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Rikhail Mubinchik believes that the current definition of prime numbers is obsolete as they are too complex and unpredictable. A palindromic number is another matter. It is aesthetically pleasing, and it has a number of remarkable properties. Help Rikhail to convince the scientific community in this!Let us remind you that a number is called prime if it is integer larger than one, and is not divisible by any positive integer other than itself and one.Rikhail calls a number a palindromic if it is integer, positive, and its decimal representation without leading zeros is a palindrome, i.e. reads the same from left to right and right to left.One problem with prime numbers is that there are too many of them. Let's introduce the following notation: Ο(n) β the number of primes no larger than n, rub(n) β the number of palindromic numbers no larger than n. Rikhail wants to prove that there are a lot more primes than palindromic ones.He asked you to solve the following problem: for a given value of the coefficient A find the maximum n, such that Ο(n)ββ€βAΒ·rub(n). | Input: ['1 1'] Output:['40'] | [
0,
3
] |
Alice and Bob love playing one-dimensional battle ships. They play on the field in the form of a line consisting of n square cells (that is, on a 1βΓβn table).At the beginning of the game Alice puts k ships on the field without telling their positions to Bob. Each ship looks as a 1βΓβa rectangle (that is, it occupies a sequence of a consecutive squares of the field). The ships cannot intersect and even touch each other.After that Bob makes a sequence of "shots". He names cells of the field and Alice either says that the cell is empty ("miss"), or that the cell belongs to some ship ("hit").But here's the problem! Alice like to cheat. May be that is why she responds to each Bob's move with a "miss". Help Bob catch Alice cheating β find Bob's first move, such that after it you can be sure that Alice cheated. | Input: ['11 3 354 8 6 1 11'] Output:['3'] | [
2,
4
] |
Polycarp loves geometric progressions very much. Since he was only three years old, he loves only the progressions of length three. He also has a favorite integer k and a sequence a, consisting of n integers.He wants to know how many subsequences of length three can be selected from a, so that they form a geometric progression with common ratio k.A subsequence of length three is a combination of three such indexes i1,βi2,βi3, that 1ββ€βi1β<βi2β<βi3ββ€βn. That is, a subsequence of length three are such groups of three elements that are not necessarily consecutive in the sequence, but their indexes are strictly increasing.A geometric progression with common ratio k is a sequence of numbers of the form bΒ·k0,βbΒ·k1,β...,βbΒ·krβ-β1.Polycarp is only three years old, so he can not calculate this number himself. Help him to do it. | Input: ['5 21 1 2 2 4'] Output:['4'] | [
4
] |
All cities of Lineland are located on the Ox coordinate axis. Thus, each city is associated with its position xi β a coordinate on the Ox axis. No two cities are located at a single point.Lineland residents love to send letters to each other. A person may send a letter only if the recipient lives in another city (because if they live in the same city, then it is easier to drop in).Strange but true, the cost of sending the letter is exactly equal to the distance between the sender's city and the recipient's city.For each city calculate two values ββmini and maxi, where mini is the minimum cost of sending a letter from the i-th city to some other city, and maxi is the the maximum cost of sending a letter from the i-th city to some other city | Input: ['4-5 -2 2 7'] Output:['3 123 94 75 12'] | [
2
] |
As you must know, the maximum clique problem in an arbitrary graph is NP-hard. Nevertheless, for some graphs of specific kinds it can be solved effectively.Just in case, let us remind you that a clique in a non-directed graph is a subset of the vertices of a graph, such that any two vertices of this subset are connected by an edge. In particular, an empty set of vertexes and a set consisting of a single vertex, are cliques.Let's define a divisibility graph for a set of positive integers Aβ=β{a1,βa2,β...,βan} as follows. The vertices of the given graph are numbers from set A, and two numbers ai and aj (iββ βj) are connected by an edge if and only if either ai is divisible by aj, or aj is divisible by ai.You are given a set of non-negative integers A. Determine the size of a maximum clique in a divisibility graph for set A. | Input: ['83 4 6 8 10 18 21 24'] Output:['3'] | [
3
] |
