkqiyns\njbuhjjkziw\nomjmbaggsw\n100\nCpRzrPqPngYvrVJFCWRPMRwrpXcbtiwfoFcAkRaNjzpMMKOQAzBxSrxGbIHaYgmSqhhxhZTmhFttKnhFzRfKxYXshUZRvtKJIzZq",
"output": "12"
},
{
"input": "10 10 2\nfriuxvShvg\nerslojqtgu\nzeqsmdewry\nwvhbeeyeSu\ngkofbjaavr\ntwkcdxugps\nnzlylSmafu\nstamkpxnzt\nuwxwximkrm\nmzxyboazbl\n100\nmRIfAtrLKmztpVkAmojDCiIgseBwlUilBIixDQhqNhNAqVLLIobuCIretLdSvixNNdCiouFMXtwHZFlObCeaygmIiFBfaCirbmCa",
"output": "19"
},
{
"input": "10 10 2\nbddahSqkmk\npxbocxayjs\nottvdazstk\nlaxuidqlqb\nkfjwdpdfat\nxlipuubkgv\niqyomzfktm\niwbgidmwyu\nrngqkeupsf\nbqndtekryw\n100\nMNQgWFLhHycqwjSsbTkbgMYAIHFYARRmOsinYMFjOxxnLjiKfeiBbMpoeTdzUMORPaAxRNfvdAPFaKkPdxdAjjJgGCxkDzmSasqq",
"output": "37"
},
{
"input": "10 10 2\nnxcwdrsmrv\nSyjahsosvp\nvkrqbxhgbv\nwkxywavtnn\nepkyoviqbi\nsfmpvhuwwq\nnlsostrotx\ntcdguorhny\nimixrqzSdu\nxzhdhdwibt\n100\nUzzaWiRFYbAqxIDMrRBBDoGQhSzSqSLEddAiJsZcxbemdeuddamNYdWOvzlYSCuHIRpnuxdNxAsnZMiLXBYwnrMcrbNeLrUYhZOB",
"output": "17"
},
{
"input": "10 10 23\nhtyvouoiqi\nvySvsfqadv\nxvqyqjyutq\npjcrrphzbk\nhlqfyoqfmo\nezcSwleoew\nxkwqrajxyg\nngSiftgoso\njyndgicccr\nlgjvokydhp\n100\nJzVVfotldIRcyjhTNRcFlTxFeZKRwavZxYcvdDOQyUvTmryFRuRBcRvmscegtspkPuchqlFEKbrfpTOSlSFOARsbbvSenMwNmaRj",
"output": "0"
},
{
"input": "10 10 7\nifcwalsdbj\njpykymrbei\nrylzgkyefh\noilvvexpjp\niptgodpfim\ndSrqejaixu\npksxlsniwa\nmoSenxtfbc\noqssptcenz\nqdhmouvyas\n100\nqtMDVUXJpSEFgPsLKyRJVRbfVoYaCKJDnQDLFVngVjSPzzVyMnMyuyahMRiBJuNhKtgpVqvukUolLvYEmidvXotgQUJukYwIweUW",
"output": "0"
},
{
"input": "10 10 1\nmdxafehbkr\nyuhenybjps\ntvfwmiwcoh\njmzrepzjvx\nnqyorkSnuk\ntSmztmwidv\ncmmajnlqrw\nfiqewpdwax\nuesmkdcplt\nlgkomdcqbo\n100\nmcEQmAvFqKYMXLHQUDeIulkmAMRkIUtbKihTFJwJYQfcAelNrZWSAwHunwZTrdHaRWokgCyLqbubOpEHuZiDVoFHjvkMSoBPyGOI",
"output": "39"
},
{
"input": "10 10 2\nnhfafdwqhh\neyvitpcthk\nrpiotuoqzh\nnxxnhuaxee\nyevrtirzwf\nkbtSsamyel\nfeenjvxsmo\nkqpenxjmde\nlqsamthlwp\njdyyqsbtbk\n100\nUHucxPWDaKonVpXEctuqYUAQnrFEZaTYxhoacNbHIMevlbDejXjitEzyVrTfcfBHWRMdJvaTkbkqccyHjtzpTbKmRAXwlXCtFKNX",
"output": "29"
},
{
"input": "10 10 1\nsufnxxpdnx\nvttibpllhv\nlvbrjmfdjx\ngmtexvrnfh\nygsqrsSwxd\nkxbbjxgbzs\nedutwocmzd\nfebjgknyai\nvcvquagvrs\ndrdoarhgoc\n100\nZoZJXhUWyaLgBTpgbznABKHuyFcKzJmGaMhoKkKfyOGacLwBspaKtAEdwMZJFYiZUFNDxdDIDgKSCRvsbGUOXRqalbpuEqkduYpW",
"output": "44"
},
{
"input": "10 10 2\ncstcrltzsl\nblotmquzvj\nuiitiytlgx\nwumpfdaprd\ntfxohqpztn\nvfrpsccddo\nneegusrkxw\niijfjozqjq\nioegbvuhew\npjjpqdxvqu\n100\nkPCBONfZLkeXzWVuSgvinPENazcnRoBcUHXwRzPyvNIiDlDSeKOYmiUmjooXuzTCtIRxKDAYeTLgjsenxHoymVazMALUADQpjVjV",
"output": "-1"
},
{
"input": "10 10 1\nqztnjglyrc\nnukswgzajl\nqnpbdwjvbb\nliiakzcrlz\nnolwfzzvxd\nmqvhiySttx\nqwuizSjuto\nqbgwiwjukx\nkomyvblgkc\ntkzlxzgsru\n100\nYUzTZDzLFkMUhjQWbwljJCRyZGFzgJcozvROiwPktRGxkMKiPyiTvhDrtusPYhMgVAOFIjAvlpzcrUvrMrMbhkpUiyAytKfYOGTF",
"output": "37"
},
{
"input": "10 10 1\nmgziiihbkq\niobjknuogh\nvntwahSopu\nsjsxjpaqvm\nwqgrodizst\nselzugktoi\nvbhfzvgjfn\nliqlfdcjhf\nbpbtpmimxb\npksfiydpfw\n100\nwAVZXEhKTuajdCauVTIwgnfbxWuUSmtXkjHZtNVcfTsiSAPLdpdEFdTJLZRjptUcRhAmrNjKMXmuDGatAQoaIpbddnzRGHsJrhoq",
"output": "39"
},
{
"input": "10 10 2\nshbqxycvfm\notydudkttw\nqhatsxsngz\nixvyujtyjc\nsbvqhnjbak\neggcguuuka\nxcydfgjzeb\nytpdkcdrsq\nefqlpywggu\nfcnfrhnouo\n100\nHPqtuVckdUOhsnuhnbpekWvWKUnAEaOCihpeEvmaOKOPcIZiMixGJGEuXAaOxuUNyrIesmldLEqGnvyDKPDvFkCbRebCORHmUgeV",
"output": "-1"
},
{
"input": "1 1 50\nS\n29\nargjhoaiogjiSjqfhjksdvjkSvcvn",
"output": "-1"
},
{
"input": "1 1 50\nS\n1\nS",
"output": "-1"
},
{
"input": "1 1 50\na\n29\nargjhoaiogjiSjqfhjksdvjkSvcvn",
"output": "-1"
},
{
"input": "1 1 50\nz\n29\nargjhoaiogjiSjqfhjksdvjkSvcvn",
"output": "-1"
},
{
"input": "2 1 2\nS\nc\n4\nCSSA",
"output": "-1"
}
] | 46 | 0 | 0 | 5,093 |
328 | IQ Test | [
"implementation"
] | null | null | Petya is preparing for IQ test and he has noticed that there many problems like: you are given a sequence, find the next number. Now Petya can solve only problems with arithmetic or geometric progressions.
Arithmetic progression is a sequence *a*1, *a*1<=+<=*d*, *a*1<=+<=2*d*, ..., *a*1<=+<=(*n*<=-<=1)*d*, where *a*1 and *d* are any numbers.
Geometric progression is a sequence *b*1, *b*2<==<=*b*1*q*, ..., *b**n*<==<=*b**n*<=-<=1*q*, where *b*1<=β <=0, *q*<=β <=0, *q*<=β <=1.
Help Petya and write a program to determine if the given sequence is arithmetic or geometric. Also it should found the next number. If the sequence is neither arithmetic nor geometric, print 42 (he thinks it is impossible to find better answer). You should also print 42 if the next element of progression is not integer. So answer is always integer. | The first line contains exactly four integer numbers between 1 and 1000, inclusively. | Print the required number. If the given sequence is arithmetic progression, print the next progression element. Similarly, if the given sequence is geometric progression, print the next progression element.
Print 42 if the given sequence is not an arithmetic or geometric progression. | [
"836 624 412 200\n",
"1 334 667 1000\n"
] | [
"-12\n",
"1333\n"
] | This problem contains very weak pretests! | [
{
"input": "836 624 412 200",
"output": "-12"
},
{
"input": "1 334 667 1000",
"output": "1333"
},
{
"input": "501 451 400 350",
"output": "42"
},
{
"input": "836 624 412 200",
"output": "-12"
},
{
"input": "1 334 667 1000",
"output": "1333"
},
{
"input": "11 234 457 680",
"output": "903"
},
{
"input": "640 431 222 13",
"output": "-196"
},
{
"input": "1 1 1 1",
"output": "1"
},
{
"input": "1 10 100 1000",
"output": "10000"
},
{
"input": "3 18 108 648",
"output": "3888"
},
{
"input": "512 384 288 216",
"output": "162"
},
{
"input": "891 297 99 33",
"output": "11"
},
{
"input": "64 160 400 1000",
"output": "2500"
},
{
"input": "501 451 400 350",
"output": "42"
},
{
"input": "501 450 400 350",
"output": "42"
},
{
"input": "4 32 48 64",
"output": "42"
},
{
"input": "9 8 7 5",
"output": "42"
},
{
"input": "992 994 998 1000",
"output": "42"
},
{
"input": "2 6 6 8",
"output": "42"
},
{
"input": "2 4 8 8",
"output": "42"
},
{
"input": "2 4 6 14",
"output": "42"
},
{
"input": "2 12 4 14",
"output": "42"
},
{
"input": "2 4 4 2",
"output": "42"
},
{
"input": "1000 100 10 1",
"output": "42"
},
{
"input": "2 9 27 81",
"output": "42"
},
{
"input": "2 4 9 16",
"output": "42"
},
{
"input": "2 4 9 18",
"output": "42"
},
{
"input": "256 64 16 8",
"output": "42"
},
{
"input": "256 385 576 864",
"output": "42"
},
{
"input": "343 147 63 27",
"output": "42"
},
{
"input": "729 648 576 512",
"output": "42"
},
{
"input": "1000 980 960 941",
"output": "42"
},
{
"input": "2 5 10 16",
"output": "42"
},
{
"input": "1 2 3 10",
"output": "42"
},
{
"input": "24 36 54 81",
"output": "42"
},
{
"input": "1 2 4 8",
"output": "16"
},
{
"input": "16 24 36 54",
"output": "81"
},
{
"input": "8 4 2 1",
"output": "42"
},
{
"input": "16 8 4 2",
"output": "1"
},
{
"input": "32 16 8 4",
"output": "2"
},
{
"input": "10 11 12 12",
"output": "42"
},
{
"input": "1 2 10 20",
"output": "42"
},
{
"input": "27 9 3 1",
"output": "42"
},
{
"input": "81 108 144 192",
"output": "256"
},
{
"input": "2 3 4 6",
"output": "42"
},
{
"input": "1000 500 170 40",
"output": "42"
}
] | 92 | 0 | 0 | 5,110 |
|
793 | Igor and his way to work | [
"dfs and similar",
"graphs",
"implementation",
"shortest paths"
] | null | null | Woken up by the alarm clock Igor the financial analyst hurried up to the work. He ate his breakfast and sat in his car. Sadly, when he opened his GPS navigator, he found that some of the roads in Bankopolis, the city where he lives, are closed due to road works. Moreover, Igor has some problems with the steering wheel, so he can make no more than two turns on his way to his office in bank.
Bankopolis looks like a grid of *n* rows and *m* columns. Igor should find a way from his home to the bank that has no more than two turns and doesn't contain cells with road works, or determine that it is impossible and he should work from home. A turn is a change in movement direction. Igor's car can only move to the left, to the right, upwards and downwards. Initially Igor can choose any direction. Igor is still sleepy, so you should help him. | The first line contains two integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=1000)Β β the number of rows and the number of columns in the grid.
Each of the next *n* lines contains *m* characters denoting the corresponding row of the grid. The following characters can occur:
- "." β an empty cell; - "*" β a cell with road works; - "S" β the cell where Igor's home is located; - "T" β the cell where Igor's office is located.
It is guaranteed that "S" and "T" appear exactly once each. | In the only line print "YES" if there is a path between Igor's home and Igor's office with no more than two turns, and "NO" otherwise. | [
"5 5\n..S..\n****.\nT....\n****.\n.....\n",
"5 5\nS....\n****.\n.....\n.****\n..T..\n"
] | [
"YES",
"NO"
] | The first sample is shown on the following picture:
In the second sample it is impossible to reach Igor's office using less that 4 turns, thus there exists no path using no more than 2 turns. The path using exactly 4 turns is shown on this picture: | [
{
"input": "5 5\nS....\n****.\n.....\n.****\n..T..",
"output": "NO"
},
{
"input": "1 2\nST",
"output": "YES"
},
{
"input": "3 1\nS\n*\nT",
"output": "NO"
},
{
"input": "3 3\n*..\n...\nTS.",
"output": "YES"
},
{
"input": "3 3\nT.*\n*.*\n*S*",
"output": "YES"
},
{
"input": "7 7\n.S.****\n...*.*.\n.****..\n.*.**.*\n..T*...\n***..*.\n*******",
"output": "YES"
},
{
"input": "3 3\n**T\n*S*\n***",
"output": "NO"
},
{
"input": "2 2\nST\n*.",
"output": "YES"
},
{
"input": "2 2\nS.\n.T",
"output": "YES"
},
{
"input": "2 2\nTS\n.*",
"output": "YES"
},
{
"input": "2 2\n.T\nS*",
"output": "YES"
}
] | 46 | 5,529,600 | -1 | 5,118 |
|
375 | Divisible by Seven | [
"math",
"number theory"
] | null | null | You have number *a*, whose decimal representation quite luckily contains digits 1, 6, 8, 9. Rearrange the digits in its decimal representation so that the resulting number will be divisible by 7.
Number *a* doesn't contain any leading zeroes and contains digits 1, 6, 8, 9 (it also can contain another digits). The resulting number also mustn't contain any leading zeroes. | The first line contains positive integer *a* in the decimal record. It is guaranteed that the record of number *a* contains digits: 1, 6, 8, 9. Number *a* doesn't contain any leading zeroes. The decimal representation of number *a* contains at least 4 and at most 106 characters. | Print a number in the decimal notation without leading zeroes β the result of the permutation.
If it is impossible to rearrange the digits of the number *a* in the required manner, print 0. | [
"1689\n",
"18906\n"
] | [
"1869\n",
"18690\n"
] | none | [
{
"input": "1689",
"output": "1869"
},
{
"input": "18906",
"output": "18690"
},
{
"input": "2419323689",
"output": "2432391689"
},
{
"input": "8589157262",
"output": "5857221986"
},
{
"input": "2717172350336955863014903670481525170997949309274087058935108848979319747543008692128164875210350026",
"output": "2771723503355630149036704815251709979493092740870589351088489793197475430086921281648752103500261986"
},
{
"input": "9825995656040286793128006047268547610068699214477842995873286607346639816314908021369221299622234988",
"output": "2599556040286793280060472685476100686992144778429958732866073466398163149080213692212996222349881968"
},
{
"input": "100000000689",
"output": "186900000000"
},
{
"input": "16891",
"output": "16198"
},
{
"input": "16892",
"output": "21896"
},
{
"input": "16893",
"output": "31689"
},
{
"input": "16894",
"output": "41986"
},
{
"input": "16895",
"output": "51968"
},
{
"input": "16896",
"output": "61698"
},
{
"input": "16897",
"output": "71869"
},
{
"input": "16898",
"output": "86198"
},
{
"input": "16899",
"output": "91896"
},
{
"input": "4048169",
"output": "4041968"
},
{
"input": "10994168",
"output": "94116890"
},
{
"input": "168903",
"output": "316890"
},
{
"input": "11689",
"output": "16198"
},
{
"input": "91111168",
"output": "11111968"
},
{
"input": "16890000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"output": "18690000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
},
{
"input": "1689999999999",
"output": "9999999991968"
},
{
"input": "9883291673084",
"output": "8329730841698"
},
{
"input": "6198",
"output": "1869"
}
] | 1,000 | 12,902,400 | 0 | 5,119 |
|
766 | Mahmoud and a Triangle | [
"constructive algorithms",
"geometry",
"greedy",
"math",
"number theory",
"sortings"
] | null | null | Mahmoud has *n* line segments, the *i*-th of them has length *a**i*. Ehab challenged him to use exactly 3 line segments to form a non-degenerate triangle. Mahmoud doesn't accept challenges unless he is sure he can win, so he asked you to tell him if he should accept the challenge. Given the lengths of the line segments, check if he can choose exactly 3 of them to form a non-degenerate triangle.
Mahmoud should use exactly 3 line segments, he can't concatenate two line segments or change any length. A non-degenerate triangle is a triangle with positive area. | The first line contains single integer *n* (3<=β€<=*n*<=β€<=105)Β β the number of line segments Mahmoud has.
The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=109)Β β the lengths of line segments Mahmoud has. | In the only line print "YES" if he can choose exactly three line segments and form a non-degenerate triangle with them, and "NO" otherwise. | [
"5\n1 5 3 2 4\n",
"3\n4 1 2\n"
] | [
"YES\n",
"NO\n"
] | For the first example, he can use line segments with lengths 2, 4 and 5 to form a non-degenerate triangle. | [
{
"input": "5\n1 5 3 2 4",
"output": "YES"
},
{
"input": "3\n4 1 2",
"output": "NO"
},
{
"input": "30\n197 75 517 39724 7906061 1153471 3 15166 168284 3019844 272293 316 16 24548 42 118 5792 5 9373 1866366 4886214 24 2206 712886 104005 1363 836 64273 440585 3576",
"output": "NO"
},
{
"input": "30\n229017064 335281886 247217656 670601882 743442492 615491486 544941439 911270108 474843964 803323771 177115397 62179276 390270885 754889875 881720571 902691435 154083299 328505383 761264351 182674686 94104683 357622370 573909964 320060691 33548810 247029007 812823597 946798893 813659359 710111761",
"output": "YES"
},
{
"input": "40\n740553458 532562042 138583675 75471987 487348843 476240280 972115023 103690894 546736371 915774563 35356828 819948191 138721993 24257926 761587264 767176616 608310208 78275645 386063134 227581756 672567198 177797611 87579917 941781518 274774331 843623616 981221615 630282032 118843963 749160513 354134861 132333165 405839062 522698334 29698277 541005920 856214146 167344951 398332403 68622974",
"output": "YES"
},
{
"input": "40\n155 1470176 7384 765965701 1075 4 561554 6227772 93 16304522 1744 662 3 292572860 19335 908613 42685804 347058 20 132560 3848974 69067081 58 2819 111752888 408 81925 30 11951 4564 251 26381275 473392832 50628 180819969 2378797 10076746 9 214492 31291",
"output": "NO"
},
{
"input": "3\n1 1000000000 1000000000",
"output": "YES"
},
{
"input": "4\n1 1000000000 1000000000 1000000000",
"output": "YES"
},
{
"input": "3\n1 1000000000 1",
"output": "NO"
},
{
"input": "5\n1 2 3 5 2",
"output": "YES"
},
{
"input": "41\n19 161 4090221 118757367 2 45361275 1562319 596751 140871 97 1844 310910829 10708344 6618115 698 1 87059 33 2527892 12703 73396090 17326460 3 368811 20550 813975131 10 53804 28034805 7847 2992 33254 1139 227930 965568 261 4846 503064297 192153458 57 431",
"output": "NO"
},
{
"input": "42\n4317083 530966905 202811311 104 389267 35 1203 18287479 125344279 21690 859122498 65 859122508 56790 1951 148683 457 1 22 2668100 8283 2 77467028 13405 11302280 47877251 328155592 35095 29589769 240574 4 10 1019123 6985189 629846 5118 169 1648973 91891 741 282 3159",
"output": "YES"
},
{
"input": "43\n729551585 11379 5931704 330557 1653 15529406 729551578 278663905 1 729551584 2683 40656510 29802 147 1400284 2 126260 865419 51 17 172223763 86 1 534861 450887671 32 234 25127103 9597697 48226 7034 389 204294 2265706 65783617 4343 3665990 626 78034 106440137 5 18421 1023",
"output": "YES"
},
{
"input": "44\n719528276 2 235 444692918 24781885 169857576 18164 47558 15316043 9465834 64879816 2234575 1631 853530 8 1001 621 719528259 84 6933 31 1 3615623 719528266 40097928 274835337 1381044 11225 2642 5850203 6 527506 18 104977753 76959 29393 49 4283 141 201482 380 1 124523 326015",
"output": "YES"
},
{
"input": "45\n28237 82 62327732 506757 691225170 5 970 4118 264024506 313192 367 14713577 73933 691225154 6660 599 691225145 3473403 51 427200630 1326718 2146678 100848386 1569 27 163176119 193562 10784 45687 819951 38520653 225 119620 1 3 691225169 691225164 17445 23807072 1 9093493 5620082 2542 139 14",
"output": "YES"
},
{
"input": "44\n165580141 21 34 55 1 89 144 17711 2 377 610 987 2584 13 5 4181 6765 10946 1597 8 28657 3 233 75025 121393 196418 317811 9227465 832040 1346269 2178309 3524578 5702887 1 14930352 102334155 24157817 39088169 63245986 701408733 267914296 433494437 514229 46368",
"output": "NO"
},
{
"input": "3\n1 1000000000 999999999",
"output": "NO"
},
{
"input": "5\n1 1 1 1 1",
"output": "YES"
},
{
"input": "10\n1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000",
"output": "NO"
},
{
"input": "5\n2 3 4 10 20",
"output": "YES"
},
{
"input": "6\n18 23 40 80 160 161",
"output": "YES"
},
{
"input": "4\n5 6 7 888",
"output": "YES"
},
{
"input": "9\n1 1 2 2 4 5 10 10 20",
"output": "YES"
},
{
"input": "7\n3 150 900 4 500 1500 5",
"output": "YES"
},
{
"input": "3\n2 2 3",
"output": "YES"
},
{
"input": "7\n1 2 100 200 250 1000000 2000000",
"output": "YES"
},
{
"input": "8\n2 3 5 5 5 6 6 13",
"output": "YES"
},
{
"input": "3\n2 3 4",
"output": "YES"
},
{
"input": "6\n1 1 1 4 5 100",
"output": "YES"
},
{
"input": "13\n1 2 3 5 8 13 22 34 55 89 144 233 377",
"output": "YES"
},
{
"input": "4\n2 3 4 8",
"output": "YES"
},
{
"input": "3\n5 6 7",
"output": "YES"
},
{
"input": "5\n1 4 5 6 1000000",
"output": "YES"
},
{
"input": "4\n5 6 7 20",
"output": "YES"
},
{
"input": "6\n1 1 1 1 1 65",
"output": "YES"
},
{
"input": "4\n3 4 5 100",
"output": "YES"
},
{
"input": "3\n2 4 5",
"output": "YES"
},
{
"input": "7\n1 1 1 1 1 10 1000",
"output": "YES"
},
{
"input": "4\n1 1 2 3",
"output": "NO"
},
{
"input": "11\n1 2 5 6 7 8 9 17 18 19 100",
"output": "YES"
},
{
"input": "4\n5 16 20 200",
"output": "YES"
},
{
"input": "5\n17 6 3 3 1",
"output": "YES"
},
{
"input": "3\n1 1 1",
"output": "YES"
},
{
"input": "6\n1 1 1 2 3 5",
"output": "YES"
},
{
"input": "4\n2 4 6 6",
"output": "YES"
},
{
"input": "9\n1 2 4 4 4 4 7 8 20",
"output": "YES"
},
{
"input": "9\n1 1 2 5 5 5 10 10 20",
"output": "YES"
},
{
"input": "7\n3 150 600 4 1700 6000 5",
"output": "YES"
},
{
"input": "5\n5761 20966 27841 28800 29399",
"output": "YES"
},
{
"input": "9\n1 2 3 6 7 10 11 12 24",
"output": "YES"
},
{
"input": "4\n1 2 1 1",
"output": "YES"
},
{
"input": "5\n1 1 2 3 4",
"output": "YES"
}
] | 2,000 | 20,172,800 | 0 | 5,147 |
|
958 | Maximum Control (easy) | [
"implementation"
] | null | null | The Resistance is trying to take control over all planets in a particular solar system. This solar system is shaped like a tree. More precisely, some planets are connected by bidirectional hyperspace tunnels in such a way that there is a path between every pair of the planets, but removing any tunnel would disconnect some of them.
The Resistance already has measures in place that will, when the time is right, enable them to control every planet that is not remote. A planet is considered to be remote if it is connected to the rest of the planets only via a single hyperspace tunnel.
How much work is there left to be done: that is, how many remote planets are there? | The first line of the input contains an integer *N* (2<=β€<=*N*<=β€<=1000) β the number of planets in the galaxy.
The next *N*<=-<=1 lines describe the hyperspace tunnels between the planets. Each of the *N*<=-<=1 lines contains two space-separated integers *u* and *v* (1<=β€<=*u*,<=*v*<=β€<=*N*) indicating that there is a bidirectional hyperspace tunnel between the planets *u* and *v*. It is guaranteed that every two planets are connected by a path of tunnels, and that each tunnel connects a different pair of planets. | A single integer denoting the number of remote planets. | [
"5\n4 1\n4 2\n1 3\n1 5\n",
"4\n1 2\n4 3\n1 4\n"
] | [
"3\n",
"2\n"
] | In the first example, only planets 2, 3 and 5 are connected by a single tunnel.
In the second example, the remote planets are 2 and 3.
Note that this problem has only two versions β easy and medium. | [
{
"input": "5\n4 1\n4 2\n1 3\n1 5",
"output": "3"
},
{
"input": "4\n1 2\n4 3\n1 4",
"output": "2"
},
{
"input": "10\n4 3\n2 6\n10 1\n5 7\n5 8\n10 6\n5 9\n9 3\n2 9",
"output": "4"
}
] | 46 | 0 | 3 | 5,151 |
|
587 | Duff and Weight Lifting | [
"greedy"
] | null | null | Recently, Duff has been practicing weight lifting. As a hard practice, Malek gave her a task. He gave her a sequence of weights. Weight of *i*-th of them is 2*w**i* pounds. In each step, Duff can lift some of the remaining weights and throw them away. She does this until there's no more weight left. Malek asked her to minimize the number of steps.
Duff is a competitive programming fan. That's why in each step, she can only lift and throw away a sequence of weights 2*a*1,<=...,<=2*a**k* if and only if there exists a non-negative integer *x* such that 2*a*1<=+<=2*a*2<=+<=...<=+<=2*a**k*<==<=2*x*, i. e. the sum of those numbers is a power of two.
Duff is a competitive programming fan, but not a programmer. That's why she asked for your help. Help her minimize the number of steps. | The first line of input contains integer *n* (1<=β€<=*n*<=β€<=106), the number of weights.
The second line contains *n* integers *w*1,<=...,<=*w**n* separated by spaces (0<=β€<=*w**i*<=β€<=106 for each 1<=β€<=*i*<=β€<=*n*), the powers of two forming the weights values. | Print the minimum number of steps in a single line. | [
"5\n1 1 2 3 3\n",
"4\n0 1 2 3\n"
] | [
"2\n",
"4\n"
] | In the first sample case: One optimal way would be to throw away the first three in the first step and the rest in the second step. Also, it's not possible to do it in one step because their sum is not a power of two.
In the second sample case: The only optimal way is to throw away one weight in each step. It's not possible to do it in less than 4 steps because there's no subset of weights with more than one weight and sum equal to a power of two. | [
{
"input": "5\n1 1 2 3 3",
"output": "2"
},
{
"input": "4\n0 1 2 3",
"output": "4"
},
{
"input": "1\n120287",
"output": "1"
},
{
"input": "2\n28288 0",
"output": "2"
},
{
"input": "2\n95745 95745",
"output": "1"
},
{
"input": "13\n92 194 580495 0 10855 41704 13 96429 33 213 0 92 140599",
"output": "11"
},
{
"input": "13\n688743 688743 1975 688743 688743 688743 688743 688743 688743 0 0 688743 688743",
"output": "4"
},
{
"input": "35\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0",
"output": "3"
},
{
"input": "35\n130212 3176 77075 8071 18 1369 7539 1683 80757 1847 0 1374 122 8524 4 2 21333 270264 4 9254 151921 0 1 33596 73002 54382 0 1 29233 75952 15 38892 1877 6167 4",
"output": "31"
},
{
"input": "35\n0 0 298 0 0 0 0 0 689063 65442 0 984598 2054 43668 0 369 0 2054 0 996220 0 16327 369 0 996220 0 0 0 4693 2054 348 0 118 0 0",
"output": "16"
},
{
"input": "100\n196 1681 196 0 61 93 196 196 196 196 196 0 0 96 18 1576 0 93 666463 18 93 1 1278 8939 93 196 196 1278 3 0 67416 869956 10 56489 196 745 39 783 196 8939 196 81 69634 4552 39 3 14 20 25 8 10 4 7302 0 19579 20 1140 15990 7302 0 19579 4142 11 1354 75252 93 311 1278 0 79475 10 75252 93 7302 0 81 408441 19579 10 39 19 37748 4364 31135 47700 105818 47700 10 4142 543356 3 30647 45917 60714 8939 18 22925 7302 93 75252",
"output": "59"
}
] | 1,000 | 69,427,200 | 0 | 5,172 |
|
771 | Bear and Different Names | [
"constructive algorithms",
"greedy"
] | null | null | In the army, it isn't easy to form a group of soldiers that will be effective on the battlefield. The communication is crucial and thus no two soldiers should share a name (what would happen if they got an order that Bob is a scouter, if there are two Bobs?).
A group of soldiers is effective if and only if their names are different. For example, a group (John, Bob, Limak) would be effective, while groups (Gary, Bob, Gary) and (Alice, Alice) wouldn't.
You are a spy in the enemy's camp. You noticed *n* soldiers standing in a row, numbered 1 through *n*. The general wants to choose a group of *k* consecutive soldiers. For every *k* consecutive soldiers, the general wrote down whether they would be an effective group or not.
You managed to steal the general's notes, with *n*<=-<=*k*<=+<=1 strings *s*1,<=*s*2,<=...,<=*s**n*<=-<=*k*<=+<=1, each either "YES" or "NO".
- The string *s*1 describes a group of soldiers 1 through *k* ("YES" if the group is effective, and "NO" otherwise). - The string *s*2 describes a group of soldiers 2 through *k*<=+<=1. - And so on, till the string *s**n*<=-<=*k*<=+<=1 that describes a group of soldiers *n*<=-<=*k*<=+<=1 through *n*.
Your task is to find possible names of *n* soldiers. Names should match the stolen notes. Each name should be a string that consists of between 1 and 10 English letters, inclusive. The first letter should be uppercase, and all other letters should be lowercase. Names don't have to be existing namesΒ β it's allowed to print "Xyzzzdj" or "T" for example.
Find and print any solution. It can be proved that there always exists at least one solution. | The first line of the input contains two integers *n* and *k* (2<=β€<=*k*<=β€<=*n*<=β€<=50)Β β the number of soldiers and the size of a group respectively.
The second line contains *n*<=-<=*k*<=+<=1 strings *s*1,<=*s*2,<=...,<=*s**n*<=-<=*k*<=+<=1. The string *s**i* is "YES" if the group of soldiers *i* through *i*<=+<=*k*<=-<=1 is effective, and "NO" otherwise. | Find any solution satisfying all given conditions. In one line print *n* space-separated strings, denoting possible names of soldiers in the order. The first letter of each name should be uppercase, while the other letters should be lowercase. Each name should contain English letters only and has length from 1 to 10.
If there are multiple valid solutions, print any of them. | [
"8 3\nNO NO YES YES YES NO\n",
"9 8\nYES NO\n",
"3 2\nNO NO\n"
] | [
"Adam Bob Bob Cpqepqwer Limak Adam Bob Adam",
"R Q Ccccccccc Ccocc Ccc So Strong Samples Ccc",
"Na Na Na"
] | In the first sample, there are 8 soldiers. For every 3 consecutive ones we know whether they would be an effective group. Let's analyze the provided sample output:
- First three soldiers (i.e. Adam, Bob, Bob) wouldn't be an effective group because there are two Bobs. Indeed, the string *s*<sub class="lower-index">1</sub> is "NO". - Soldiers 2 through 4 (Bob, Bob, Cpqepqwer) wouldn't be effective either, and the string *s*<sub class="lower-index">2</sub> is "NO". - Soldiers 3 through 5 (Bob, Cpqepqwer, Limak) would be effective, and the string *s*<sub class="lower-index">3</sub> is "YES". - ..., - Soldiers 6 through 8 (Adam, Bob, Adam) wouldn't be effective, and the string *s*<sub class="lower-index">6</sub> is "NO". | [
{
"input": "8 3\nNO NO YES YES YES NO",
"output": "Ab Ac Ab Ac Af Ag Ah Ag "
},
{
"input": "9 8\nYES NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Ac "
},
{
"input": "3 2\nNO NO",
"output": "Ab Ab Ab "
},
{
"input": "2 2\nYES",
"output": "Ab Ac "
},
{
"input": "2 2\nNO",
"output": "Ab Ab "
},
{
"input": "7 2\nYES NO YES YES NO YES",
"output": "Ab Ac Ac Ae Af Af Ah "
},
{
"input": "18 7\nYES YES YES YES YES YES YES NO NO NO NO NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ai Aj Ak Al Am "
},
{
"input": "50 3\nNO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO YES NO",
"output": "Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Ab Ac Bx Ac "
},
{
"input": "19 15\nNO YES YES YES NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ab Aq Ar As Af "
},
{
"input": "3 2\nNO NO",
"output": "Ab Ab Ab "
},
{
"input": "3 2\nNO YES",
"output": "Ab Ab Ad "
},
{
"input": "3 2\nYES NO",
"output": "Ab Ac Ac "
},
{
"input": "3 2\nYES YES",
"output": "Ab Ac Ad "
},
{
"input": "26 17\nNO YES YES YES NO YES NO YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ab As At Au Af Aw Ah Ay Az Ba "
},
{
"input": "12 2\nYES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am "
},
{
"input": "16 2\nNO NO NO NO NO NO NO NO NO NO NO NO NO NO NO",
"output": "Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab Ab "
},
{
"input": "42 20\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq "
},
{
"input": "37 14\nNO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al "
},
{
"input": "29 10\nYES NO YES NO YES NO YES YES YES YES YES NO NO NO NO NO YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Ac Am Ae Ao Ag Aq Ar As At Au Am Ae Ao Ag Aq Ba Bb Bc Bd "
},
{
"input": "37 3\nYES NO YES NO YES NO YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES NO NO YES NO NO YES YES YES YES NO",
"output": "Ab Ac Ad Ac Af Ac Ah Ac Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Ba Bb Be Bb Be Bh Bi Bj Bk Bj "
},
{
"input": "44 11\nNO NO YES NO YES NO YES YES YES YES YES YES YES YES YES YES YES YES YES NO YES YES YES YES YES NO NO YES NO NO YES YES YES NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Ab Ac An Ae Ap Ag Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Au Bf Bg Bh Bi Bj Ba Bb Bm Bd Au Bp Bq Br Bi "
},
{
"input": "50 49\nNO YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Ab By "
},
{
"input": "50 49\nYES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "50 49\nNO NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Ab Ac "
},
{
"input": "50 49\nYES NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx Ac "
},
{
"input": "46 42\nNO YES YES YES NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Ab Br Bs Bt Af "
},
{
"input": "45 26\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt "
},
{
"input": "45 26\nNO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au "
},
{
"input": "50 3\nNO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES",
"output": "Ab Ac Ab Ae Ab Ag Ab Ai Ab Ak Ab Am Ab Ao Ab Aq Ab As Ab Au Ab Aw Ab Ay Ab Ba Ab Bc Ab Be Ab Bg Ab Bi Ab Bk Ab Bm Ab Bo Ab Bq Ab Bs Ab Bu Ab Bw Ab By "
},
{
"input": "50 2\nNO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO",
"output": "Ab Ab Ad Ad Af Af Ah Ah Aj Aj Al Al An An Ap Ap Ar Ar At At Av Av Ax Ax Az Az Bb Bb Bd Bd Bf Bf Bh Bh Bj Bj Bl Bl Bn Bn Bp Bp Br Br Bt Bt Bv Bv Bx Bx "
},
{
"input": "50 3\nNO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES YES YES YES YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES",
"output": "Ab Ac Ab Ae Ab Ag Ab Ai Ab Ak Ab Am Ab Ao Ab Aq Ab As Ab Au Ab Aw Ab Ay Ab Ba Ab Bc Bd Be Bf Bg Bf Bi Bf Bk Bf Bm Bf Bo Bf Bq Bf Bs Bf Bu Bf Bw Bf By "
},
{
"input": "49 2\nNO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO NO NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES NO YES",
"output": "Ab Ab Ad Ad Af Af Ah Ah Aj Aj Al Al An An Ap Ap Ar Ar At At Av Av Ax Ax Ax Ax Bb Bb Bd Bd Bf Bf Bh Bh Bj Bj Bl Bl Bn Bn Bp Bp Br Br Bt Bt Bv Bv Bx "
},
{
"input": "35 22\nNO NO NO NO NO NO NO NO NO NO NO NO NO NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao "
},
{
"input": "46 41\nYES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu "
},
{
"input": "12 4\nYES YES NO NO NO NO NO YES YES",
"output": "Ab Ac Ad Ae Af Ad Ae Af Ad Ae Al Am "
},
{
"input": "50 2\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "50 4\nYES YES YES YES YES NO YES YES YES YES NO NO YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES NO YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Ag Ak Al Am An Al Am Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bc Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "34 5\nYES YES YES YES YES NO YES YES YES YES NO NO YES YES YES NO NO YES NO YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ag Al Am An Ao Al Am Ar As At Am Ar Aw At Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi "
},
{
"input": "50 43\nYES NO YES NO YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Ac Bt Ae Bv Bw Bx By "
},
{
"input": "38 30\nNO NO YES NO YES NO NO NO NO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Ab Ac Bg Ae Bi Ag Ah Ai Aj "
},
{
"input": "50 50\nNO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx Ab "
},
{
"input": "50 50\nYES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "5 3\nYES NO YES",
"output": "Ab Ac Ad Ac Af "
},
{
"input": "30 2\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be "
},
{
"input": "50 50\nYES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "27 27\nYES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb "
},
{
"input": "28 2\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc "
},
{
"input": "50 2\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "8 3\nYES NO YES NO YES NO",
"output": "Ab Ac Ad Ac Af Ac Ah Ac "
},
{
"input": "42 30\nNO YES YES NO NO YES NO YES NO YES NO NO YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Ab Bf Bg Ae Af Bj Ah Bl Aj Bn Al Am Bq "
},
{
"input": "50 49\nYES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "50 3\nYES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx By "
},
{
"input": "7 5\nYES NO YES",
"output": "Ab Ac Ad Ae Af Ac Ah "
},
{
"input": "8 4\nNO YES NO YES NO",
"output": "Ab Ac Ad Ab Af Ad Ah Af "
},
{
"input": "50 50\nNO",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Bx Ab "
},
{
"input": "50 48\nYES NO YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ap Aq Ar As At Au Av Aw Ax Ay Az Ba Bb Bc Bd Be Bf Bg Bh Bi Bj Bk Bl Bm Bn Bo Bp Bq Br Bs Bt Bu Bv Bw Ac By "
},
{
"input": "29 14\nYES NO YES NO NO YES YES NO NO YES YES NO NO YES YES YES",
"output": "Ab Ac Ad Ae Af Ag Ah Ai Aj Ak Al Am An Ao Ac Aq Ae Af At Au Ai Aj Ax Ay Am An Bb Bc Bd "
},
{
"input": "10 3\nNO YES NO YES NO YES NO YES",
"output": "Ab Ac Ab Ae Ab Ag Ab Ai Ab Ak "
},
{
"input": "10 5\nYES NO YES NO YES NO",
"output": "Ab Ac Ad Ae Af Ac Ah Ae Aj Ac "
}
] | 202 | 2,662,400 | -1 | 5,189 |
|
160 | Unlucky Ticket | [
"greedy",
"sortings"
] | null | null | Each of you probably has your personal experience of riding public transportation and buying tickets. After a person buys a ticket (which traditionally has an even number of digits), he usually checks whether the ticket is lucky. Let us remind you that a ticket is lucky if the sum of digits in its first half matches the sum of digits in its second half.
But of course, not every ticket can be lucky. Far from it! Moreover, sometimes one look at a ticket can be enough to say right away that the ticket is not lucky. So, let's consider the following unluckiness criterion that can definitely determine an unlucky ticket. We'll say that a ticket is definitely unlucky if each digit from the first half corresponds to some digit from the second half so that each digit from the first half is strictly less than the corresponding digit from the second one or each digit from the first half is strictly more than the corresponding digit from the second one. Each digit should be used exactly once in the comparisons. In other words, there is such bijective correspondence between the digits of the first and the second half of the ticket, that either each digit of the first half turns out strictly less than the corresponding digit of the second half or each digit of the first half turns out strictly more than the corresponding digit from the second half.
For example, ticket 2421 meets the following unluckiness criterion and will not be considered lucky (the sought correspondence is 2<=><=1 and 4<=><=2), ticket 0135 also meets the criterion (the sought correspondence is 0<=<<=3 and 1<=<<=5), and ticket 3754 does not meet the criterion.