A Large Software Company develops its own social network. Analysts have found that during the holidays, major sporting events and other significant events users begin to enter the network more frequently, resulting in great load increase on the infrastructure.As part of this task, we assume that the social network is 4n processes running on the n servers. All servers are absolutely identical machines, each of which has a volume of RAM of 1 GB = 1024 MB (1). Each process takes 100 MB of RAM on the server. At the same time, the needs of maintaining the viability of the server takes about 100 more megabytes of RAM. Thus, each server may have up to 9 different processes of social network.Now each of the n servers is running exactly 4 processes. However, at the moment of peak load it is sometimes necessary to replicate the existing 4n processes by creating 8n new processes instead of the old ones. More formally, there is a set of replication rules, the i-th (1ββ€βiββ€β4n) of which has the form of aiβββ(bi,βci), where ai, bi and ci (1ββ€βai,βbi,βciββ€βn) are the numbers of servers. This means that instead of an old process running on server ai, there should appear two new copies of the process running on servers bi and ci. The two new replicated processes can be on the same server (i.e., bi may be equal to ci) or even on the same server where the original process was (i.e. ai may be equal to bi or ci). During the implementation of the rule aiβββ(bi,βci) first the process from the server ai is destroyed, then appears a process on the server bi, then appears a process on the server ci.There is a set of 4n rules, destroying all the original 4n processes from n servers, and creating after their application 8n replicated processes, besides, on each of the n servers will be exactly 8 processes. However, the rules can only be applied consecutively, and therefore the amount of RAM of the servers imposes limitations on the procedure for the application of the rules.According to this set of rules determine the order in which you want to apply all the 4n rules so that at any given time the memory of each of the servers contained at most 9 processes (old and new together), or tell that it is impossible. | Input: ['21 2 21 2 21 2 21 2 22 1 12 1 12 1 12 1 1'] Output:['YES1 2 5 6 3 7 4 8'] | [
2
] |
Giant chess is quite common in Geraldion. We will not delve into the rules of the game, we'll just say that the game takes place on an hβΓβw field, and it is painted in two colors, but not like in chess. Almost all cells of the field are white and only some of them are black. Currently Gerald is finishing a game of giant chess against his friend Pollard. Gerald has almost won, and the only thing he needs to win is to bring the pawn from the upper left corner of the board, where it is now standing, to the lower right corner. Gerald is so confident of victory that he became interested, in how many ways can he win?The pawn, which Gerald has got left can go in two ways: one cell down or one cell to the right. In addition, it can not go to the black cells, otherwise the Gerald still loses. There are no other pawns or pieces left on the field, so that, according to the rules of giant chess Gerald moves his pawn until the game is over, and Pollard is just watching this process. | Input: ['3 4 22 22 3'] Output:['2'] | [
3
] |
Gerald got a very curious hexagon for his birthday. The boy found out that all the angles of the hexagon are equal to . Then he measured the length of its sides, and found that each of them is equal to an integer number of centimeters. There the properties of the hexagon ended and Gerald decided to draw on it.He painted a few lines, parallel to the sides of the hexagon. The lines split the hexagon into regular triangles with sides of 1 centimeter. Now Gerald wonders how many triangles he has got. But there were so many of them that Gerald lost the track of his counting. Help the boy count the triangles. | Input: ['1 1 1 1 1 1'] Output:['6'] | [
0,
3
] |
Amr loves Chemistry, and specially doing experiments. He is preparing for a new interesting experiment.Amr has n different types of chemicals. Each chemical i has an initial volume of ai liters. For this experiment, Amr has to mix all the chemicals together, but all the chemicals volumes must be equal first. So his task is to make all the chemicals volumes equal.To do this, Amr can do two different kind of operations. Choose some chemical i and double its current volume so the new volume will be 2ai Choose some chemical i and divide its volume by two (integer division) so the new volume will be Suppose that each chemical is contained in a vessel of infinite volume. Now Amr wonders what is the minimum number of operations required to make all the chemicals volumes equal? | Input: ['34 8 2'] Output:['2'] | [
0,
2,
3
] |
Amr lives in Lala Land. Lala Land is a very beautiful country that is located on a coordinate line. Lala Land is famous with its apple trees growing everywhere.Lala Land has exactly n apple trees. Tree number i is located in a position xi and has ai apples growing on it. Amr wants to collect apples from the apple trees. Amr currently stands in xβ=β0 position. At the beginning, he can choose whether to go right or left. He'll continue in his direction until he meets an apple tree he didn't visit before. He'll take all of its apples and then reverse his direction, continue walking in this direction until he meets another apple tree he didn't visit before and so on. In the other words, Amr reverses his direction when visiting each new apple tree. Amr will stop collecting apples when there are no more trees he didn't visit in the direction he is facing.What is the maximum number of apples he can collect? | Input: ['2-1 51 5'] Output:['10'] | [