You have a ticket in your hands, it contains 2*n* digits. Your task is to check whether it meets the unluckiness criterion. | The first line contains an integer *n* (1<=β€<=*n*<=β€<=100). The second line contains a string that consists of 2*n* digits and defines your ticket. | In the first line print "YES" if the ticket meets the unluckiness criterion. Otherwise, print "NO" (without the quotes). | [
"2\n2421\n",
"2\n0135\n",
"2\n3754\n"
] | [
"YES\n",
"YES\n",
"NO\n"
] | none | [
{
"input": "2\n2421",
"output": "YES"
},
{
"input": "2\n0135",
"output": "YES"
},
{
"input": "2\n3754",
"output": "NO"
},
{
"input": "1\n33",
"output": "NO"
},
{
"input": "2\n3444",
"output": "NO"
},
{
"input": "3\n221323",
"output": "YES"
},
{
"input": "3\n132432",
"output": "YES"
},
{
"input": "1\n10",
"output": "YES"
},
{
"input": "3\n999000",
"output": "YES"
},
{
"input": "5\n2563434512",
"output": "YES"
},
{
"input": "10\n01101001000011011110",
"output": "NO"
},
{
"input": "10\n10001222212022211120",
"output": "NO"
},
{
"input": "10\n36828132853144011224",
"output": "YES"
},
{
"input": "20\n1011022122111202122200100211021100001122",
"output": "NO"
},
{
"input": "20\n5232324254212415411311123313002001301121",
"output": "YES"
},
{
"input": "20\n7405800505032736115894335199688161431589",
"output": "YES"
},
{
"input": "20\n3415010010430312351463661555326552265642",
"output": "YES"
},
{
"input": "50\n2102200200102000012010102011211201121112001112220022023331220132002222113003003302101312001033110321",
"output": "NO"
},
{
"input": "50\n5612454122355331521225634515354651153334442245234623042403102434401340330012200102111030242232001423",
"output": "YES"
},
{
"input": "50\n0013011201111112210231333121030031021132323232322331422253215312454431312252454531121325154332452522",
"output": "YES"
},
{
"input": "50\n1333113332002310001130333200002120101112101000001001122200021012010112000102121102212021200102011000",
"output": "NO"
},
{
"input": "50\n7768982292275759939882751465173844816331588199736866065335518782157581162167237401803021840688341656",
"output": "YES"
},
{
"input": "50\n5060172568971658079607579942843871533766899530593457744544240062187820782803777264583028807003285606",
"output": "NO"
},
{
"input": "100\n32033233210213232101210131232021120310331112120033001231123232221200213021203033300033131302232100038528951495743459997297531816949698487426212357538284284222536535855445278621151486932989238531899512",
"output": "YES"
},
{
"input": "100\n02002102210011010100120120200220102011120101221112212222120020210120100100210020110121012200202122003345665163205330111020604514053164225655212253500113103534213313020162345540026653211623642123220355",
"output": "NO"
},
{
"input": "100\n77183123282838517843664381789267288922656323541699343586762218319159218294863295482798464649254394971213132422224212223202404302223411433322333414121022024111412343110143421202444434024400100413442214",
"output": "YES"
},
{
"input": "100\n10001111012200211011000121001200011210000020102102001022212010122102202221201112010122020001101100108897949728635541168542364573471936555772537461654157812311614931827469976934765219573155999659346292",
"output": "YES"
},
{
"input": "100\n01232301021031212111013002303211223032012113201031332103213332222202203330122103103121131233013000116022330435355138573123144360458655075068170808157467335580232261005471574645456707410743351868832288",
"output": "NO"
},
{
"input": "100\n29984263744168545119858476736999712929651758223788987449661283528958984743292587725324189134223179864351053241163312352223630541424435625146656004416300322106250255412140420461130552626644306153634053",
"output": "YES"
},
{
"input": "100\n31600324621210624556500610052054505630313425345404534213653266122646254136660603332516425411106060211654812165791554127683771773326741719787895359171717963263779732526239927838412657412425615852874991",
"output": "YES"
},
{
"input": "1\n09",
"output": "YES"
},
{
"input": "10\n11111111112222222222",
"output": "YES"
},
{
"input": "100\n88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"output": "YES"
},
{
"input": "100\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110",
"output": "NO"
},
{
"input": "100\n88888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"output": "YES"
},
{
"input": "2\n2231",
"output": "NO"
},
{
"input": "100\n11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222",
"output": "YES"
},
{
"input": "100\n10101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010",
"output": "NO"
},
{
"input": "3\n123022",
"output": "NO"
},
{
"input": "2\n2322",
"output": "NO"
},
{
"input": "6\n123456789000",
"output": "NO"
},
{
"input": "10\n22222222224444444444",
"output": "YES"
},
{
"input": "100\n24242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424",
"output": "NO"
},
{
"input": "5\n1257823589",
"output": "NO"
},
{
"input": "3\n158159",
"output": "NO"
},
{
"input": "100\n11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"output": "NO"
},
{
"input": "100\n99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"output": "YES"
},
{
"input": "100\n22343424233121404112342221440103014430444234223303320243202210332120013031314432132430043330110313112023440313043212221301033103041340034304442240323002140112031424013224122404204110340334110122004100",
"output": "NO"
},
{
"input": "3\n378954",
"output": "NO"
},
{
"input": "100\n22222222222222222222222222222222222222222222222222111111111111111111111111111111111111111111111111112222222222222222222222222222222222222222222222222233333333333333333333333333333333333333333333333333",
"output": "YES"
},
{
"input": "3\n123012",
"output": "YES"
},
{
"input": "100\n43242352435435435423653231443242342313412343253241432423524354354354236532314432423423134123432532417897987897897979897879879878979787987987987987989978979878978979798978798798789797879879879879879899",
"output": "YES"
},
{
"input": "3\n000100",
"output": "NO"
},
{
"input": "2\n0001",
"output": "NO"
},
{
"input": "3\n111117",
"output": "NO"
}
] | 62 | 0 | 0 | 5,192 |
|
797 | Broken BST | [
"data structures",
"dfs and similar"
] | null | null | Let *T* be arbitrary binary tree β tree, every vertex of which has no more than two children. Given tree is rooted, so there exists only one vertex which doesn't have a parent β it's the root of a tree. Every vertex has an integer number written on it. Following algorithm is run on every value from the tree *T*:
1. Set pointer to the root of a tree. 1. Return success if the value in the current vertex is equal to the number you are looking for 1. Go to the left child of the vertex if the value in the current vertex is greater than the number you are looking for 1. Go to the right child of the vertex if the value in the current vertex is less than the number you are looking for 1. Return fail if you try to go to the vertex that doesn't exist
Here is the pseudo-code of the described algorithm:
The described algorithm works correctly if the tree is binary search tree (i.e. for each node the values of left subtree are less than the value in the node, the values of right subtree are greater than the value in the node). But it can return invalid result if tree is not a binary search tree.
Since the given tree is not necessarily a binary search tree, not all numbers can be found this way. Your task is to calculate, how many times the search will fail being running on every value from the tree.
If the tree has multiple vertices with the same values on them then you should run algorithm on every one of them separately. | First line contains integer number *n* (1<=β€<=*n*<=β€<=105) β number of vertices in the tree.
Each of the next *n* lines contains 3 numbers *v*, *l*, *r* (0<=β€<=*v*<=β€<=109) β value on current vertex, index of the left child of the vertex and index of the right child of the vertex, respectively. If some child doesn't exist then number <=-<=1 is set instead. Note that different vertices of the tree may contain the same values. | Print number of times when search algorithm will fail. | [
"3\n15 -1 -1\n10 1 3\n5 -1 -1\n",
"8\n6 2 3\n3 4 5\n12 6 7\n1 -1 8\n4 -1 -1\n5 -1 -1\n14 -1 -1\n2 -1 -1\n"
] | [
"2\n",
"1\n"
] | In the example the root of the tree in vertex 2. Search of numbers 5 and 15 will return fail because on the first step algorithm will choose the subtree which doesn't contain numbers you are looking for. | [
{
"input": "3\n15 -1 -1\n10 1 3\n5 -1 -1",
"output": "2"
},
{
"input": "8\n6 2 3\n3 4 5\n12 6 7\n1 -1 8\n4 -1 -1\n5 -1 -1\n14 -1 -1\n2 -1 -1",
"output": "1"
},
{
"input": "1\n493041212 -1 -1",
"output": "0"
},
{
"input": "10\n921294733 5 9\n341281094 -1 -1\n35060484 10 -1\n363363160 -1 -1\n771156014 6 8\n140806462 -1 -1\n118732846 4 2\n603229555 -1 -1\n359289513 3 7\n423237010 -1 -1",
"output": "7"
},
{
"input": "10\n911605217 -1 -1\n801852416 -1 -1\n140035920 -1 9\n981454947 10 2\n404988051 6 3\n307545107 8 7\n278188888 4 1\n523010786 -1 -1\n441817740 -1 -1\n789680429 -1 -1",
"output": "7"
},
{
"input": "10\n921072710 6 8\n727122964 -1 -1\n248695736 2 -1\n947477665 -1 -1\n41229309 -1 -1\n422047611 3 9\n424558429 -1 4\n665046372 -1 5\n74510531 -1 -1\n630373520 7 1",
"output": "7"
},
{
"input": "1\n815121916 -1 -1",
"output": "0"
},
{
"input": "1\n901418150 -1 -1",
"output": "0"
},
{
"input": "3\n2 -1 -1\n1 1 3\n2 -1 -1",
"output": "0"
},
{
"input": "4\n20 2 3\n16 4 -1\n20 -1 -1\n20 -1 -1",
"output": "0"
},
{
"input": "3\n2 2 3\n1 -1 -1\n1 -1 -1",
"output": "0"
},
{
"input": "4\n7122 2 3\n87 4 -1\n7122 -1 -1\n7122 -1 -1",
"output": "0"
},
{
"input": "4\n712222 2 3\n98887 4 -1\n712222 -1 -1\n712222 -1 -1",
"output": "0"
},
{
"input": "3\n6 2 3\n5 -1 -1\n5 -1 -1",
"output": "0"
},
{
"input": "4\n1 -1 2\n0 3 -1\n100 -1 4\n1 -1 -1",
"output": "2"
},
{
"input": "4\n98 2 3\n95 4 -1\n98 -1 -1\n98 -1 -1",
"output": "0"
},
{
"input": "3\n15 2 3\n1 -1 -1\n1 -1 -1",
"output": "0"
},
{
"input": "4\n6 2 -1\n6 3 4\n6 -1 -1\n7 -1 -1",
"output": "1"
},
{
"input": "3\n2 2 3\n3 -1 -1\n3 -1 -1",
"output": "0"
},
{
"input": "4\n1 -1 2\n0 3 -1\n1 -1 4\n0 -1 -1",
"output": "2"
},
{
"input": "4\n1 2 3\n2 -1 -1\n3 4 -1\n2 -1 -1",
"output": "0"
},
{
"input": "1\n0 -1 -1",
"output": "0"
},
{
"input": "3\n5 2 -1\n6 -1 3\n5 -1 -1",
"output": "1"
},
{
"input": "10\n2 -1 -1\n1 -1 8\n2 4 9\n5 -1 2\n5 7 6\n1 -1 1\n4 -1 -1\n0 -1 -1\n8 5 10\n5 -1 -1",
"output": "3"
},
{
"input": "8\n6 -1 -1\n0 5 -1\n4 6 7\n3 -1 -1\n4 3 1\n1 -1 -1\n2 8 4\n2 -1 -1",
"output": "7"
},
{
"input": "4\n5 3 -1\n1 4 -1\n3 -1 2\n1 -1 -1",
"output": "2"
},
{
"input": "3\n10 2 3\n5 -1 -1\n5 -1 -1",
"output": "0"
}
] | 982 | 96,153,600 | 3 | 5,196 |
|
266 | Queue at the School | [
"constructive algorithms",
"graph matchings",
"implementation",
"shortest paths"
] | null | null | During the break the schoolchildren, boys and girls, formed a queue of *n* people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second.
Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from 1 to *n*, at that the person in the position number 1 is served first. Then, if at time *x* a boy stands on the *i*-th position and a girl stands on the (*i*<=+<=1)-th position, then at time *x*<=+<=1 the *i*-th position will have a girl and the (*i*<=+<=1)-th position will have a boy. The time is given in seconds.
You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after *t* seconds. | The first line contains two integers *n* and *t* (1<=β€<=*n*,<=*t*<=β€<=50), which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find.
The next line contains string *s*, which represents the schoolchildren's initial arrangement. If the *i*-th position in the queue contains a boy, then the *i*-th character of string *s* equals "B", otherwise the *i*-th character equals "G". | Print string *a*, which describes the arrangement after *t* seconds. If the *i*-th position has a boy after the needed time, then the *i*-th character *a* must equal "B", otherwise it must equal "G". | [
"5 1\nBGGBG\n",
"5 2\nBGGBG\n",
"4 1\nGGGB\n"
] | [
"GBGGB\n",
"GGBGB\n",
"GGGB\n"
] | none | [
{
"input": "5 1\nBGGBG",
"output": "GBGGB"
},
{
"input": "5 2\nBGGBG",
"output": "GGBGB"
},
{
"input": "4 1\nGGGB",
"output": "GGGB"
},
{
"input": "2 1\nBB",
"output": "BB"
},
{
"input": "2 1\nBG",
"output": "GB"
},
{
"input": "6 2\nBBGBBG",
"output": "GBBGBB"
},
{
"input": "8 3\nBBGBGBGB",
"output": "GGBGBBBB"
},
{
"input": "10 3\nBBGBBBBBBG",
"output": "GBBBBBGBBB"
},
{
"input": "22 7\nGBGGBGGGGGBBBGGBGBGBBB",
"output": "GGGGGGGGBGGBGGBBBBBBBB"
},
{
"input": "50 4\nGBBGBBBGGGGGBBGGBBBBGGGBBBGBBBGGBGGBGBBBGGBGGBGGBG",
"output": "GGBGBGBGBGBGGGBBGBGBGBGBBBGBGBGBGBGBGBGBGBGBGGBGBB"
},
{
"input": "50 8\nGGGGBGGBGGGBGBBBGGGGGGGGBBGBGBGBBGGBGGBGGGGGGGGBBG",
"output": "GGGGGGGGGGGGBGGBGBGBGBGBGGGGGGBGBGBGBGBGBGGBGGBGBB"
},
{
"input": "50 30\nBGGGGGGBGGBGBGGGGBGBBGBBBGGBBBGBGBGGGGGBGBBGBGBGGG",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBBBBBBBBBBBBBBBBBBB"
},
{
"input": "20 20\nBBGGBGGGGBBBGBBGGGBB",
"output": "GGGGGGGGGGBBBBBBBBBB"
},
{
"input": "27 6\nGBGBGBGGGGGGBGGBGGBBGBBBGBB",
"output": "GGGGGGGBGBGBGGGGGBGBBBBBBBB"
},
{
"input": "46 11\nBGGGGGBGBGGBGGGBBGBBGBBGGBBGBBGBGGGGGGGBGBGBGB",
"output": "GGGGGGGGGGGBGGGGGBBGBGBGBGBGBGBGBGBGBGBGBBBBBB"
},
{
"input": "50 6\nBGGBBBBGGBBBBBBGGBGBGBBBBGBBBBBBGBBBBBBBBBBBBBBBBB",
"output": "GGGGBBBBBGBGBGBGBBBGBBBBBBGBBBBBBBBBBBBBBBBBBBBBBB"
},
{
"input": "50 10\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"
},
{
"input": "50 8\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG"
},
{
"input": "50 10\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGB",
"output": "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBB"
},
{
"input": "50 13\nGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG",
"output": "GGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG"
},
{
"input": "1 1\nB",
"output": "B"
},
{
"input": "1 1\nG",
"output": "G"
},
{
"input": "1 50\nB",
"output": "B"
},
{
"input": "1 50\nG",
"output": "G"
},
{
"input": "50 50\nBBBBBBBBGGBBBBBBGBBBBBBBBBBBGBBBBBBBBBBBBBBGBBBBBB",
"output": "GGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"
},
{
"input": "50 50\nGGBBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBGGGGGGBG",
"output": "GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBBBB"
},
{
"input": "6 3\nGGBBBG",
"output": "GGGBBB"
},
{
"input": "26 3\nGBBGBBBBBGGGBGBGGGBGBGGBBG",
"output": "GGBBBBGBGBGBGGGBGBGGGBGBBB"
},
{
"input": "46 3\nGGBBGGGGBBGBGBBBBBGGGBGGGBBGGGBBBGGBGGBBBGBGBB",
"output": "GGGGBGBGGGBBBBBGBGBGBGGGBGGBGBGBGBGBGBGBGBBBBB"
},
{
"input": "44 8\nBGBBBBBBBBBGGBBGBGBGGBBBBBGBBGBBBBBBBBBGBBGB",
"output": "GBBGBGBGBGBGBGBBBBGBBGBBBBBBBBBGBBGBBBBBBBBB"
},
{
"input": "20 20\nBBGGBGGGGBBBGBBGGGBB",
"output": "GGGGGGGGGGBBBBBBBBBB"
},
{
"input": "30 25\nBGGBBGBGGBGBGBBGBGGGGBGBGGBBBB",
"output": "GGGGGGGGGGGGGGGBBBBBBBBBBBBBBB"
},
{
"input": "17 42\nBBGBGBGGGGGGBBGGG",
"output": "GGGGGGGGGGGBBBBBB"
},
{
"input": "30 50\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG",
"output": "GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB"
},
{
"input": "31 33\nBBGGBBGGBGBBBBGGBGBBBGBGGBBGBBB",
"output": "GGGGGGGGGGGGBBBBBBBBBBBBBBBBBBB"
},
{
"input": "2 2\nBG",
"output": "GB"
},
{
"input": "8 8\nGGGBGGBB",
"output": "GGGGGBBB"
},
{
"input": "34 34\nBGGBBBBGGBBGBGGGGGGBBGGGGGBGGBGGGB",
"output": "GGGGGGGGGGGGGGGGGGGGGBBBBBBBBBBBBB"
},
{
"input": "34 20\nBBBBGBGGGBGGGBGBGGBBBBGGBBGGGBGBBG",
"output": "GGGGGGGGGGGGGGGGGBBBBBBBBBBBBBBBBB"
},
{
"input": "50 50\nBBGBBBBBBBBBBBBGBBBGBBBBBBBGBBBBBBGBBBGBBGBBGBBBGG",
"output": "GGGGGGGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB"
},
{
"input": "10 10\nGGGGGGGGGG",
"output": "GGGGGGGGGG"
},
{
"input": "10 10\nBBBBBBBBBB",
"output": "BBBBBBBBBB"
},
{
"input": "10 10\nBGBGBGBGBG",
"output": "GGGGGBBBBB"
},
{
"input": "1 1\nB",
"output": "B"
}
] | 62 | 0 | 0 | 5,201 |
|
604 | More Cowbell | [
"binary search",
"greedy"
] | null | null | Kevin Sun wants to move his precious collection of *n* cowbells from Naperthrill to Exeter, where there is actually grass instead of corn. Before moving, he must pack his cowbells into *k* boxes of a fixed size. In order to keep his collection safe during transportation, he won't place more than two cowbells into a single box. Since Kevin wishes to minimize expenses, he is curious about the smallest size box he can use to pack his entire collection.
Kevin is a meticulous cowbell collector and knows that the size of his *i*-th (1<=β€<=*i*<=β€<=*n*) cowbell is an integer *s**i*. In fact, he keeps his cowbells sorted by size, so *s**i*<=-<=1<=β€<=*s**i* for any *i*<=><=1. Also an expert packer, Kevin can fit one or two cowbells into a box of size *s* if and only if the sum of their sizes does not exceed *s*. Given this information, help Kevin determine the smallest *s* for which it is possible to put all of his cowbells into *k* boxes of size *s*. | The first line of the input contains two space-separated integers *n* and *k* (1<=β€<=*n*<=β€<=2Β·*k*<=β€<=100<=000), denoting the number of cowbells and the number of boxes, respectively.
The next line contains *n* space-separated integers *s*1,<=*s*2,<=...,<=*s**n* (1<=β€<=*s*1<=β€<=*s*2<=β€<=...<=β€<=*s**n*<=β€<=1<=000<=000), the sizes of Kevin's cowbells. It is guaranteed that the sizes *s**i* are given in non-decreasing order. | Print a single integer, the smallest *s* for which it is possible for Kevin to put all of his cowbells into *k* boxes of size *s*. | [
"2 1\n2 5\n",
"4 3\n2 3 5 9\n",
"3 2\n3 5 7\n"
] | [
"7\n",
"9\n",
"8\n"
] | In the first sample, Kevin must pack his two cowbells into the same box.
In the second sample, Kevin can pack together the following sets of cowbells: {2,β3}, {5} and {9}.