0
] |
After Vitaly was expelled from the university, he became interested in the graph theory.Vitaly especially liked the cycles of an odd length in which each vertex occurs at most once.Vitaly was wondering how to solve the following problem. You are given an undirected graph consisting of n vertices and m edges, not necessarily connected, without parallel edges and loops. You need to find t β the minimum number of edges that must be added to the given graph in order to form a simple cycle of an odd length, consisting of more than one vertex. Moreover, he must find w β the number of ways to add t edges in order to form a cycle of an odd length (consisting of more than one vertex). It is prohibited to add loops or parallel edges.Two ways to add edges to the graph are considered equal if they have the same sets of added edges.Since Vitaly does not study at the university, he asked you to help him with this task. | Input: ['4 41 21 34 24 3'] Output:['1 2'] | [
3
] |
Arthur has bought a beautiful big table into his new flat. When he came home, Arthur noticed that the new table is unstable.In total the table Arthur bought has n legs, the length of the i-th leg is li.Arthur decided to make the table stable and remove some legs. For each of them Arthur determined number di β the amount of energy that he spends to remove the i-th leg.A table with k legs is assumed to be stable if there are more than half legs of the maximum length. For example, to make a table with 5 legs stable, you need to make sure it has at least three (out of these five) legs of the maximum length. Also, a table with one leg is always stable and a table with two legs is stable if and only if they have the same lengths.Your task is to help Arthur and count the minimum number of energy units Arthur should spend on making the table stable. | Input: ['21 53 2'] Output:['2'] | [
0,
2,
3
] |
Pasha decided to invite his friends to a tea party. For that occasion, he has a large teapot with the capacity of w milliliters and 2n tea cups, each cup is for one of Pasha's friends. The i-th cup can hold at most ai milliliters of water.It turned out that among Pasha's friends there are exactly n boys and exactly n girls and all of them are going to come to the tea party. To please everyone, Pasha decided to pour the water for the tea as follows: Pasha can boil the teapot exactly once by pouring there at most w milliliters of water; Pasha pours the same amount of water to each girl; Pasha pours the same amount of water to each boy; if each girl gets x milliliters of water, then each boy gets 2x milliliters of water. In the other words, each boy should get two times more water than each girl does.Pasha is very kind and polite, so he wants to maximize the total amount of the water that he pours to his friends. Your task is to help him and determine the optimum distribution of cups between Pasha's friends. | Input: ['2 41 1 1 1'] Output:['3'] | [
3
] |
Soon a school Olympiad in Informatics will be held in Berland, n schoolchildren will participate there.At a meeting of the jury of the Olympiad it was decided that each of the n participants, depending on the results, will get a diploma of the first, second or third degree. Thus, each student will receive exactly one diploma.They also decided that there must be given at least min1 and at most max1 diplomas of the first degree, at least min2 and at most max2 diplomas of the second degree, and at least min3 and at most max3 diplomas of the third degree.After some discussion it was decided to choose from all the options of distributing diplomas satisfying these limitations the one that maximizes the number of participants who receive diplomas of the first degree. Of all these options they select the one which maximizes the number of the participants who receive diplomas of the second degree. If there are multiple of these options, they select the option that maximizes the number of diplomas of the third degree.Choosing the best option of distributing certificates was entrusted to Ilya, one of the best programmers of Berland. However, he found more important things to do, so it is your task now to choose the best option of distributing of diplomas, based on the described limitations.It is guaranteed that the described limitations are such that there is a way to choose such an option of distributing diplomas that all n participants of the Olympiad will receive a diploma of some degree. | Input: ['61 52 63 7'] Output:['1 2 3 '] | [
2,
3
] |