In the third sample, the optimal solution is {3,β5} and {7}. | [
{
"input": "2 1\n2 5",
"output": "7"
},
{
"input": "4 3\n2 3 5 9",
"output": "9"
},
{
"input": "3 2\n3 5 7",
"output": "8"
},
{
"input": "20 11\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1",
"output": "2"
},
{
"input": "10 10\n3 15 31 61 63 63 68 94 98 100",
"output": "100"
},
{
"input": "100 97\n340 402 415 466 559 565 649 689 727 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1599 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 3615 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 8534 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983",
"output": "9983"
},
{
"input": "10 9\n7 29 35 38 41 47 54 56 73 74",
"output": "74"
},
{
"input": "1 2342\n12345",
"output": "12345"
},
{
"input": "10 5\n15 15 20 28 38 44 46 52 69 94",
"output": "109"
},
{
"input": "10 9\n6 10 10 32 36 38 69 80 82 93",
"output": "93"
},
{
"input": "10 10\n4 19 22 24 25 43 49 56 78 88",
"output": "88"
},
{
"input": "100 89\n474 532 759 772 803 965 1043 1325 1342 1401 1411 1452 1531 1707 1906 1928 2034 2222 2335 2606 2757 2968 2978 3211 3513 3734 3772 3778 3842 3948 3976 4038 4055 4113 4182 4267 4390 4408 4478 4595 4668 4792 4919 5133 5184 5255 5312 5341 5476 5628 5683 5738 5767 5806 5973 6051 6134 6254 6266 6279 6314 6342 6599 6676 6747 6777 6827 6842 7057 7097 7259 7340 7378 7405 7510 7520 7698 7796 8148 8351 8507 8601 8805 8814 8826 8978 9116 9140 9174 9338 9394 9403 9407 9423 9429 9519 9764 9784 9838 9946",
"output": "9946"
},
{
"input": "100 74\n10 211 323 458 490 592 979 981 1143 1376 1443 1499 1539 1612 1657 1874 2001 2064 2123 2274 2346 2471 2522 2589 2879 2918 2933 2952 3160 3164 3167 3270 3382 3404 3501 3522 3616 3802 3868 3985 4007 4036 4101 4580 4687 4713 4714 4817 4955 5257 5280 5343 5428 5461 5566 5633 5727 5874 5925 6233 6309 6389 6500 6701 6731 6847 6916 7088 7088 7278 7296 7328 7564 7611 7646 7887 7887 8065 8075 8160 8300 8304 8316 8355 8404 8587 8758 8794 8890 9038 9163 9235 9243 9339 9410 9587 9868 9916 9923 9986",
"output": "9986"
},
{
"input": "100 61\n82 167 233 425 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 4819 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927",
"output": "9927"
},
{
"input": "100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 4095 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 5511 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6843 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970",
"output": "9970"
},
{
"input": "100 50\n130 248 312 312 334 589 702 916 921 1034 1047 1346 1445 1500 1585 1744 1951 2123 2273 2362 2400 2455 2496 2530 2532 2944 3074 3093 3094 3134 3698 3967 4047 4102 4109 4260 4355 4466 4617 4701 4852 4892 4915 4917 4936 4981 4999 5106 5152 5203 5214 5282 5412 5486 5525 5648 5897 5933 5969 6251 6400 6421 6422 6558 6805 6832 6908 6924 6943 6980 7092 7206 7374 7417 7479 7546 7672 7756 7973 8020 8028 8079 8084 8085 8137 8153 8178 8239 8639 8667 8829 9263 9333 9370 9420 9579 9723 9784 9841 9993",
"output": "11103"
},
{
"input": "100 50\n156 182 208 409 496 515 659 761 772 794 827 912 1003 1236 1305 1388 1412 1422 1428 1465 1613 2160 2411 2440 2495 2684 2724 2925 3033 3035 3155 3260 3378 3442 3483 3921 4031 4037 4091 4113 4119 4254 4257 4442 4559 4614 4687 4839 4896 5054 5246 5316 5346 5859 5928 5981 6148 6250 6422 6433 6448 6471 6473 6485 6503 6779 6812 7050 7064 7074 7141 7378 7424 7511 7574 7651 7808 7858 8286 8291 8446 8536 8599 8628 8636 8768 8900 8981 9042 9055 9114 9146 9186 9411 9480 9590 9681 9749 9757 9983",
"output": "10676"
},
{
"input": "100 50\n145 195 228 411 577 606 629 775 1040 1040 1058 1187 1307 1514 1784 1867 1891 2042 2042 2236 2549 2555 2560 2617 2766 2807 2829 2917 3070 3072 3078 3095 3138 3147 3149 3196 3285 3287 3309 3435 3531 3560 3563 3769 3830 3967 4081 4158 4315 4387 4590 4632 4897 4914 5128 5190 5224 5302 5402 5416 5420 5467 5517 5653 5820 5862 5941 6053 6082 6275 6292 6316 6490 6530 6619 6632 6895 7071 7234 7323 7334 7412 7626 7743 8098 8098 8136 8158 8264 8616 8701 8718 8770 8803 8809 8983 9422 9530 9811 9866",
"output": "10011"
},
{
"input": "100 50\n56 298 387 456 518 532 589 792 870 1041 1055 1122 1141 1166 1310 1329 1523 1548 1626 1730 1780 1833 1850 1911 2006 2157 2303 2377 2403 2442 2450 2522 2573 2822 2994 3200 3238 3252 3280 3311 3345 3422 3429 3506 3526 3617 3686 3791 4134 4467 4525 4614 4633 4792 5017 5220 5243 5338 5445 5536 5639 5675 5763 5875 6129 6220 6228 6287 6385 6616 6789 6822 6940 6959 6985 7297 7304 7391 7443 7580 7824 7884 7981 8055 8063 8223 8280 8322 8346 8473 8688 8986 9087 9323 9477 9489 9518 9621 9699 9804",
"output": "10009"
},
{
"input": "100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2289 2298 2360 2441 2454 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 6998 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934",
"output": "9934"
},
{
"input": "1 50000\n2",
"output": "2"
},
{
"input": "1 40000\n23456",
"output": "23456"
},
{
"input": "1 2\n10",
"output": "10"
},
{
"input": "1 1\n1",
"output": "1"
},
{
"input": "2 2\n2 3",
"output": "3"
},
{
"input": "4 2\n1 2 8 9",
"output": "10"
}
] | 62 | 7,065,600 | 0 | 5,214 |
|
0 | none | [
"none"
] | null | null | Arpa has found a list containing *n* numbers. He calls a list bad if and only if it is not empty and gcd (see notes section for more information) of numbers in the list is 1.
Arpa can perform two types of operations:
- Choose a number and delete it with cost *x*. - Choose a number and increase it by 1 with cost *y*.
Arpa can apply these operations to as many numbers as he wishes, and he is allowed to apply the second operation arbitrarily many times on the same number.
Help Arpa to find the minimum possible cost to make the list good. | First line contains three integers *n*, *x* and *y* (1<=β€<=*n*<=β€<=5Β·105, 1<=β€<=*x*,<=*y*<=β€<=109)Β β the number of elements in the list and the integers *x* and *y*.
Second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=β€<=*a**i*<=β€<=106)Β β the elements of the list. | Print a single integer: the minimum possible cost to make the list good. | [
"4 23 17\n1 17 17 16\n",
"10 6 2\n100 49 71 73 66 96 8 60 41 63\n"
] | [
"40\n",
"10\n"
] | In example, number 1 must be deleted (with cost 23) and number 16 must increased by 1 (with cost 17).
A gcd (greatest common divisor) of a set of numbers is the maximum integer that divides all integers in the set. Read more about gcd [here](https://en.wikipedia.org/wiki/Greatest_common_divisor). | [] | 0 | 0 | -1 | 5,217 |
|
125 | Measuring Lengths in Baden | [
"math"
] | null | null | Lengths are measures in Baden in inches and feet. To a length from centimeters it is enough to know that an inch equals three centimeters in Baden and one foot contains 12 inches.
You are given a length equal to *n* centimeters. Your task is to convert it to feet and inches so that the number of feet was maximum. The result should be an integer rounded to the closest value containing an integral number of inches.
Note that when you round up, 1 cm rounds up to 0 inches and 2 cm round up to 1 inch. | The only line contains an integer *n* (1<=β€<=*n*<=β€<=10000). | Print two non-negative space-separated integers *a* and *b*, where *a* is the numbers of feet and *b* is the number of inches. | [
"42\n",
"5\n"
] | [
"1 2\n",
"0 2\n"
] | none | [
{
"input": "42",
"output": "1 2"
},
{
"input": "5",
"output": "0 2"
},
{
"input": "24",
"output": "0 8"
},
{
"input": "1",
"output": "0 0"
},
{
"input": "2",
"output": "0 1"
},
{
"input": "3",
"output": "0 1"
},
{
"input": "4",
"output": "0 1"
},
{
"input": "8",
"output": "0 3"
},
{
"input": "10",
"output": "0 3"
},
{
"input": "12",
"output": "0 4"
},
{
"input": "13",
"output": "0 4"
},
{
"input": "100",
"output": "2 9"
},
{
"input": "120",
"output": "3 4"
},
{
"input": "199",
"output": "5 6"
},
{
"input": "501",
"output": "13 11"
},
{
"input": "1000",
"output": "27 9"
},
{
"input": "1233",
"output": "34 3"
},
{
"input": "9876",
"output": "274 4"
},
{
"input": "9999",
"output": "277 9"
},
{
"input": "10000",
"output": "277 9"
},
{
"input": "35",
"output": "1 0"
},
{
"input": "71",
"output": "2 0"
}
] | 218 | 0 | 0 | 5,224 |
|
441 | Valera and Swaps | [
"constructive algorithms",
"dsu",
"graphs",
"implementation",
"math",
"string suffix structures"
] | null | null | A permutation *p* of length *n* is a sequence of distinct integers *p*1,<=*p*2,<=...,<=*p**n* (1<=β€<=*p**i*<=β€<=*n*). A permutation is an identity permutation, if for any *i* the following equation holds *p**i*<==<=*i*.
A swap (*i*,<=*j*) is the operation that swaps elements *p**i* and *p**j* in the permutation. Let's assume that *f*(*p*) is the minimum number of swaps that you need to make the permutation *p* an identity permutation.
Valera wonders, how he can transform permutation *p* into any permutation *q*, such that *f*(*q*)<==<=*m*, using the minimum number of swaps. Help him do that. | The first line contains integer *n* (1<=β€<=*n*<=β€<=3000) β the length of permutation *p*. The second line contains *n* distinct integers *p*1,<=*p*2,<=...,<=*p**n* (1<=β€<=*p**i*<=β€<=*n*) β Valera's initial permutation. The last line contains integer *m* (0<=β€<=*m*<=<<=*n*). | In the first line, print integer *k* β the minimum number of swaps.
In the second line, print 2*k* integers *x*1,<=*x*2,<=...,<=*x*2*k* β the description of the swap sequence. The printed numbers show that you need to consecutively make swaps (*x*1,<=*x*2), (*x*3,<=*x*4), ..., (*x*2*k*<=-<=1,<=*x*2*k*).
If there are multiple sequence swaps of the minimum length, print the lexicographically minimum one. | [
"5\n1 2 3 4 5\n2\n",
"5\n2 1 4 5 3\n2\n"
] | [
"2\n1 2 1 3 ",
"1\n1 2 "
] | Sequence *x*<sub class="lower-index">1</sub>,β*x*<sub class="lower-index">2</sub>,β...,β*x*<sub class="lower-index">*s*</sub> is lexicographically smaller than sequence *y*<sub class="lower-index">1</sub>,β*y*<sub class="lower-index">2</sub>,β...,β*y*<sub class="lower-index">*s*</sub>, if there is such integer *r* (1ββ€β*r*ββ€β*s*), that *x*<sub class="lower-index">1</sub>β=β*y*<sub class="lower-index">1</sub>,β*x*<sub class="lower-index">2</sub>β=β*y*<sub class="lower-index">2</sub>,β...,β*x*<sub class="lower-index">*r*β-β1</sub>β=β*y*<sub class="lower-index">*r*β-β1</sub> and *x*<sub class="lower-index">*r*</sub>β<β*y*<sub class="lower-index">*r*</sub>. | [] | 0 | 0 | -1 | 5,233 |
|
932 | Permutation Cycle | [
"brute force",
"constructive algorithms"
] | null | null | For a permutation *P*[1... *N*] of integers from 1 to *N*, function *f* is defined as follows:
Let *g*(*i*) be the minimum positive integer *j* such that *f*(*i*,<=*j*)<==<=*i*. We can show such *j* always exists.
For given *N*,<=*A*,<=*B*, find a permutation *P* of integers from 1 to *N* such that for 1<=β€<=*i*<=β€<=*N*, *g*(*i*) equals either *A* or *B*. | The only line contains three integers *N*,<=*A*,<=*B* (1<=β€<=*N*<=β€<=106,<=1<=β€<=*A*,<=*B*<=β€<=*N*). | If no such permutation exists, output -1. Otherwise, output a permutation of integers from 1 to *N*. | [
"9 2 5\n",
"3 2 1\n"
] | [
"6 5 8 3 4 1 9 2 7",
"1 2 3 "
] | In the first example, *g*(1)β=β*g*(6)β=β*g*(7)β=β*g*(9)β=β2 and *g*(2)β=β*g*(3)β=β*g*(4)β=β*g*(5)β=β*g*(8)β=β5
In the second example, *g*(1)β=β*g*(2)β=β*g*(3)β=β1 | [
{
"input": "9 2 5",
"output": "2 1 4 3 6 7 8 9 5 "
},
{
"input": "3 2 1",
"output": "1 2 3 "
},
{
"input": "7 4 4",
"output": "-1"
},
{
"input": "1000000 999998 3",
"output": "-1"
},
{
"input": "1 1 1",
"output": "1 "
},
{
"input": "993012 997 1001",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "1000000 2017 881",
"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "390612 20831 55790",
"output": "-1"
},
{
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"output": "2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 1..."
},
{
"input": "99929 99929 2",
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{
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{
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{
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{
"input": "414372 59196 93713",
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{
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{
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{
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{
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{
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{
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},
{
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{
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},
{
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},
{
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"output": "2 1 4 3 "
},
{
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"output": "2 3 4 5 1 "
},
{
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},
{
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},
{
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"output": "-1"
},
{
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"output": "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "999999 2 2",
"output": "-1"
}
] | 1,559 | 30,105,600 | 3 | 5,237 |
|
962 | Students in Railway Carriage | [
"constructive algorithms",
"greedy",
"implementation"
] | null | null | There are $n$ consecutive seat places in a railway carriage. Each place is either empty or occupied by a passenger.
The university team for the Olympiad consists of $a$ student-programmers and $b$ student-athletes. Determine the largest number of students from all $a+b$ students, which you can put in the railway carriage so that:
- no student-programmer is sitting next to the student-programmer; - and no student-athlete is sitting next to the student-athlete.
In the other words, there should not be two consecutive (adjacent) places where two student-athletes or two student-programmers are sitting.
Consider that initially occupied seat places are occupied by jury members (who obviously are not students at all). | The first line contain three integers $n$, $a$ and $b$ ($1 \le n \le 2\cdot10^{5}$, $0 \le a, b \le 2\cdot10^{5}$, $a + b > 0$) β total number of seat places in the railway carriage, the number of student-programmers and the number of student-athletes.
The second line contains a string with length $n$, consisting of characters "." and "*". The dot means that the corresponding place is empty. The asterisk means that the corresponding place is occupied by the jury member. | Print the largest number of students, which you can put in the railway carriage so that no student-programmer is sitting next to a student-programmer and no student-athlete is sitting next to a student-athlete. | [
"5 1 1\n*...*\n",
"6 2 3\n*...*.\n",
"11 3 10\n.*....**.*.\n",
"3 2 3\n***\n"
] | [
"2\n",
"4\n",
"7\n",
"0\n"
] | In the first example you can put all student, for example, in the following way: *.AB*
In the second example you can put four students, for example, in the following way: *BAB*B
In the third example you can put seven students, for example, in the following way: B*ABAB**A*B
The letter A means a student-programmer, and the letter B β student-athlete. | [
{
"input": "5 1 1\n*...*",
"output": "2"
},
{
"input": "6 2 3\n*...*.",
"output": "4"
},
{
"input": "11 3 10\n.*....**.*.",
"output": "7"
},
{
"input": "3 2 3\n***",
"output": "0"
},
{
"input": "9 5 3\n*...*...*",
"output": "6"
},
{
"input": "9 2 4\n*...*...*",
"output": "6"
},
{
"input": "9 2 200000\n*...*...*",
"output": "6"
},
{
"input": "1 0 1\n.",
"output": "1"
},
{
"input": "14 3 7\n.*.......*..*.",
"output": "10"
},
{
"input": "6 1 3\n*....*",
"output": "3"
},
{
"input": "5 1 2\n...*.",
"output": "3"
},
{
"input": "2 2 0\n..",
"output": "1"
},
{
"input": "2 0 2\n..",
"output": "1"
},
{
"input": "5 3 3\n...**",
"output": "3"
},
{
"input": "3 0 1\n.*.",
"output": "1"
},
{
"input": "13 3 3\n*...*...*...*",
"output": "6"
},
{
"input": "7 0 4\n...*..*",
"output": "3"
},
{
"input": "20 5 5\n.*.*.............*..",
"output": "10"
},
{
"input": "64 59 2\n.*.***......****.*..**..**..****.*.*.*.**...**..***.***.*..*..*.",
"output": "23"
},
{
"input": "2 1 1\n..",
"output": "2"
},
{
"input": "10 7 0\n.*...*..*.",
"output": "5"
},
{
"input": "4 1 1\n..*.",
"output": "2"
},
{
"input": "10 4 3\n.*..*...*.",
"output": "7"
},
{
"input": "5 0 1\n*.*.*",
"output": "1"
},
{
"input": "6 1 1\n*...*.",
"output": "2"
},
{
"input": "1 1 1\n.",
"output": "1"
},
{
"input": "11 6 2\n.*...*...*.",
"output": "8"
},
{
"input": "11 7 1\n.*...*...*.",
"output": "7"
}
] | 109 | 0 | 0 | 5,242 |
|
355 | Vasya and Public Transport | [
"greedy",
"implementation"
] | null | null | Vasya often uses public transport. The transport in the city is of two types: trolleys and buses. The city has *n* buses and *m* trolleys, the buses are numbered by integers from 1 to *n*, the trolleys are numbered by integers from 1 to *m*.
Public transport is not free. There are 4 types of tickets:
1. A ticket for one ride on some bus or trolley. It costs *c*1 burles; 1. A ticket for an unlimited number of rides on some bus or on some trolley. It costs *c*2 burles; 1. A ticket for an unlimited number of rides on all buses or all trolleys. It costs *c*3 burles; 1. A ticket for an unlimited number of rides on all buses and trolleys. It costs *c*4 burles.
Vasya knows for sure the number of rides he is going to make and the transport he is going to use. He asked you for help to find the minimum sum of burles he will have to spend on the tickets. | The first line contains four integers *c*1,<=*c*2,<=*c*3,<=*c*4 (1<=β€<=*c*1,<=*c*2,<=*c*3,<=*c*4<=β€<=1000) β the costs of the tickets.
The second line contains two integers *n* and *m* (1<=β€<=*n*,<=*m*<=β€<=1000) β the number of buses and trolleys Vasya is going to use.
The third line contains *n* integers *a**i* (0<=β€<=*a**i*<=β€<=1000) β the number of times Vasya is going to use the bus number *i*.
The fourth line contains *m* integers *b**i* (0<=β€<=*b**i*<=β€<=1000) β the number of times Vasya is going to use the trolley number *i*. | Print a single number β the minimum sum of burles Vasya will have to spend on the tickets. | [
"1 3 7 19\n2 3\n2 5\n4 4 4\n",
"4 3 2 1\n1 3\n798\n1 2 3\n",
"100 100 8 100\n3 5\n7 94 12\n100 1 47 0 42\n"
] | [
"12\n",
"1\n",
"16\n"
] | In the first sample the profitable strategy is to buy two tickets of the first type (for the first bus), one ticket of the second type (for the second bus) and one ticket of the third type (for all trolleys). It totals to (2Β·1)β+β3β+β7β=β12 burles.
In the second sample the profitable strategy is to buy one ticket of the fourth type.
In the third sample the profitable strategy is to buy two tickets of the third type: for all buses and for all trolleys. | [
{
"input": "1 3 7 19\n2 3\n2 5\n4 4 4",
"output": "12"
},
{
"input": "4 3 2 1\n1 3\n798\n1 2 3",
"output": "1"
},
{
"input": "100 100 8 100\n3 5\n7 94 12\n100 1 47 0 42",
"output": "16"
},
{
"input": "3 103 945 1000\n7 9\n34 35 34 35 34 35 34\n0 0 0 0 0 0 0 0 0",
"output": "717"
},
{
"input": "7 11 597 948\n4 1\n5 1 0 11\n7",
"output": "40"
},
{
"input": "7 32 109 645\n1 3\n0\n0 0 0",
"output": "0"
},
{
"input": "680 871 347 800\n10 100\n872 156 571 136 703 201 832 213 15 333\n465 435 870 95 660 237 694 594 423 405 27 866 325 490 255 989 128 345 278 125 708 210 771 848 961 448 871 190 745 343 532 174 103 999 874 221 252 500 886 129 185 208 137 425 800 34 696 39 198 981 91 50 545 885 194 583 475 415 162 712 116 911 313 488 646 189 429 756 728 30 985 114 823 111 106 447 296 430 307 388 345 458 84 156 169 859 274 934 634 62 12 839 323 831 24 907 703 754 251 938",
"output": "694"
},
{
"input": "671 644 748 783\n100 10\n520 363 816 957 635 753 314 210 763 819 27 970 520 164 195 230 708 587 568 707 343 30 217 227 755 277 773 497 900 589 826 666 115 784 494 467 217 892 658 388 764 812 248 447 876 581 94 915 675 967 508 754 768 79 261 934 603 712 20 199 997 501 465 91 897 257 820 645 217 105 564 8 668 171 168 18 565 840 418 42 808 918 409 617 132 268 13 161 194 628 213 199 545 448 113 410 794 261 211 539\n147 3 178 680 701 193 697 666 846 389",
"output": "783"
},
{
"input": "2 7 291 972\n63 92\n7 0 0 6 0 13 0 20 2 8 0 17 7 0 0 0 0 2 2 0 0 8 20 0 0 0 3 0 0 0 4 20 0 0 0 12 0 8 17 9 0 0 0 0 4 0 0 0 17 11 3 0 2 15 0 18 11 19 14 0 0 20 13\n0 0 0 3 7 0 0 0 0 8 13 6 15 0 7 0 0 20 0 0 12 0 12 0 15 0 0 1 11 14 0 11 12 0 0 0 0 0 16 16 0 17 20 0 11 0 0 20 14 0 16 0 3 6 12 0 0 0 0 0 15 3 0 9 17 12 20 17 0 0 0 0 15 9 0 14 10 10 1 20 16 17 20 6 6 0 0 16 4 6 0 7",
"output": "494"
},
{
"input": "4 43 490 945\n63 92\n0 0 0 0 0 0 6 5 18 0 6 4 0 17 0 19 0 19 7 16 0 0 0 9 10 13 7 0 10 16 0 0 0 0 0 14 0 14 9 15 0 0 2 0 0 0 0 5 0 0 0 11 11 0 0 0 0 0 10 12 3 0 0\n0 12 0 18 7 7 0 0 9 0 0 13 17 0 18 12 4 0 0 14 18 20 0 0 12 9 17 1 19 0 11 0 5 0 0 14 0 0 16 0 19 15 9 14 7 10 0 19 19 0 0 1 0 0 0 6 0 0 0 6 0 20 1 9 0 0 10 17 5 2 5 4 16 6 0 11 0 8 13 4 0 2 0 0 13 10 0 13 0 0 8 4",
"output": "945"
},
{
"input": "2 50 258 922\n42 17\n0 2 0 1 0 1 0 11 18 9 0 0 0 0 10 15 17 4 20 0 5 0 0 13 13 0 0 2 0 7 0 20 4 0 19 3 7 0 0 0 0 0\n8 4 19 0 0 19 14 17 6 0 18 0 0 0 0 9 0",
"output": "486"
},
{
"input": "1 1 3 4\n2 3\n1 1\n1 1 1",
"output": "4"
},
{
"input": "4 4 4 1\n1 1\n0\n0",
"output": "0"
},
{
"input": "100 100 1 100\n10 10\n100 100 100 100 100 100 100 100 100 100\n100 100 100 100 100 100 100 100 100 100",
"output": "2"
}
] | 92 | 0 | 0 | 5,262 |
|
993 | Two Squares | [
"geometry",
"implementation"
] | null | null | You are given two squares, one with sides parallel to the coordinate axes, and another one with sides at 45 degrees to the coordinate axes. Find whether the two squares intersect.
The interior of the square is considered to be part of the square, i.e. if one square is completely inside another, they intersect. If the two squares only share one common point, they are also considered to intersect. | The input data consists of two lines, one for each square, both containing 4 pairs of integers. Each pair represents coordinates of one vertex of the square. Coordinates within each line are either in clockwise or counterclockwise order.
The first line contains the coordinates of the square with sides parallel to the coordinate axes, the second line contains the coordinates of the square at 45 degrees.
All the values are integer and between $-100$ and $100$. | Print "Yes" if squares intersect, otherwise print "No".
You can print each letter in any case (upper or lower). | [
"0 0 6 0 6 6 0 6\n1 3 3 5 5 3 3 1\n",
"0 0 6 0 6 6 0 6\n7 3 9 5 11 3 9 1\n",
"6 0 6 6 0 6 0 0\n7 4 4 7 7 10 10 7\n"
] | [
"YES\n",
"NO\n",
"YES\n"
] | In the first example the second square lies entirely within the first square, so they do intersect.
In the second sample squares do not have any points in common.
Here are images corresponding to the samples: | [
{
"input": "0 0 6 0 6 6 0 6\n1 3 3 5 5 3 3 1",
"output": "YES"
},
{
"input": "0 0 6 0 6 6 0 6\n7 3 9 5 11 3 9 1",
"output": "NO"
},
{
"input": "6 0 6 6 0 6 0 0\n7 4 4 7 7 10 10 7",
"output": "YES"
},
{
"input": "0 0 6 0 6 6 0 6\n8 4 4 8 8 12 12 8",
"output": "YES"
},
{
"input": "2 2 4 2 4 4 2 4\n0 3 3 6 6 3 3 0",
"output": "YES"
},
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] | 62 | 0 | 0 | 5,284 |
|
702 | Road to Post Office | [
"math"
] | null | null | Vasiliy has a car and he wants to get from home to the post office. The distance which he needs to pass equals to *d* kilometers.
Vasiliy's car is not new β it breaks after driven every *k* kilometers and Vasiliy needs *t* seconds to repair it. After repairing his car Vasiliy can drive again (but after *k* kilometers it will break again, and so on). In the beginning of the trip the car is just from repair station.
To drive one kilometer on car Vasiliy spends *a* seconds, to walk one kilometer on foot he needs *b* seconds (*a*<=<<=*b*).
Your task is to find minimal time after which Vasiliy will be able to reach the post office. Consider that in every moment of time Vasiliy can left his car and start to go on foot. | The first line contains 5 positive integers *d*,<=*k*,<=*a*,<=*b*,<=*t* (1<=β€<=*d*<=β€<=1012; 1<=β€<=*k*,<=*a*,<=*b*,<=*t*<=β€<=106; *a*<=<<=*b*), where:
- *d* β the distance from home to the post office; - *k* β the distance, which car is able to drive before breaking; - *a* β the time, which Vasiliy spends to drive 1 kilometer on his car; - *b* β the time, which Vasiliy spends to walk 1 kilometer on foot; - *t* β the time, which Vasiliy spends to repair his car. | Print the minimal time after which Vasiliy will be able to reach the post office. | [
"5 2 1 4 10\n",
"5 2 1 4 5\n"
] | [
"14\n",
"13\n"
] | In the first example Vasiliy needs to drive the first 2 kilometers on the car (in 2 seconds) and then to walk on foot 3 kilometers (in 12 seconds). So the answer equals to 14 seconds.
In the second example Vasiliy needs to drive the first 2 kilometers on the car (in 2 seconds), then repair his car (in 5 seconds) and drive 2 kilometers more on the car (in 2 seconds). After that he needs to walk on foot 1 kilometer (in 4 seconds). So the answer equals to 13 seconds. | [
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{
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"output": "259694"
},
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"output": "4"
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"output": "1036"
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"output": "100"
},
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"output": "10"
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{
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},
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"input": "100 120 1 2 1",
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},
{
"input": "1 999999 1 2 1000000",
"output": "1"
},
{
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"output": "8020"
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{
"input": "3 9 8 9 4",
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{
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},
{
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{
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},
{
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"output": "100"
},
{
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},
{
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},
{
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{
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{
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{
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{
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{
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{
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"output": "10"
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{
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"output": "78"
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{
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"output": "9"
},
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"output": "124"
},
{
"input": "14 3 14 16 5",
"output": "215"
},
{
"input": "2000002 1000000 1 3 1000000",
"output": "3000006"
},
{
"input": "2 1 3 8 14",
"output": "11"
},
{
"input": "18 6 8 9 7",
"output": "156"
},
{
"input": "10 20 10 20 7",
"output": "100"
},
{
"input": "12 7 8 18 1",
"output": "97"
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{
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"output": "78"
},
{
"input": "5 1000 1 4 10",
"output": "5"
}
] | 61 | 0 | 0 | 5,288 |
|
472 | Design Tutorial: Inverse the Problem | [
"dfs and similar",
"dsu",
"shortest paths",
"trees"
] | null | null | There is an easy way to obtain a new task from an old one called "Inverse the problem": we give an output of the original task, and ask to generate an input, such that solution to the original problem will produce the output we provided. The hard task of Topcoder Open 2014 Round 2C, InverseRMQ, is a good example.
Now let's create a task this way. We will use the task: you are given a tree, please calculate the distance between any pair of its nodes. Yes, it is very easy, but the inverse version is a bit harder: you are given an *n*<=Γ<=*n* distance matrix. Determine if it is the distance matrix of a weighted tree (all weights must be positive integers). | The first line contains an integer *n* (1<=β€<=*n*<=β€<=2000) β the number of nodes in that graph.
Then next *n* lines each contains *n* integers *d**i*,<=*j* (0<=β€<=*d**i*,<=*j*<=β€<=109) β the distance between node *i* and node *j*. | If there exists such a tree, output "YES", otherwise output "NO". | [
"3\n0 2 7\n2 0 9\n7 9 0\n",
"3\n1 2 7\n2 0 9\n7 9 0\n",
"3\n0 2 2\n7 0 9\n7 9 0\n",
"3\n0 1 1\n1 0 1\n1 1 0\n",
"2\n0 0\n0 0\n"
] | [
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
] | In the first example, the required tree exists. It has one edge between nodes 1 and 2 with weight 2, another edge between nodes 1 and 3 with weight 7.
In the second example, it is impossible because *d*<sub class="lower-index">1,β1</sub> should be 0, but it is 1.
In the third example, it is impossible because *d*<sub class="lower-index">1,β2</sub> should equal *d*<sub class="lower-index">2,β1</sub>. | [
{
"input": "3\n0 2 7\n2 0 9\n7 9 0",
"output": "YES"
},
{
"input": "3\n1 2 7\n2 0 9\n7 9 0",
"output": "NO"
},
{
"input": "3\n0 2 2\n7 0 9\n7 9 0",
"output": "NO"
},
{
"input": "3\n0 1 1\n1 0 1\n1 1 0",
"output": "NO"
},
{
"input": "2\n0 0\n0 0",
"output": "NO"
},
{
"input": "1\n0",
"output": "YES"
},
{
"input": "1\n1",
"output": "NO"
},
{
"input": "2\n0 1000000000\n1000000000 0",
"output": "YES"
},
{
"input": "5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0",
"output": "NO"
},
{
"input": "2\n0 1\n1 0",
"output": "YES"
},
{
"input": "4\n0 3 7 6\n3 0 4 9\n7 4 0 2\n6 9 2 0",
"output": "NO"
},
{
"input": "3\n0 1 2\n1 0 2\n2 2 0",
"output": "NO"
},
{
"input": "3\n0 2 7\n2 0 10\n7 10 0",
"output": "NO"
}
] | 30 | 0 | 0 | 5,293 |
|
6 | Lizards and Basements 2 | [
"brute force",
"dp"
] | D. Lizards and Basements 2 | 2 | 64 | This is simplified version of the problem used on the original contest. The original problem seems to have too difiicult solution. The constraints for input data have been reduced.
Polycarp likes to play computer role-playing game Β«Lizards and BasementsΒ». At the moment he is playing it as a magician. At one of the last levels he has to fight the line of archers. The only spell with which he can damage them is a fire ball. If Polycarp hits the *i*-th archer with his fire ball (they are numbered from left to right), the archer loses *a* health points. At the same time the spell damages the archers adjacent to the *i*-th (if any) β they lose *b* (1<=β€<=*b*<=<<=*a*<=β€<=10) health points each.
As the extreme archers (i.e. archers numbered 1 and *n*) are very far, the fire ball cannot reach them. Polycarp can hit any other archer with his fire ball.
The amount of health points for each archer is known. An archer will be killed when this amount is less than 0. What is the minimum amount of spells Polycarp can use to kill all the enemies?
Polycarp can throw his fire ball into an archer if the latter is already killed. | The first line of the input contains three integers *n*,<=*a*,<=*b* (3<=β€<=*n*<=β€<=10; 1<=β€<=*b*<=<<=*a*<=β€<=10). The second line contains a sequence of *n* integers β *h*1,<=*h*2,<=...,<=*h**n* (1<=β€<=*h**i*<=β€<=15), where *h**i* is the amount of health points the *i*-th archer has. | In the first line print *t* β the required minimum amount of fire balls.
In the second line print *t* numbers β indexes of the archers that Polycarp should hit to kill all the archers in *t* shots. All these numbers should be between 2 and *n*<=-<=1. Separate numbers with spaces. If there are several solutions, output any of them. Print numbers in any order. | [
"3 2 1\n2 2 2\n",
"4 3 1\n1 4 1 1\n"
] | [
"3\n2 2 2 ",
"4\n2 2 3 3 "
] | none | [
{
"input": "3 2 1\n2 2 2",
"output": "3\n2 2 2 "
},
{
"input": "4 3 1\n1 4 1 1",
"output": "4\n2 2 3 3 "
},
{
"input": "3 5 3\n1 2 1",
"output": "1\n2 "
},
{
"input": "3 5 3\n3 2 2",
"output": "2\n2 2 "
},
{
"input": "3 5 3\n3 2 2",
"output": "2\n2 2 "
},
{
"input": "3 5 1\n10 10 10",
"output": "11\n2 2 2 2 2 2 2 2 2 2 2 "
},
{
"input": "3 5 3\n10 9 7",
"output": "4\n2 2 2 2 "
},
{
"input": "3 5 1\n1 9 10",
"output": "11\n2 2 2 2 2 2 2 2 2 2 2 "
},
{
"input": "3 5 3\n10 9 7",
"output": "4\n2 2 2 2 "
},
{
"input": "3 5 2\n9 3 6",
"output": "5\n2 2 2 2 2 "
},
{
"input": "4 5 3\n2 2 2 1",
"output": "2\n2 3 "
},
{
"input": "4 5 3\n2 3 2 2",
"output": "2\n2 3 "
},
{
"input": "4 5 3\n4 2 4 2",
"output": "3\n2 2 3 "
},
{
"input": "4 5 1\n4 9 1 8",
"output": "14\n2 2 2 2 2 3 3 3 3 3 3 3 3 3 "
},
{
"input": "4 5 3\n9 9 3 4",
"output": "6\n2 2 2 2 3 3 "
},
{
"input": "4 5 1\n8 8 9 8",
"output": "18\n2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 "
},
{
"input": "4 5 3\n10 10 10 10",
"output": "8\n2 2 2 2 3 3 3 3 "
},
{
"input": "4 5 2\n7 3 8 5",
"output": "7\n2 2 2 2 3 3 3 "
},
{
"input": "4 5 3\n5 10 7 7",
"output": "5\n2 2 3 3 3 "
},
{
"input": "4 3 1\n8 10 9 7",
"output": "17\n2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 "
},
{
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"output": "10\n2 2 2 4 5 6 7 9 9 9 "
},
{
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"output": "13\n2 2 2 2 2 2 2 4 5 5 7 9 9 "
},
{
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"output": "25\n2 2 2 2 2 2 3 4 5 5 5 6 7 8 9 9 9 9 9 9 9 9 9 9 9 "
},
{
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{
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},
{
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},
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},
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},
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{
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"output": "10\n2 2 2 4 5 7 8 9 9 9 "
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{
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},
{
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"output": "4\n2 5 8 9 "
},
{
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},
{
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},
{
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{
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{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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"output": "11\n2 2 2 4 4 6 6 7 9 9 9 "
},
{
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"output": "7\n2 2 5 5 7 9 9 "
},
{
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"output": "7\n2 2 5 5 7 9 9 "
},
{
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"output": "29\n2 2 2 2 2 2 2 2 2 2 2 4 4 5 6 7 7 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
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},
{
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},
{
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"output": "10\n2 2 2 2 5 5 7 9 9 9 "
},
{
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"output": "8\n2 2 2 5 5 7 9 9 "
},
{
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"output": "18\n2 2 2 2 2 2 4 4 5 5 5 7 7 8 9 9 9 9 "
},
{
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},
{
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},
{
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},
{
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"output": "13\n2 2 2 2 4 5 6 7 8 9 9 9 9 "
},
{
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"output": "7\n2 2 5 5 7 9 9 "
},
{
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"output": "11\n2 2 2 5 5 5 7 7 9 9 9 "
},
{
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"output": "8\n2 2 2 5 7 8 9 9 "
},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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"output": "11\n2 2 2 5 5 5 7 7 9 9 9 "
},
{
"input": "10 5 1\n7 10 15 5 15 5 5 5 11 7",
"output": "24\n2 2 2 2 2 2 2 2 3 3 5 5 5 5 7 7 9 9 9 9 9 9 9 9 "
},
{
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"output": "10\n2 2 2 4 5 7 7 9 9 9 "
},
{
"input": "10 6 2\n5 8 4 5 1 3 6 7 5 3",
"output": "8\n2 2 2 4 7 7 9 9 "
},
{
"input": "10 5 2\n10 12 10 10 11 9 11 11 9 9",
"output": "18\n2 2 2 2 2 2 4 5 5 5 7 7 8 9 9 9 9 9 "
},
{
"input": "10 6 5\n9 8 10 10 11 11 8 9 10 11",
"output": "9\n2 2 4 5 6 7 9 9 9 "
},
{
"input": "10 3 2\n3 5 1 4 5 3 3 1 3 4",
"output": "9\n2 2 4 5 6 8 9 9 9 "
},
{
"input": "10 3 2\n4 9 6 9 6 8 4 5 6 9",
"output": "15\n2 2 2 3 5 5 5 5 7 8 9 9 9 9 9 "
},
{
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"output": "17\n2 2 2 2 2 4 4 5 5 7 7 7 9 9 9 9 9 "
},
{
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},
{
"input": "10 6 1\n4 5 5 3 7 5 6 5 6 8",
"output": "18\n2 2 2 2 2 4 5 6 7 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 9 6\n15 14 14 12 15 10 9 14 13 8",
"output": "9\n2 2 2 4 5 6 8 9 9 "
},
{
"input": "10 7 1\n9 9 9 9 9 9 9 9 9 9",
"output": "26\n2 2 2 2 2 2 2 2 2 2 4 4 5 6 7 7 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 6 5\n4 5 4 1 3 6 3 2 2 2",
"output": "4\n2 5 7 9 "
},
{
"input": "10 10 3\n10 8 11 11 10 11 11 9 7 10",
"output": "12\n2 2 2 2 4 5 6 7 9 9 9 9 "
},
{
"input": "10 3 2\n7 8 11 6 8 7 2 3 8 7",
"output": "13\n2 2 2 2 4 4 5 6 6 9 9 9 9 "
},
{
"input": "10 8 6\n9 9 8 10 7 13 7 11 13 12",
"output": "8\n2 2 5 5 7 9 9 9 "
},
{
"input": "10 3 2\n9 13 9 10 12 10 14 13 11 11",
"output": "21\n2 2 2 2 2 4 5 5 5 5 7 7 7 7 7 9 9 9 9 9 9 "
},
{
"input": "10 3 2\n12 12 14 15 15 12 12 14 12 14",
"output": "26\n2 2 2 2 2 2 2 4 4 4 4 5 5 6 7 7 7 8 9 9 9 9 9 9 9 9 "
},
{
"input": "10 7 4\n6 4 8 4 8 7 10 6 8 6",
"output": "8\n2 2 4 6 6 8 9 9 "
},
{
"input": "10 5 4\n14 14 14 10 13 15 13 13 10 14",
"output": "14\n2 2 2 2 5 5 5 7 7 8 9 9 9 9 "
},
{
"input": "10 10 2\n10 10 13 10 10 12 6 8 11 12",
"output": "17\n2 2 2 2 2 2 4 5 6 7 9 9 9 9 9 9 9 "
},
{
"input": "10 6 4\n5 6 5 6 6 7 5 7 9 9",
"output": "8\n2 2 5 5 7 9 9 9 "
},
{
"input": "10 7 5\n10 10 10 10 10 10 10 10 10 10",
"output": "10\n2 2 2 4 5 7 7 9 9 9 "
},
{
"input": "10 5 1\n11 10 10 10 11 11 11 10 11 11",
"output": "32\n2 2 2 2 2 2 2 2 2 2 2 2 4 4 5 5 6 6 7 7 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 10 4\n13 13 13 13 13 13 13 13 13 13",
"output": "12\n2 2 2 2 4 5 6 7 9 9 9 9 "
},
{
"input": "10 5 2\n4 5 3 6 7 8 4 4 9 6",
"output": "11\n2 2 2 4 5 6 7 9 9 9 9 "
},
{
"input": "10 7 3\n5 9 8 8 8 7 6 7 6 5",
"output": "8\n2 2 4 5 7 7 9 9 "
},
{
"input": "10 2 1\n12 13 15 14 14 11 12 14 11 15",
"output": "46\n2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 5 5 5 5 5 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 2 1\n13 12 15 12 14 14 14 15 13 15",
"output": "48\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 2 1\n14 15 15 14 14 15 14 15 14 15",
"output": "50\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 5 5 5 5 5 5 5 6 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 2 1\n9 7 14 8 14 15 15 9 12 13",
"output": "42\n2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 2 1\n14 15 15 14 15 14 15 14 15 15",
"output": "50\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 2 1\n9 7 14 8 14 15 15 9 12 13",
"output": "42\n2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
},
{
"input": "10 2 1\n4 14 13 15 14 5 8 11 12 14",
"output": "38\n2 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 "
}
] | 248 | 307,200 | 3.935711 | 5,309 |
47 | Crossword | [
"implementation"
] | C. Crossword | 2 | 256 | Vasya trains to compose crossword puzzles. He can only compose crosswords of a very simplΠ΅ type so far. All of them consist of exactly six words; the words can be read only from top to bottom vertically and from the left to the right horizontally. The words are arranged in the form of a rectangular "eight" or infinity sign, not necessarily symmetrical.
The top-left corner of the crossword coincides with the top-left corner of the rectangle. The same thing is correct for the right-bottom corners. The crossword can't degrade, i.e. it always has exactly four blank areas, two of which are surrounded by letters. Look into the output for the samples for clarification.
Help Vasya β compose a crossword of the described type using the given six words. It is allowed to use the words in any order. | Six lines contain the given words. Every word consists of no more than 30 and no less than 3 uppercase Latin letters. | If it is impossible to solve the problem, print Impossible. Otherwise, print the sought crossword. All the empty squares should be marked as dots.
If there can be several solutions to that problem, print the lexicographically minimum one. I.e. the solution where the first line is less than the first line of other solutions should be printed. If the two lines are equal, compare the second lines and so on. The lexicographical comparison of lines is realized by the < operator in the modern programming languages. | [
"NOD\nBAA\nYARD\nAIRWAY\nNEWTON\nBURN\n",
"AAA\nAAA\nAAAAA\nAAA\nAAA\nAAAAA\n",
"PTC\nJYNYFDSGI\nZGPPC\nIXEJNDOP\nJJFS\nSSXXQOFGJUZ\n"
] | [
"BAA...\nU.I...\nR.R...\nNEWTON\n..A..O\n..YARD\n",
"AAA..\nA.A..\nAAAAA\n..A.A\n..AAA\n",
"JJFS....\nY..S....\nN..X....\nY..X....\nF..Q....\nD..O....\nS..F....\nG..G....\nIXEJNDOP\n...U...T\n...ZGPPC\n"
] | none | [
{
"input": "NOD\nBAA\nYARD\nAIRWAY\nNEWTON\nBURN",
"output": "BAA...\nU.I...\nR.R...\nNEWTON\n..A..O\n..YARD"
},
{
"input": "AAA\nAAA\nAAAAA\nAAA\nAAA\nAAAAA",
"output": "AAA..\nA.A..\nAAAAA\n..A.A\n..AAA"
},
{
"input": "PTC\nJYNYFDSGI\nZGPPC\nIXEJNDOP\nJJFS\nSSXXQOFGJUZ",
"output": "JJFS....\nY..S....\nN..X....\nY..X....\nF..Q....\nD..O....\nS..F....\nG..G....\nIXEJNDOP\n...U...T\n...ZGPPC"
},
{
"input": "BAMSVFSFVUWRXSABRGSOINNWAQR\nUWHQCTMHVKWAWVT\nUACWQUGQUXXTBLUDFGCHB\nTXHHXRYEEAMLFWKSRUEBAZSUEYU\nROCCNYN\nUCWYOHJYZQGYN",
"output": "UACWQUGQUXXTBLUDFGCHB......\nW...................A......\nH...................M......\nQ...................S......\nC...................V......\nT...................F......\nM...................S......\nH...................F......\nV...................V......\nK...................U......\nW...................W......\nA...................R......\nW...................X......\nV...................S......\nTXHHXRYEEAMLFWKSRUEBAZSUEYU\n....................B.....C\n....................R.....W\n....................."
},
{
"input": "ABA\nCABA\nDABA\nCABA\nGIP\nTOII",
"output": "Impossible"
},
{
"input": "XOWGMRPLRJMSMEDRTRILIDA\nFBCLMSVFHHIZTET\nNSGPLHVZDUAKAEGQAKNBDWTFUGVF\nMJFPXT\nXBSN\nAIDTUQHDNBIGUFXSLM",
"output": "XBSN..............\nO..S..............\nW..G..............\nG..P..............\nM..L..............\nR..H..............\nP..V..............\nL..Z..............\nR..D..............\nJ..U..............\nM..A..............\nS..K..............\nM..A..............\nE..E..............\nD..G..............\nR..Q..............\nT..A..............\nR..K..............\nI..N..............\nL..B..............\nI..D..............\nD..W..............\nAIDTUQHDNBIGUFXSLM\n...F.............J\n...U.............F\n...G.........."
},
{
"input": "ABA\nABA\nABA\nABA\nGIP\nOII",
"output": "Impossible"
},
{
"input": "WYDA\nMZXCVQ\nQPXNMDHNAUDARCFUPMGJCKBJEDK\nTCUCDYWRWPVINAWNMTVGBTTZTFESZF\nFTK\nWCUM",
"output": "Impossible"
},
{
"input": "HYICDCIW\nEIECPPAK\nIBBA\nEEUEJ\nWPA\nJVZDCDJDVI",
"output": "Impossible"
},
{
"input": "LVQZ\nZBLJFSGLCYVYUTFLANXZFTNTFY\nSAGRNV\nLTRTFEQLHQOUGMNWMMVNR\nDSLZCNFAEAUXV\nRFRFAQROQTUPDVMS",
"output": "Impossible"
},
{
"input": "VNXHTKFCPQZP\nHPMNZITLOOV\nVDUIDDDXTFBZKVFN\nPTBZUNZAUYZFZ\nNTS\nZZAWS",
"output": "Impossible"
},
{
"input": "AKRXIAOOLSZCZRJCSDJ\nYJSJBWWLHZLZBMOOUNMHYEOWKFA\nOBEVVITJMVCWWBEVGX\nSGPMNIBFOJ\nOQIHQY\nXLQVENDKVPOEWGPMNWIEFNQD",
"output": "Impossible"
},
{
"input": "CRLCDW\nFPCMKMXOPTZRKQJODSUJHUY\nZXVTHYXDDZQSPAXGYWCHOKYMWC\nYTXIHVOPPYFQALS\nSNMX\nFPUSSZRJZZ",
"output": "Impossible"
},
{
"input": "ZCMQCHLKTNCDCS\nSXGHQFXL\nSIARIKRS\nXGNZ\nXSDIGPS\nSXIGL",
"output": "Impossible"
},
{
"input": "NOD\nBAA\nYARD\nAIRWAY\nNEWWON\nBURNN",
"output": "Impossible"
},
{
"input": "NOD\nBAAA\nYARD\nAIRWAY\nNWWWON\nBURN",
"output": "Impossible"
},
{
"input": "ZASGJLWETPH\nKQUSYJEWMY\nZXRXTEW\nHUGYHIVIHCSGHLVJK\nWSGKKOFWMVVGMQFLVUOR\nRXDWRSNSXIY",
"output": "ZASGJLWETPH.........\nX.........U.........\nR.........G.........\nX.........Y.........\nT.........H.........\nE.........I.........\nWSGKKOFWMVVGMQFLVUOR\n..........I........X\n..........H........D\n..........C........W\n..........S........R\n..........G........S\n..........H........N\n..........L........S\n..........V........X\n..........J........I\n..........KQUSYJEWMY"
},
{
"input": "PTC\nJYNYFDSGI\nZGPPC\nIXEJNDOP\nJJFS\nSSXXQOFGJUZ",
"output": "JJFS....\nY..S....\nN..X....\nY..X....\nF..Q....\nD..O....\nS..F....\nG..G....\nIXEJNDOP\n...U...T\n...ZGPPC"
},
{
"input": "PJDACTKMAOBOBWTHNM\nCOJQJIP\nPQVMNXDVQIMSREMAXM\nBCWFFBLZABP\nMTYTPCGFMVMJVCKZNLAJBGOB\nMYOMOIARJUOIIRTDULENUGJWUDEC",
"output": "PJDACTKMAOBOBWTHNM......\nQ................Y......\nV................O......\nM................M......\nN................O......\nX................I......\nD................A......\nV................R......\nQ................J......\nI................U......\nM................O......\nS................I......\nR................I......\nE................R......\nM................T......\nA................D......\nX................U......\nMTYTPCGFMVMJVCKZNLAJBGOB\n.................E.....C\n...................."
},
{
"input": "BGNWYIWSBQRCVXIYPJYNW\nBTRTRDBEUWEQYPYFKFB\nWEWEU\nBWDLJNESQLSFWJJYLSYQPBP\nPXU\nBFAAUKACMJGYOPVSCUB",
"output": "BFAAUKACMJGYOPVSCUB..\nT.................W..\nR.................D..\nT.................L..\nR.................J..\nD.................N..\nB.................E..\nE.................S..\nU.................Q..\nW.................L..\nE.................S..\nQ.................F..\nY.................W..\nP.................J..\nY.................J..\nF.................Y..\nK.................L..\nF.................S..\nBGNWYIWSBQRCVXIYPJYNW\n..................Q.E\n..................P.W\n..................B.E\n........"
},
{
"input": "PRWPFIUESVKYVBXLUWJGJTCWE\nVFQBNWCOOVKOYPPU\nPITNTWVBZVCGFV\nMMBYZZOFBP\nELGFU\nMDOVPZHPZP",
"output": "MDOVPZHPZP....\nM........R....\nB........W....\nY........P....\nZ........F....\nZ........I....\nO........U....\nF........E....\nB........S....\nPITNTWVBZVCGFV\n.........K...F\n.........Y...Q\n.........V...B\n.........B...N\n.........X...W\n.........L...C\n.........U...O\n.........W...O\n.........J...V\n.........G...K\n.........J...O\n.........T...Y\n.........C...P\n.........W...P\n.........ELGFU"
},
{
"input": "AFZIF\nELO\nAOZOPMME\nITA\nITA\nFQCKBO",
"output": "ITA..\nT.O..\nAFZIF\n..O.Q\n..P.C\n..M.K\n..M.B\n..ELO"
},
{
"input": "SAYRFLLIJHFTHVXAJUSAE\nAMSRRV\nVKKRTVWHZLKVIURJMOAZNUIQAZ\nVCEDJVWS\nAEKQPV\nZWE",
"output": "AEKQPV..\nM....K..\nS....K..\nR....R..\nR....T..\nVCEDJVWS\n.....W.A\n.....H.Y\n.....Z.R\n.....L.F\n.....K.L\n.....V.L\n.....I.I\n.....U.J\n.....R.H\n.....J.F\n.....M.T\n.....O.H\n.....A.V\n.....Z.X\n.....N.A\n.....U.J\n.....I.U\n.....Q.S\n.....A.A\n.....ZWE"
},
{
"input": "DDAPQFUHPBXORXYSSFQEEWCCYP\nXQDOVJCOYITVSIVDOD\nPRLVJIHDYGWU\nDPWNDKJUYNRUBWUJBFBWYKXOKNOIC\nCLKQBKXEU\nXRGTZPFWLWUGXWOIVD",
"output": "XQDOVJCOYITVSIVDOD........\nR................P........\nG................W........\nT................N........\nZ................D........\nP................K........\nF................J........\nW................U........\nL................Y........\nW................N........\nU................R........\nG................U........\nX................B........\nW................W........\nO................U........\nI................J........\nV................B........\nDDAPQFUHPBXORXYSSFQEEWCCYP\n.........."
},
{
"input": "VEWMK\nEQMAIRNYLGPGZGTLJJBBG\nKIMYVTCE\nKVRUVGVLTCXSWDPNYPPMWMRAK\nKWBG\nVIXPK",
"output": "VEWMK...\nI...V...\nX...R...\nP...U...\nKIMYVTCE\n....G..Q\n....V..M\n....L..A\n....T..I\n....C..R\n....X..N\n....S..Y\n....W..L\n....D..G\n....P..P\n....N..G\n....Y..Z\n....P..G\n....P..T\n....M..L\n....W..J\n....M..J\n....R..B\n....A..B\n....KWBG"
},
{
"input": "BBBBB\nAABBABBAABABBABBAAAABBABB\nBAABBBBBBB\nAABBABBABABAAABAAABAA\nAABBBBABBA\nABAAAAAABBABABAAABB",
"output": "AABBABBABABAAABAAABAA....\nA...................B....\nB...................A....\nB...................A....\nB...................A....\nB...................A....\nA...................A....\nB...................A....\nB...................B....\nAABBABBAABABBABBAAAABBABB\n....................A...A\n....................B...A\n....................A...B\n....................B...B\n....................A...B\n....................A...B\n....................A...B\n....................B...B\n....................BBBBB..."
},
{
"input": "AABAAABABB\nAAABAB\nBAAAAAABAAAABABABBBAA\nBBBBBBAAAABABA\nABBBBABBAABABBAA\nAAABA",
"output": "AAABAB...............\nA....B...............\nB....B...............\nA....B...............\nA....B...............\nA....B...............\nB....A...............\nA....A...............\nB....A...............\nBAAAAAABAAAABABABBBAA\n.....B..............A\n.....A..............A\n.....B..............B\n.....ABBBBABBAABABBAA"
},
{
"input": "ABBAAAAAAABBAB\nBAABBBBBBBABBBAABAAABABB\nAAABBAABABA\nBABAA\nAAB\nBBA",
"output": "AAB..\nB.A..\nB.A..\nA.B..\nA.B..\nA.B..\nA.B..\nA.B..\nA.B..\nA.B..\nB.A..\nB.B..\nA.B..\nBABAA\n..A.A\n..A.A\n..B.B\n..A.B\n..A.A\n..A.A\n..B.B\n..A.A\n..B.B\n..BBA"
},
{
"input": "ABBABABAABABBBBBBBBBAA\nABBBBBAABAABBBBBAABBBAA\nBBB\nBBBAABABBBABBBBABAAAABAAA\nABBABBBBBAABAABBABBA\nBAA",
"output": "BAA......................\nB.B......................\nBBBAABABBBABBBBABAAAABAAA\n..A.....................B\n..B.....................B\n..A.....................A\n..B.....................B\n..A.....................B\n..A.....................B\n..B.....................B\n..A.....................B\n..B.....................A\n..B.....................A\n..B.....................B\n..B.....................A\n..B.....................A\n..B.....................B\n..B.....................B\n..B.....................A..."
},
{
"input": "AABBBAABABBAAAABAABAAAA\nABBBBBABAABAABAAAAAAAB\nAABAABB\nAABBABABABABAAAA\nABBAAAABBBBBA\nBBBBAAABAAB",
"output": "AABBABABABABAAAA......\nB..............A......\nB..............B......\nA..............B......\nA..............B......\nA..............A......\nA..............A......\nB..............B......\nB..............A......\nB..............B......\nB..............B......\nB..............A......\nABBBBBABAABAABAAAAAAAB\n...............A.....B\n...............A.....B\n...............B.....B\n...............A.....A\n...............A.....A\n...............B.....A\n...............A.....B\n...............A.....A\n.........."
},
{
"input": "BBBBAABBBAABBBABBBABAABBBABBBA\nABBAAABBBBBAB\nBAAAAAAAABBAABAAABBBBBBB\nBBAAAAABABAAABBABB\nABAABABABBBBBAB\nABAABAAABB",
"output": "ABAABAAABB..............\nB........B..............\nB........B..............\nA........B..............\nA........A..............\nA........A..............\nB........B..............\nB........B..............\nB........B..............\nB........A..............\nB........A..............\nA........B..............\nBAAAAAAAABBAABAAABBBBBBB\n.........B.............B\n.........A.............A\n.........B.............A\n.........B.............A\n.........B.............A\n.........A.............A\n.........B.........."
},
{
"input": "ABABAAB\nBABB\nAAAABBBAAABBABBBBAAABBBBBABAAB\nBAABA\nBBAABBABABAABBBAAAAABABBAB\nBBAA",
"output": "BAABA.........................\nB...B.........................\nA...A.........................\nAAAABBBAAABBABBBBAAABBBBBABAAB\n....A........................A\n....A........................B\n....BBAABBABABAABBBAAAAABABBAB"
},
{
"input": "ABABBBBABAABAAAA\nBBBABBAAB\nBBBABABBAABAAAABABAAAABABBABAB\nAABAABABAABBAABBBBABA\nABABBABB\nABBBBBAAAB",
"output": "AABAABABAABBAABBBBABA.........\nB...................B.........\nA...................A.........\nB...................B.........\nB...................B.........\nA...................B.........\nB...................B.........\nBBBABABBAABAAAABABAAAABABBABAB\n....................B........B\n....................A........B\n....................A........A\n....................B........B\n....................A........B\n....................A........A\n....................A........A\n....................ABBBBBAAAB\n..."
},
{
"input": "BABAAA\nAABBAAAABBAABAAAAB\nABAAAABBBBBBABAABAAAABABA\nBBBAAABABAAAA\nBAAABBBAABAAABABABAB\nAAABABBABBBAABABAAABBBABAABAAB",
"output": "BABAAA...................\nB....A...................\nB....A...................\nA....B...................\nA....A...................\nA....B...................\nB....B...................\nA....A...................\nB....B...................\nA....B...................\nA....B...................\nA....A...................\nABAAAABBBBBBABAABAAAABABA\n.....B..................A\n.....A..................B\n.....B..................B\n.....A..................A\n.....A..................A\n.....A..................A..."
},
{
"input": "BAAA\nABABAAABAABBBABABBBBAAAABBB\nAABAABBA\nBABAA\nBAAB\nAAAABAABBAAABBABAAABBBBBBBAABB",
"output": "BAAA..........................\nA..A..........................\nB..B..........................\nA..A..........................\nAAAABAABBAAABBABAAABBBBBBBAABB\n...B.........................A\n...B.........................A\n...ABABAAABAABBBABABBBBAAAABBB"
},
{
"input": "BABABAAAABBABABABBBB\nBBABAAAAAAABBAA\nBAABBBBABABBBAAABAAABABAAAABBB\nBBBBAABBAABAAAAA\nBBAABBABABA\nABBABAAAABAABBABBBAAABAAABBBAB",
"output": "BABABAAAABBABABABBBB..........\nB..................A..........\nA..................A..........\nB..................B..........\nA..................B..........\nA..................B..........\nA..................B..........\nA..................A..........\nA..................B..........\nA..................A..........\nA..................B..........\nB..................B..........\nB..................B..........\nA..................A..........\nABBABAAAABAABBABBBAAABAAABBBAB\n...................A.........B\n..."
},
{
"input": "AABABAABAAAAABBAAAABAAAAABBAAB\nAABAAABBABBAAABBABB\nBBABBBAABABB\nBAABABBBABABABAABAAAABAA\nBABBBAB\nBBABABBBABBAAABAAABBBBBABABABA",
"output": "BAABABBBABABABAABAAAABAA......\nB......................A......\nA......................B......\nB......................A......\nB......................B......\nB......................A......\nA......................A......\nA......................B......\nB......................A......\nA......................A......\nB......................A......\nBBABABBBABBAAABAAABBBBBABABABA\n.......................A.....A\n.......................B.....B\n.......................B.....A\n.......................A.....A\n..."
},
{
"input": "BABAAABBAABBAABABAAAAAA\nABAAAAAAABBBBBABBBBAABBBAABABB\nBBAABAAAABAABAAAAAABBBABBAA\nAAAA\nABBAAAAA\nAABAABABBBBABABAABBAABAAAABBAB",
"output": "AAAA..........................\nB..B..........................\nB..A..........................\nA..A..........................\nA..A..........................\nA..A..........................\nA..A..........................\nAABAABABBBBABABAABBAABAAAABBAB\n...A.........................A\n...B.........................B\n...B.........................A\n...B.........................A\n...B.........................A\n...B.........................B\n...A.........................B\n...B.........................A\n..."
},
{
"input": "ABBAAAABBBB\nBBABAAAABAABAB\nBAABABBBABBBBBAAA\nBABABAAABBAAABBAAAAB\nABAAAABBBBBABAABABBAAAAABBBBBB\nBBBBAABBAABBBBABAAABAABBAABBAA",
"output": "BAABABBBABBBBBAAA.............\nA...............B.............\nB...............A.............\nA...............A.............\nB...............A.............\nA...............A.............\nA...............B.............\nA...............B.............\nB...............B.............\nB...............B.............\nA...............B.............\nA...............A.............\nA...............B.............\nB...............A.............\nB...............A.............\nA...............B.............\n..."
},
{
"input": "AABAABBAABBBBB\nBBBBBABBBBBBBABBA\nBAABBBAAABBAAAABAAAAAAAAAAAAAB\nBBAABBBAAAABBAAABBAABBABABBAAA\nABBAABAAABBBAB\nAABAABABBAABBABAA",
"output": "AABAABBAABBBBB................\nB............A................\nB............A................\nA............B................\nA............B................\nB............B................\nA............A................\nA............A................\nA............A................\nB............B................\nB............B................\nB............A................\nA............A................\nBBAABBBAAAABBAAABBAABBABABBAAA\n.............A...............A\n.............B...............B\n..."
},
{
"input": "AAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAA\nAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA",
"output": "AAAAAA........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\nA....A........................\n..."
},
{
"input": "AAAAAAA\nAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAA",
"output": "AAAAAAA.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA.....A.....................\nA..."
},
{
"input": "AAAAA\nAAA\nAAAAAAAA\nAAAAAAAA\nAAAA\nAAAAAAAAAA",
"output": "AAA.......\nA.A.......\nA.A.......\nA.A.......\nAAAAAAAAAA\n..A......A\n..A......A\n..AAAAAAAA"
},
{
"input": "AAAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAA\nAAAAAAAAAAAAAAA\nAAA\nAAAAAAAAAAAAA\nAAAAAAAAAAA",
"output": "AAA............\nA.A............\nA.A............\nA.A............\nA.A............\nA.A............\nA.A............\nA.A............\nA.A............\nA.A............\nAAAAAAAAAAAAAAA\n..A...........A\n..A...........A\n..A...........A\n..A...........A\n..A...........A\n..A...........A\n..A...........A\n..A...........A\n..A...........A\n..AAAAAAAAAAAAA"
},
{
"input": "AAAAAAAA\nAAAAAAA\nAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAA",
"output": "AAAAAAA..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nA.....A..............\nAAAAAAAAAAAAAAAAAAAAA\n........"
},
{
"input": "ALODGYLDVVVCNNYJHEKRZKDVKTDGWM\nVXIRITVNCSAIFEIDGSNKBDVKA\nMVRYOA\nKZTJSHZOHERJGEOHYRZSPGXHNPVOVL\nLGKXYPVKYEGRMVTXIA\nVYVBSAQQJGZDK",
"output": "VXIRITVNCSAIFEIDGSNKBDVKA.....\nY.......................L.....\nV.......................O.....\nB.......................D.....\nS.......................G.....\nA.......................Y.....\nQ.......................L.....\nQ.......................D.....\nJ.......................V.....\nG.......................V.....\nZ.......................V.....\nD.......................C.....\nKZTJSHZOHERJGEOHYRZSPGXHNPVOVL\n........................N....G\n........................Y....K\n........................J....X\n..."
},
{
"input": "IKSQUZVQPOXCQAYJWJNLEKUQMQ\nRMJQK\nIAMARYXCRAMWXJTEIUXPBLQVZJTSKI\nKJDERASNVOBNXHERVIPVCGGSANVYCH\nHWESXEWWYPNWDGKQKVHRPLLZTQ\nRVFMI",
"output": "RMJQK.........................\nV...J.........................\nF...D.........................\nM...E.........................\nIAMARYXCRAMWXJTEIUXPBLQVZJTSKI\n....A........................K\n....S........................S\n....N........................Q\n....V........................U\n....O........................Z\n....B........................V\n....N........................Q\n....X........................P\n....H........................O\n....E........................X\n....R........................C\n..."
},
{
"input": "JTNYGQJIRCXSVGBGJDKMR\nJCMPLZWRGCZ\nHLRFWYWJQL\nZVOSYSEBWIMXRQZAAJVBHUJUCQVXYL\nLMLLDHDOLMUNSTTZEBZL\nRMCXXRVIAEHUHHOKHPTIWTUXKHKLDH",
"output": "JCMPLZWRGCZ...................\nT.........V...................\nN.........O...................\nY.........S...................\nG.........Y...................\nQ.........S...................\nJ.........E...................\nI.........B...................\nR.........W...................\nC.........I...................\nX.........M...................\nS.........X...................\nV.........R...................\nG.........Q...................\nB.........Z...................\nG.........A...................\n..."
},
{
"input": "GQXICYVDGNWMN\nGRNONBKFFHYNDFWXZI\nCKHDCDVUNWEFD\nIQYBKTNWVSYPOTNNHRJMCWWABXIRRC\nXHWMCWFGSQYYOMXCVD\nNCZWIMGGKEICSYZWBOHUDGVLUQSTXX",
"output": "GQXICYVDGNWMN.................\nR...........C.................\nN...........Z.................\nO...........W.................\nN...........I.................\nB...........M.................\nK...........G.................\nF...........G.................\nF...........K.................\nH...........E.................\nY...........I.................\nN...........C.................\nD...........S.................\nF...........Y.................\nW...........Z.................\nX...........W.................\n..."
},
{
"input": "OSSFERQNJVMYTHQJHLQBYQLBVJNVBW\nWQFQAUIQONUATMPOYEZTEULQJ\nWXIELJLELMGUQNKLVAJQTTFHMQYDEG\nOZUTTO\nOFEEAZIVROYOCKIW\nGMPZLGWIXVXLXNJ",
"output": "OFEEAZIVROYOCKIW..............\nZ..............X..............\nU..............I..............\nT..............E..............\nT..............L..............\nOSSFERQNJVMYTHQJHLQBYQLBVJNVBW\n...............L.............Q\n...............E.............F\n...............L.............Q\n...............M.............A\n...............G.............U\n...............U.............I\n...............Q.............Q\n...............N.............O\n...............K.............N\n...............L.............U\n..."
},
{
"input": "MPISMEYTWWBYTHA\nEJHYPZICDDONIUA\nEJOT\nYGLLIXXKFPBEPSTKPE\nEVBIY\nTNKLLGVGTIKQWUYLLXM",
"output": "EJOT..............\nV..N..............\nB..K..............\nI..L..............\nYGLLIXXKFPBEPSTKPE\n...G.............J\n...V.............H\n...G.............Y\n...T.............P\n...I.............Z\n...K.............I\n...Q.............C\n...W.............D\n...U.............D\n...Y.............O\n...L.............N\n...L.............I\n...X.............U\n...MPISMEYTWWBYTHA"
}
] | 310 | 0 | 3.9225 | 5,319 |
157 | Game Outcome | [
"brute force"
] | null | null | Sherlock Holmes and Dr. Watson played some game on a checkered board *n*<=Γ<=*n* in size. During the game they put numbers on the board's squares by some tricky rules we don't know. However, the game is now over and each square of the board contains exactly one number. To understand who has won, they need to count the number of winning squares. To determine if the particular square is winning you should do the following. Calculate the sum of all numbers on the squares that share this column (including the given square) and separately calculate the sum of all numbers on the squares that share this row (including the given square). A square is considered winning if the sum of the column numbers is strictly greater than the sum of the row numbers.
For instance, lets game was ended like is shown in the picture. Then the purple cell is winning, because the sum of its column numbers equals 8<=+<=3<=+<=6<=+<=7<==<=24, sum of its row numbers equals 9<=+<=5<=+<=3<=+<=2<==<=19, and 24<=><=19. | The first line contains an integer *n* (1<=β€<=*n*<=β€<=30). Each of the following *n* lines contain *n* space-separated integers. The *j*-th number on the *i*-th line represents the number on the square that belongs to the *j*-th column and the *i*-th row on the board. All number on the board are integers from 1 to 100. | Print the single number β the number of the winning squares. | [
"1\n1\n",
"2\n1 2\n3 4\n",
"4\n5 7 8 4\n9 5 3 2\n1 6 6 4\n9 5 7 3\n"
] | [
"0\n",
"2\n",
"6\n"
] | In the first example two upper squares are winning.
In the third example three left squares in the both middle rows are winning: | [
{
"input": "1\n1",
"output": "0"
},
{
"input": "2\n1 2\n3 4",
"output": "2"
},
{
"input": "4\n5 7 8 4\n9 5 3 2\n1 6 6 4\n9 5 7 3",
"output": "6"
},
{
"input": "2\n1 1\n1 1",
"output": "0"
},
{
"input": "3\n1 2 3\n4 5 6\n7 8 9",
"output": "4"
},
{
"input": "3\n1 2 3\n3 1 2\n2 3 1",
"output": "0"
},
{
"input": "4\n1 2 3 4\n8 7 6 5\n9 10 11 12\n16 15 14 13",
"output": "8"
},
{
"input": "1\n53",
"output": "0"
},
{
"input": "5\n1 98 22 9 39\n10 9 44 49 66\n79 17 23 8 47\n59 69 72 47 14\n94 91 98 19 54",
"output": "13"
},
{
"input": "1\n31",
"output": "0"
},
{
"input": "1\n92",
"output": "0"
},
{
"input": "5\n61 45 70 19 48\n52 29 98 21 74\n21 66 12 6 55\n62 75 66 62 57\n94 74 9 86 24",
"output": "13"
},
{
"input": "2\n73 99\n13 100",
"output": "2"
},
{
"input": "4\n89 79 14 89\n73 24 58 89\n62 88 69 65\n58 92 18 83",
"output": "10"
},
{
"input": "5\n99 77 32 20 49\n93 81 63 7 58\n37 1 17 35 53\n18 94 38 80 23\n91 50 42 61 63",
"output": "12"
},
{
"input": "4\n81 100 38 54\n8 64 39 59\n6 12 53 65\n79 50 99 71",
"output": "8"
},
{
"input": "5\n42 74 45 85 14\n68 94 11 3 89\n68 67 97 62 66\n65 76 96 18 84\n61 98 28 94 74",
"output": "12"
},
{
"input": "9\n53 80 94 41 58 49 88 24 42\n85 11 32 64 40 56 63 95 73\n17 85 60 41 13 71 54 67 87\n38 14 21 81 66 59 52 33 86\n29 34 46 18 19 80 10 44 51\n4 27 65 75 77 21 15 49 50\n35 68 86 98 98 62 69 52 71\n43 28 56 91 89 21 14 57 79\n27 27 29 26 15 76 21 70 78",
"output": "40"
},
{
"input": "7\n80 81 45 81 72 19 65\n31 24 15 52 47 1 14\n81 35 42 24 96 59 46\n16 2 59 56 60 98 76\n20 95 10 68 68 56 93\n60 16 68 77 89 52 43\n11 22 43 36 99 2 11",
"output": "21"
},
{
"input": "9\n33 80 34 56 56 33 27 74 57\n14 69 78 44 56 70 26 73 47\n13 42 17 33 78 83 94 70 37\n96 78 92 6 16 68 8 31 46\n67 97 21 10 44 64 15 77 28\n34 44 83 96 63 52 29 27 79\n23 23 57 54 35 16 5 64 36\n29 71 36 78 47 81 72 97 36\n24 83 70 58 36 82 42 44 26",
"output": "41"
},
{
"input": "9\n57 70 94 69 77 59 88 63 83\n6 79 46 5 9 43 20 39 48\n46 35 58 22 17 3 81 82 34\n77 10 40 53 71 84 14 58 56\n6 92 77 81 13 20 77 29 40\n59 53 3 97 21 97 22 11 64\n52 91 82 20 6 3 99 17 44\n79 25 43 69 85 55 95 61 31\n89 24 50 84 54 93 54 60 87",
"output": "46"
},
{
"input": "5\n77 44 22 21 20\n84 3 35 86 35\n97 50 1 44 92\n4 88 56 20 3\n32 56 26 17 80",
"output": "13"
},
{
"input": "7\n62 73 50 63 66 92 2\n27 13 83 84 88 81 47\n60 41 25 2 68 32 60\n7 94 18 98 41 25 72\n69 37 4 10 82 49 91\n76 26 67 27 30 49 18\n44 78 6 1 41 94 80",
"output": "26"
},
{
"input": "9\n40 70 98 28 44 78 15 73 20\n25 74 46 3 27 59 33 96 19\n100 47 99 68 68 67 66 87 31\n26 39 8 91 58 20 91 69 81\n77 43 90 60 17 91 78 85 68\n41 46 47 50 96 18 69 81 26\n10 58 2 36 54 64 69 10 65\n6 86 26 7 88 20 43 92 59\n61 76 13 23 49 28 22 79 8",
"output": "44"
},
{
"input": "8\n44 74 25 81 32 33 55 58\n36 13 28 28 20 65 87 58\n8 35 52 59 34 15 33 16\n2 22 42 29 11 66 30 72\n33 47 8 61 31 64 59 63\n79 36 38 42 12 21 92 36\n56 47 44 6 6 1 37 2\n79 88 79 53 50 69 94 39",
"output": "31"
},
{
"input": "5\n4 91 100 8 48\n78 56 61 49 83\n12 21 95 77 78\n40 20 91 79 25\n32 88 94 28 55",
"output": "10"
},
{
"input": "5\n23 70 5 36 69\n83 18 19 98 40\n84 91 18 51 35\n17 18 35 47 59\n29 72 35 87 27",
"output": "13"
},
{
"input": "12\n8 42 23 20 39 5 23 86 26 65 93 82\n48 35 12 4 59 19 19 28 38 81 97 99\n93 24 31 44 97 50 44 99 50 7 10 64\n79 43 65 29 84 43 46 41 89 16 6 1\n34 90 33 1 7 12 46 84 67 30 1 58\n58 21 100 66 56 22 7 24 72 73 86 37\n2 17 85 6 2 73 85 44 43 79 34 65\n3 53 29 76 87 2 27 19 11 42 71 38\n69 82 73 52 44 23 92 10 13 72 59 16\n73 32 37 93 21 94 43 39 27 53 14 15\n86 16 90 91 14 50 73 61 77 36 93 90\n22 56 30 52 81 70 12 92 75 27 38 12",
"output": "77"
},
{
"input": "3\n41 94 58\n73 61 8\n34 88 89",
"output": "5"
},
{
"input": "3\n1 2 3\n1 1 1\n1 1 1",
"output": "4"
},
{
"input": "2\n7 3\n9 5",
"output": "2"
},
{
"input": "3\n4 3 2\n2 2 2\n2 2 2",
"output": "4"
}
] | 248 | 0 | 3 | 5,331 |
|
359 | Permutation | [
"constructive algorithms",
"dp",
"math"
] | null | null | A permutation *p* is an ordered group of numbers *p*1,<=<=<=*p*2,<=<=<=...,<=<=<=*p**n*, consisting of *n* distinct positive integers, each is no more than *n*. We'll define number *n* as the length of permutation *p*1,<=<=<=*p*2,<=<=<=...,<=<=<=*p**n*.
Simon has a positive integer *n* and a non-negative integer *k*, such that 2*k*<=β€<=*n*. Help him find permutation *a* of length 2*n*, such that it meets this equation: . | The first line contains two integers *n* and *k* (1<=β€<=*n*<=β€<=50000, 0<=β€<=2*k*<=β€<=*n*). | Print 2*n* integers *a*1,<=*a*2,<=...,<=*a*2*n* β the required permutation *a*. It is guaranteed that the solution exists. If there are multiple solutions, you can print any of them. | [
"1 0\n",
"2 1\n",
"4 0\n"
] | [
"1 2",
"3 2 1 4\n",
"2 7 4 6 1 3 5 8\n"
] | Record |*x*| represents the absolute value of number *x*.
In the first sample |1β-β2|β-β|1β-β2|β=β0.
In the second sample |3β-β2|β+β|1β-β4|β-β|3β-β2β+β1β-β4|β=β1β+β3β-β2β=β2.
In the third sample |2β-β7|β+β|4β-β6|β+β|1β-β3|β+β|5β-β8|β-β|2β-β7β+β4β-β6β+β1β-β3β+β5β-β8|β=β12β-β12β=β0. | [
{
"input": "1 0",
"output": "1 2"
},
{
"input": "2 1",
"output": "3 2 1 4"
},
{
"input": "4 0",
"output": "2 7 4 6 1 3 5 8"
},
{
"input": "50000 0",
"output": "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "50000 25000",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "50000 24999",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "49999 24999",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "49999 3",
"output": "2 1 4 3 6 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "1333 156",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "7563 3781",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "7563 3780",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "2 0",
"output": "1 2 3 4"
},
{
"input": "3 0",
"output": "1 2 3 4 5 6"
},
{
"input": "4 1",
"output": "2 1 3 4 5 6 7 8"
},
{
"input": "4 2",
"output": "2 1 4 3 5 6 7 8"
},
{
"input": "6 3",
"output": "2 1 4 3 6 5 7 8 9 10 11 12"
},
{
"input": "48888 24444",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "50000 1",
"output": "2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "50000 1000",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "34 17",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68"
},
{
"input": "43244 1233",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "213 100",
"output": "2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58 57 60 59 62 61 64 63 66 65 68 67 70 69 72 71 74 73 76 75 78 77 80 79 82 81 84 83 86 85 88 87 90 89 92 91 94 93 96 95 98 97 100 99 102 101 104 103 106 105 108 107 110 109 112 111 114 113 116 115 118 117 120 119 122 121 124 123 126 125 128 127 130 129 132 131 134 133 136 135 138 137 140 139 142 141 144 143 146 145 148 147 150 149 152 151 154 153 156..."
},
{
"input": "50 1",
"output": "2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100"
},
{
"input": "55 0",
"output": "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110"
},
{
"input": "5000 0",
"output": "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "3 1",
"output": "2 1 3 4 5 6"
},
{
"input": "7563 0",
"output": "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "7563 1",
"output": "2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "7563 2",
"output": "2 1 4 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155..."
},
{
"input": "6 0",
"output": "1 2 3 4 5 6 7 8 9 10 11 12"
}
] | 233 | 3,891,200 | 3 | 5,333 |
|
96 | Lucky Numbers (easy) | [
"binary search",
"bitmasks",
"brute force"
] | B. Lucky Numbers (easy) | 2 | 256 | Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.
One day Petya came across a positive integer *n*. Help him to find the least super lucky number which is not less than *n*. | The only line contains a positive integer *n* (1<=β€<=*n*<=β€<=109). This number doesn't have leading zeroes. | Output the least super lucky number that is more than or equal to *n*.
Please, do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator. | [
"4500\n",
"47\n"
] | [
"4747\n",
"47\n"
] | none | [
{
"input": "4500",
"output": "4747"
},
{
"input": "47",
"output": "47"
},
{
"input": "1",
"output": "47"
},
{
"input": "12",
"output": "47"
},
{
"input": "4587",
"output": "4747"
},
{
"input": "100",
"output": "4477"
},
{
"input": "1007",
"output": "4477"
},
{
"input": "99999999",
"output": "4444477777"
},
{
"input": "491020945",
"output": "4444477777"
},
{
"input": "1000000000",
"output": "4444477777"
},
{
"input": "777777",
"output": "44447777"
},
{
"input": "99999999",
"output": "4444477777"
},
{
"input": "474",
"output": "4477"
},
{
"input": "85469",
"output": "444777"
},
{
"input": "7474747",
"output": "44447777"
},
{
"input": "2145226",
"output": "44447777"
},
{
"input": "5556585",
"output": "44447777"
},
{
"input": "87584777",
"output": "4444477777"
},
{
"input": "77777777",
"output": "4444477777"
},
{
"input": "999999999",
"output": "4444477777"
},
{
"input": "74477744",
"output": "74477744"
},
{
"input": "444444444",
"output": "4444477777"
},
{
"input": "467549754",
"output": "4444477777"
},
{
"input": "147474747",
"output": "4444477777"
},
{
"input": "555",
"output": "4477"
},
{
"input": "100000",
"output": "444777"
},
{
"input": "74777443",
"output": "74777444"
},
{
"input": "4700007",
"output": "44447777"
},
{
"input": "70070077",
"output": "74444777"
},
{
"input": "123",
"output": "4477"
},
{
"input": "7474",
"output": "7474"
},
{
"input": "3696",
"output": "4477"
},
{
"input": "888999577",
"output": "4444477777"
},
{
"input": "10",
"output": "47"
},
{
"input": "7",
"output": "47"
},
{
"input": "50",
"output": "74"
},
{
"input": "70",
"output": "74"
},
{
"input": "74700",
"output": "444777"
},
{
"input": "1024",
"output": "4477"
},
{
"input": "73",
"output": "74"
},
{
"input": "74710000",
"output": "74744477"
},
{
"input": "444000000",
"output": "4444477777"
},
{
"input": "4",
"output": "47"
},
{
"input": "1",
"output": "47"
},
{
"input": "9",
"output": "47"
},
{
"input": "99",
"output": "4477"
},
{
"input": "48",
"output": "74"
},
{
"input": "47474749",
"output": "47474774"
},
{
"input": "47474774",
"output": "47474774"
},
{
"input": "77777777",
"output": "4444477777"
},
{
"input": "4777",
"output": "7447"
},
{
"input": "7748",
"output": "444777"
},
{
"input": "7773",
"output": "444777"
},
{
"input": "19",
"output": "47"
},
{
"input": "447777",
"output": "474477"
}
] | 62 | 0 | 0 | 5,336 |
362 | Two Semiknights Meet | [
"greedy",
"math"
] | null | null | A boy Petya loves chess very much. He even came up with a chess piece of his own, a semiknight. The semiknight can move in any of these four directions: 2 squares forward and 2 squares to the right, 2 squares forward and 2 squares to the left, 2 squares backward and 2 to the right and 2 squares backward and 2 to the left. Naturally, the semiknight cannot move beyond the limits of the chessboard.
Petya put two semiknights on a standard chessboard. Petya simultaneously moves with both semiknights. The squares are rather large, so after some move the semiknights can meet, that is, they can end up in the same square. After the meeting the semiknights can move on, so it is possible that they meet again. Petya wonders if there is such sequence of moves when the semiknights meet. Petya considers some squares bad. That is, they do not suit for the meeting. The semiknights can move through these squares but their meetings in these squares don't count.
Petya prepared multiple chess boards. Help Petya find out whether the semiknights can meet on some good square for each board.
Please see the test case analysis. | The first line contains number *t* (1<=β€<=*t*<=β€<=50) β the number of boards. Each board is described by a matrix of characters, consisting of 8 rows and 8 columns. The matrix consists of characters ".", "#", "K", representing an empty good square, a bad square and the semiknight's position, correspondingly. It is guaranteed that matrix contains exactly 2 semiknights. The semiknight's squares are considered good for the meeting. The tests are separated by empty line. | For each test, print on a single line the answer to the problem: "YES", if the semiknights can meet and "NO" otherwise. | [
"2\n........\n........\n......#.\nK..##..#\n.......#\n...##..#\n......#.\nK.......\n\n........\n........\n..#.....\n..#..#..\n..####..\n...##...\n........\n....K#K#\n"
] | [
"YES\nNO\n"
] | Consider the first board from the sample. We will assume the rows and columns of the matrix to be numbered 1 through 8 from top to bottom and from left to right, correspondingly. The knights can meet, for example, in square (2, 7). The semiknight from square (4, 1) goes to square (2, 3) and the semiknight goes from square (8, 1) to square (6, 3). Then both semiknights go to (4, 5) but this square is bad, so they move together to square (2, 7).
On the second board the semiknights will never meet. | [
{
"input": "2\n........\n........\n......#.\nK..##..#\n.......#\n...##..#\n......#.\nK.......\n\n........\n........\n..#.....\n..#..#..\n..####..\n...##...\n........\n....K#K#",
"output": "YES\nNO"
},
{
"input": "3\n........\n........\n..#.....\n..#..#..\n..####..\n...##...\n........\n####K#K#\n\n........\nK......K\n........\n#......#\n.#....#.\n..####..\n........\n........\n\n.#..#...\n.##.##..\n..###...\n..#K###.\n..####..\n......K.\n..#####.\n..#####.",
"output": "NO\nNO\nNO"
},
{
"input": "1\nK.#....#\n...#..#.\n..#.....\n..#.###.\n..#.....\n...#....\n.#.....#\n.#...##K",
"output": "NO"
},
{
"input": "2\n....#..K\n...#....\n..##.#..\n.#.#.#..\n.#.....#\n.#......\n###.....\nK#.#....\n\nK.#.....\n..#...#.\n#.....#.\n..#.#..#\n#.......\n..#..#..\n....#...\nK..##.##",
"output": "NO\nNO"
},
{
"input": "5\n........\n...KK...\n..####..\n...##...\n........\n..####..\n.######.\n#......#\n\n........\n.K......\n..#.....\n...#....\n....#...\n.....#..\n......#.\n.......K\n\n........\n...K....\n##...##.\n#.#.#..#\n.##.###.\n#..K#..#\n.##..##.\n........\n\n........\n.K..K...\n..##....\n..####..\n.#....#.\n.#.....#\n..#####.\n........\n\nK.......\n........\n........\n........\n........\n........\n........\n.......K",
"output": "NO\nNO\nYES\nNO\nNO"
}
] | 62 | 307,200 | 3 | 5,340 |
|
665 | Shopping | [
"brute force"
] | null | null | Ayush is a cashier at the shopping center. Recently his department has started a ''click and collect" service which allows users to shop online.
The store contains *k* items. *n* customers have already used the above service. Each user paid for *m* items. Let *a**ij* denote the *j*-th item in the *i*-th person's order.
Due to the space limitations all the items are arranged in one single row. When Ayush receives the *i*-th order he will find one by one all the items *a**ij* (1<=β€<=*j*<=β€<=*m*) in the row. Let *pos*(*x*) denote the position of the item *x* in the row at the moment of its collection. Then Ayush takes time equal to *pos*(*a**i*1)<=+<=*pos*(*a**i*2)<=+<=...<=+<=*pos*(*a**im*) for the *i*-th customer.
When Ayush accesses the *x*-th element he keeps a new stock in the front of the row and takes away the *x*-th element. Thus the values are updating.
Your task is to calculate the total time it takes for Ayush to process all the orders.
You can assume that the market has endless stock. | The first line contains three integers *n*, *m* and *k* (1<=β€<=*n*,<=*k*<=β€<=100,<=1<=β€<=*m*<=β€<=*k*) β the number of users, the number of items each user wants to buy and the total number of items at the market.
The next line contains *k* distinct integers *p**l* (1<=β€<=*p**l*<=β€<=*k*) denoting the initial positions of the items in the store. The items are numbered with integers from 1 to *k*.
Each of the next *n* lines contains *m* distinct integers *a**ij* (1<=β€<=*a**ij*<=β€<=*k*) β the order of the *i*-th person. | Print the only integer *t* β the total time needed for Ayush to process all the orders. | [
"2 2 5\n3 4 1 2 5\n1 5\n3 1\n"
] | [
"14\n"
] | Customer 1 wants the items 1 and 5.
*pos*(1)β=β3, so the new positions are: [1,β3,β4,β2,β5].
*pos*(5)β=β5, so the new positions are: [5,β1,β3,β4,β2].
Time taken for the first customer is 3β+β5β=β8.
Customer 2 wants the items 3 and 1.
*pos*(3)β=β3, so the new positions are: [3,β5,β1,β4,β2].
*pos*(1)β=β3, so the new positions are: [1,β3,β5,β4,β2].
Time taken for the second customer is 3β+β3β=β6.
Total time is 8β+β6β=β14.
Formally *pos*(*x*) is the index of *x* in the current row. | [
{
"input": "2 2 5\n3 4 1 2 5\n1 5\n3 1",
"output": "14"
},
{
"input": "4 4 4\n1 2 3 4\n3 4 2 1\n4 3 2 1\n4 1 2 3\n4 1 2 3",
"output": "59"
},
{
"input": "1 1 1\n1\n1",
"output": "1"
},
{
"input": "10 1 100\n1 55 67 75 40 86 24 84 82 26 81 23 70 79 51 54 21 78 31 98 68 93 66 88 99 65 20 52 35 85 16 12 94 100 59 56 18 33 47 46 71 8 38 57 2 92 3 95 6 4 87 22 48 80 15 29 11 45 72 76 44 60 91 90 39 74 41 36 13 27 53 83 32 5 30 63 89 64 49 17 9 97 69 14 50 77 37 96 10 42 28 34 61 19 73 7 62 43 58 25\n33\n69\n51\n7\n68\n70\n1\n35\n24\n7",
"output": "335"
},
{
"input": "100 1 1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1\n1",
"output": "100"
},
{
"input": "3 2 3\n3 1 2\n1 2\n2 1\n2 3",
"output": "13"
},
{
"input": "10 10 10\n3 4 1 2 8 9 5 10 6 7\n9 10 7 8 6 1 2 3 4 5\n2 5 3 6 1 4 9 7 8 10\n2 9 1 8 4 7 5 10 6 3\n10 9 7 1 3 6 2 8 5 4\n2 5 1 3 7 10 4 9 8 6\n6 1 8 7 9 2 3 5 4 10\n1 3 2 8 6 9 4 10 5 7\n5 2 4 8 6 1 10 9 3 7\n5 1 7 10 4 6 2 8 9 3\n2 1 3 9 7 10 6 4 8 5",
"output": "771"
}
] | 77 | 0 | 0 | 5,353 |
|
534 | Covered Path | [
"dp",
"greedy",
"math"
] | null | null | The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals *v*1 meters per second, and in the end it is *v*2 meters per second. We know that this section of the route took exactly *t* seconds to pass.
Assuming that at each of the seconds the speed is constant, and between seconds the speed can change at most by *d* meters per second in absolute value (i.e., the difference in the speed of any two adjacent seconds does not exceed *d* in absolute value), find the maximum possible length of the path section in meters. | The first line contains two integers *v*1 and *v*2 (1<=β€<=*v*1,<=*v*2<=β€<=100) β the speeds in meters per second at the beginning of the segment and at the end of the segment, respectively.
The second line contains two integers *t* (2<=β€<=*t*<=β€<=100) β the time when the car moves along the segment in seconds, *d* (0<=β€<=*d*<=β€<=10) β the maximum value of the speed change between adjacent seconds.
It is guaranteed that there is a way to complete the segment so that:
- the speed in the first second equals *v*1, - the speed in the last second equals *v*2, - the absolute value of difference of speeds between any two adjacent seconds doesn't exceed *d*. | Print the maximum possible length of the path segment in meters. | [
"5 6\n4 2\n",
"10 10\n10 0\n"
] | [
"26",
"100"
] | In the first sample the sequence of speeds of Polycarpus' car can look as follows: 5, 7, 8, 6. Thus, the total path is 5β+β7β+β8β+β6β=β26 meters.
In the second sample, as *d*β=β0, the car covers the whole segment at constant speed *v*β=β10. In *t*β=β10 seconds it covers the distance of 100 meters. | [
{
"input": "5 6\n4 2",
"output": "26"
},
{
"input": "10 10\n10 0",
"output": "100"
},
{
"input": "87 87\n2 10",
"output": "174"
},
{
"input": "1 11\n6 2",
"output": "36"
},
{
"input": "100 10\n10 10",
"output": "550"
},
{
"input": "1 1\n100 10",
"output": "24600"
},
{
"input": "1 1\n5 1",
"output": "9"
},
{
"input": "1 1\n5 2",
"output": "13"
},
{
"input": "100 100\n100 0",
"output": "10000"
},
{
"input": "100 100\n100 10",
"output": "34500"
},
{
"input": "1 100\n100 1",
"output": "5050"
},
{
"input": "1 100\n100 10",
"output": "29305"
},
{
"input": "100 1\n100 1",
"output": "5050"
},
{
"input": "100 1\n100 10",
"output": "29305"
},
{
"input": "1 10\n2 10",
"output": "11"
},
{
"input": "1 1\n2 1",
"output": "2"
},
{
"input": "1 1\n2 10",
"output": "2"
},
{
"input": "1 2\n2 1",
"output": "3"
},
{
"input": "1 2\n2 10",
"output": "3"
},
{
"input": "1 5\n3 2",
"output": "9"
},
{
"input": "2 1\n2 2",
"output": "3"
},
{
"input": "2 1\n2 10",
"output": "3"
},
{
"input": "1 11\n2 10",
"output": "12"
},
{
"input": "11 1\n2 10",
"output": "12"
},
{
"input": "1 1\n3 5",
"output": "8"
},
{
"input": "1 10\n3 5",
"output": "17"
},
{
"input": "1 21\n3 10",
"output": "33"
},
{
"input": "21 1\n3 10",
"output": "33"
},
{
"input": "100 100\n99 1",
"output": "12301"
},
{
"input": "100 100\n100 1",
"output": "12450"
},
{
"input": "99 99\n99 1",
"output": "12202"
},
{
"input": "99 99\n99 10",
"output": "33811"
},
{
"input": "1 100\n99 10",
"output": "28764"
},
{
"input": "13 31\n7 5",
"output": "182"
},
{
"input": "88 78\n8 5",
"output": "719"
},
{
"input": "34 48\n47 4",
"output": "4030"
},
{
"input": "91 29\n78 3",
"output": "8806"
},
{
"input": "90 81\n21 6",
"output": "2391"
},
{
"input": "95 89\n45 3",
"output": "5589"
},
{
"input": "48 54\n84 2",
"output": "7724"
},
{
"input": "72 31\n59 7",
"output": "8865"
},
{
"input": "51 13\n47 3",
"output": "2970"
},
{
"input": "97 91\n82 2",
"output": "10984"
},
{
"input": "71 71\n9 5",
"output": "719"
},
{
"input": "16 49\n40 3",
"output": "2350"
},
{
"input": "22 41\n68 4",
"output": "6608"
},
{
"input": "13 71\n72 6",
"output": "10444"
},
{
"input": "77 78\n46 3",
"output": "5083"
},
{
"input": "36 60\n54 2",
"output": "3924"
},
{
"input": "55 39\n93 2",
"output": "8571"
},
{
"input": "34 7\n48 6",
"output": "4266"
},
{
"input": "80 88\n79 3",
"output": "11193"
},
{
"input": "34 62\n15 4",
"output": "866"
},
{
"input": "81 40\n73 2",
"output": "6798"
},
{
"input": "13 38\n97 6",
"output": "16271"
},
{
"input": "84 87\n45 2",
"output": "4814"
},
{
"input": "42 65\n76 3",
"output": "8240"
},
{
"input": "55 6\n24 4",
"output": "1110"
},
{
"input": "41 16\n43 2",
"output": "2029"
},
{
"input": "99 93\n78 1",
"output": "8961"
},
{
"input": "10 7\n44 2",
"output": "1297"
},
{
"input": "72 54\n91 3",
"output": "11781"
},
{
"input": "48 34\n80 2",
"output": "6376"
},
{
"input": "92 85\n70 1",
"output": "7373"
}
] | 61 | 0 | 0 | 5,359 |
|
627 | Factory Repairs | [
"data structures"
] | null | null | A factory produces thimbles in bulk. Typically, it can produce up to *a* thimbles a day. However, some of the machinery is defective, so it can currently only produce *b* thimbles each day. The factory intends to choose a *k*-day period to do maintenance and construction; it cannot produce any thimbles during this time, but will be restored to its full production of *a* thimbles per day after the *k* days are complete.
Initially, no orders are pending. The factory receives updates of the form *d**i*, *a**i*, indicating that *a**i* new orders have been placed for the *d**i*-th day. Each order requires a single thimble to be produced on precisely the specified day. The factory may opt to fill as many or as few of the orders in a single batch as it likes.
As orders come in, the factory owner would like to know the maximum number of orders he will be able to fill if he starts repairs on a given day *p**i*. Help the owner answer his questions. | The first line contains five integers *n*, *k*, *a*, *b*, and *q* (1<=β€<=*k*<=β€<=*n*<=β€<=200<=000, 1<=β€<=*b*<=<<=*a*<=β€<=10 000, 1<=β€<=*q*<=β€<=200<=000)Β β the number of days, the length of the repair time, the production rates of the factory, and the number of updates, respectively.
The next *q* lines contain the descriptions of the queries. Each query is of one of the following two forms:
- 1 *d**i* *a**i* (1<=β€<=*d**i*<=β€<=*n*, 1<=β€<=*a**i*<=β€<=10 000), representing an update of *a**i* orders on day *d**i*, or - 2 *p**i* (1<=β€<=*p**i*<=β€<=*n*<=-<=*k*<=+<=1), representing a question: at the moment, how many orders could be filled if the factory decided to commence repairs on day *p**i*?
It's guaranteed that the input will contain at least one query of the second type. | For each query of the second type, print a line containing a single integer β the maximum number of orders that the factory can fill over all *n* days. | [
"5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2\n"
] | [
"3\n6\n4\n",
"7\n1\n"
] | Consider the first sample.
We produce up to 1 thimble a day currently and will produce up to 2 thimbles a day after repairs. Repairs take 2 days.
For the first question, we are able to fill 1 order on day 1, no orders on days 2 and 3 since we are repairing, no orders on day 4 since no thimbles have been ordered for that day, and 2 orders for day 5 since we are limited to our production capacity, for a total of 3 orders filled.
For the third question, we are able to fill 1 order on day 1, 1 order on day 2, and 2 orders on day 5, for a total of 4 orders. | [
{
"input": "5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3",
"output": "3\n6\n4"
},
{
"input": "5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2",
"output": "7\n1"
},
{
"input": "1 1 2 1 1\n2 1",
"output": "0"
}
] | 2,995 | 8,806,400 | 0 | 5,373 |
|
1,005 | Polycarp and Div 3 | [
"dp",
"greedy",
"number theory"
] | null | null | Polycarp likes numbers that are divisible by 3.
He has a huge number $s$. Polycarp wants to cut from it the maximum number of numbers that are divisible by $3$. To do this, he makes an arbitrary number of vertical cuts between pairs of adjacent digits. As a result, after $m$ such cuts, there will be $m+1$ parts in total. Polycarp analyzes each of the obtained numbers and finds the number of those that are divisible by $3$.
For example, if the original number is $s=3121$, then Polycarp can cut it into three parts with two cuts: $3|1|21$. As a result, he will get two numbers that are divisible by $3$.
Polycarp can make an arbitrary number of vertical cuts, where each cut is made between a pair of adjacent digits. The resulting numbers cannot contain extra leading zeroes (that is, the number can begin with 0 if and only if this number is exactly one character '0'). For example, 007, 01 and 00099 are not valid numbers, but 90, 0 and 10001 are valid.
What is the maximum number of numbers divisible by $3$ that Polycarp can obtain? | The first line of the input contains a positive integer $s$. The number of digits of the number $s$ is between $1$ and $2\cdot10^5$, inclusive. The first (leftmost) digit is not equal to 0. | Print the maximum number of numbers divisible by $3$ that Polycarp can get by making vertical cuts in the given number $s$. | [
"3121\n",
"6\n",
"1000000000000000000000000000000000\n",
"201920181\n"
] | [
"2\n",
"1\n",
"33\n",
"4\n"
] | In the first example, an example set of optimal cuts on the number is 3|1|21.
In the second example, you do not need to make any cuts. The specified number 6 forms one number that is divisible by $3$.
In the third example, cuts must be made between each pair of digits. As a result, Polycarp gets one digit 1 and $33$ digits 0. Each of the $33$ digits 0 forms a number that is divisible by $3$.
In the fourth example, an example set of optimal cuts is 2|0|1|9|201|81. The numbers $0$, $9$, $201$ and $81$ are divisible by $3$. | [
{
"input": "3121",
"output": "2"
},
{
"input": "6",
"output": "1"
},
{
"input": "1000000000000000000000000000000000",
"output": "33"
},
{
"input": "201920181",
"output": "4"
},
{
"input": "4",
"output": "0"
},
{
"input": "10",
"output": "1"
},
{
"input": "11",
"output": "0"
},
{
"input": "12",
"output": "1"
},
{
"input": "13",
"output": "1"
},
{
"input": "31",
"output": "1"
},
{
"input": "14139582796",
"output": "6"
},
{
"input": "1670000",
"output": "5"
},
{
"input": "604500",
"output": "5"
},
{
"input": "40041",
"output": "2"
},
{
"input": "10000170",
"output": "5"
}
] | 187 | 7,475,200 | 0 | 5,380 |
|
653 | Bear and Forgotten Tree 2 | [
"dfs and similar",
"dsu",
"graphs",
"trees"
] | null | null | A tree is a connected undirected graph consisting of *n* vertices and *n*<=<=-<=<=1 edges. Vertices are numbered 1 through *n*.
Limak is a little polar bear. He once had a tree with *n* vertices but he lost it. He still remembers something about the lost tree though.
You are given *m* pairs of vertices (*a*1,<=*b*1),<=(*a*2,<=*b*2),<=...,<=(*a**m*,<=*b**m*). Limak remembers that for each *i* there was no edge between *a**i* and *b**i*. He also remembers that vertex 1 was incident to exactly *k* edges (its degree was equal to *k*).
Is it possible that Limak remembers everything correctly? Check whether there exists a tree satisfying the given conditions. | The first line of the input contains three integers *n*, *m* and *k* ()Β β the number of vertices in Limak's tree, the number of forbidden pairs of vertices, and the degree of vertex 1, respectively.
The *i*-th of next *m* lines contains two distinct integers *a**i* and *b**i* (1<=β€<=*a**i*,<=*b**i*<=β€<=*n*,<=*a**i*<=β <=*b**i*)Β β the *i*-th pair that is forbidden. It's guaranteed that each pair of vertices will appear at most once in the input. | Print "possible" (without quotes) if there exists at least one tree satisfying the given conditions. Otherwise, print "impossible" (without quotes). | [
"5 4 2\n1 2\n2 3\n4 2\n4 1\n",
"6 5 3\n1 2\n1 3\n1 4\n1 5\n1 6\n"
] | [
"possible\n",
"impossible\n"
] | In the first sample, there are *n*β=β5 vertices. The degree of vertex 1 should be *k*β=β2. All conditions are satisfied for a tree with edges 1β-β5, 5β-β2, 1β-β3 and 3β-β4.
In the second sample, Limak remembers that none of the following edges existed: 1β-β2, 1β-β3, 1β-β4, 1β-β5 and 1β-β6. Hence, vertex 1 couldn't be connected to any other vertex and it implies that there is no suitable tree. | [
{
"input": "5 4 2\n1 2\n2 3\n4 2\n4 1",
"output": "possible"
},
{
"input": "6 5 3\n1 2\n1 3\n1 4\n1 5\n1 6",
"output": "impossible"
},
{
"input": "4 3 2\n2 3\n2 4\n3 4",
"output": "impossible"
},
{
"input": "4 2 2\n1 2\n1 3",
"output": "impossible"
},
{
"input": "7 11 1\n1 2\n1 3\n1 4\n1 5\n1 7\n6 2\n6 3\n6 4\n6 5\n6 7\n2 3",
"output": "impossible"
},
{
"input": "3 1 2\n1 3",
"output": "impossible"
},
{
"input": "4 2 2\n2 1\n1 4",
"output": "impossible"
},
{
"input": "4 2 3\n2 1\n2 4",
"output": "impossible"
},
{
"input": "4 5 1\n2 3\n2 4\n4 3\n3 1\n1 2",
"output": "impossible"
},
{
"input": "5 2 4\n4 3\n1 3",
"output": "impossible"
},
{
"input": "5 3 1\n2 1\n4 3\n3 1",
"output": "possible"
},
{
"input": "5 3 2\n1 2\n5 1\n1 4",
"output": "impossible"
},
{
"input": "5 3 3\n5 4\n2 4\n2 1",
"output": "possible"
},
{
"input": "5 4 2\n2 1\n4 1\n4 2\n3 5",
"output": "possible"
},
{
"input": "5 4 3\n5 1\n5 3\n3 1\n4 2",
"output": "impossible"
},
{
"input": "5 4 4\n4 5\n4 2\n1 5\n5 3",
"output": "impossible"
},
{
"input": "5 5 2\n2 1\n3 1\n5 3\n3 2\n3 4",
"output": "impossible"
},
{
"input": "5 6 1\n3 1\n4 5\n3 5\n4 3\n1 2\n2 4",
"output": "impossible"
},
{
"input": "5 6 2\n3 5\n2 1\n2 5\n1 5\n1 3\n2 4",
"output": "impossible"
},
{
"input": "5 6 3\n3 1\n4 3\n2 5\n4 5\n2 4\n3 2",
"output": "possible"
},
{
"input": "5 8 1\n1 4\n4 3\n1 5\n3 5\n2 4\n1 2\n5 2\n4 5",
"output": "impossible"
},
{
"input": "2 0 1",
"output": "possible"
},
{
"input": "2 1 1\n2 1",
"output": "impossible"
},
{
"input": "300000 0 1",
"output": "possible"
},
{
"input": "300000 0 299999",
"output": "possible"
}
] | 436 | 20,070,400 | 0 | 5,381 |
Subsets and Splits