Andrewid the Android is a galaxy-famous detective. He is now investigating a case of frauds who make fake copies of the famous Stolp's gears, puzzles that are as famous as the Rubik's cube once was.Its most important components are a button and a line of n similar gears. Each gear has n teeth containing all numbers from 0 to nβ-β1 in the counter-clockwise order. When you push a button, the first gear rotates clockwise, then the second gear rotates counter-clockwise, the the third gear rotates clockwise an so on.Besides, each gear has exactly one active tooth. When a gear turns, a new active tooth is the one following after the current active tooth according to the direction of the rotation. For example, if nβ=β5, and the active tooth is the one containing number 0, then clockwise rotation makes the tooth with number 1 active, or the counter-clockwise rotating makes the tooth number 4 active.Andrewid remembers that the real puzzle has the following property: you can push the button multiple times in such a way that in the end the numbers on the active teeth of the gears from first to last form sequence 0,β1,β2,β...,βnβ-β1. Write a program that determines whether the given puzzle is real or fake. | Input: ['31 0 0'] Output:['Yes'] | [
0
] |
Andrewid the Android is a galaxy-famous detective. In his free time he likes to think about strings containing zeros and ones.Once he thought about a string of length n consisting of zeroes and ones. Consider the following operation: we choose any two adjacent positions in the string, and if one them contains 0, and the other contains 1, then we are allowed to remove these two digits from the string, obtaining a string of length nβ-β2 as a result.Now Andreid thinks about what is the minimum length of the string that can remain after applying the described operation several times (possibly, zero)? Help him to calculate this number. | Input: ['41100'] Output:['0'] | [
2
] |
Andrewid the Android is a galaxy-famous detective. Now he is busy with a top secret case, the details of which are not subject to disclosure.However, he needs help conducting one of the investigative experiment. There are n pegs put on a plane, they are numbered from 1 to n, the coordinates of the i-th of them are (xi,β0). Then, we tie to the bottom of one of the pegs a weight on a tight rope of length l (thus, its coordinates will be equal to (xi,ββ-βl), where i is the number of the used peg). Then the weight is pushed to the right, so that it starts to rotate counterclockwise. At the same time, if the weight during rotation touches some of the other pegs, it then begins to rotate around that peg. Suppose that each peg itself is very thin and does not affect the rope length while weight is rotating around it. More formally, if at some moment the segment of the rope contains one or more pegs in addition to the peg around which the weight is rotating, the weight will then rotate around the farthermost one of them on a shorter segment of a rope. In particular, if the segment of the rope touches some peg by its endpoint, it is considered that the weight starts to rotate around that peg on a segment of the rope of length 0.At some moment the weight will begin to rotate around some peg, without affecting the rest of the pegs. Andrewid interested in determining the number of this peg.Andrewid prepared m queries containing initial conditions for pushing the weight, help him to determine for each of them, around what peg the weight will eventually rotate. | Input: ['3 20 3 52 31 8'] Output:['32'] | [
3,
4
] |
Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li,βri], besides, riβ<βliβ+β1 for 1ββ€βiββ€βnβ-β1.To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (iβ+β1)-th islads, if there are such coordinates of x and y, that liββ€βxββ€βri, liβ+β1ββ€βyββ€βriβ+β1 and yβ-βxβ=βa. The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands. | Input: ['4 41 47 89 1012 144 5 3 8'] Output:['Yes2 3 1 '] | [
2
] |
Ohana Matsumae is trying to clean a room, which is divided up into an n by n grid of squares. Each square is initially either clean or dirty. Ohana can sweep her broom over columns of the grid. Her broom is very strange: if she sweeps over a clean square, it will become dirty, and if she sweeps over a dirty square, it will become clean. She wants to sweep some columns of the room to maximize the number of rows that are completely clean. It is not allowed to sweep over the part of the column, Ohana can only sweep the whole column.Return the maximum number of rows that she can make completely clean. | Input: ['40101100011110101'] Output:['2'] | [
0,
2
] |
Kyoya Ootori is selling photobooks of the Ouran High School Host Club. He has 26 photos, labeled "a" to "z", and he has compiled them into a photo booklet with some photos in some order (possibly with some photos being duplicated). A photo booklet can be described as a string of lowercase letters, consisting of the photos in the booklet in order. He now wants to sell some "special edition" photobooks, each with one extra photo inserted anywhere in the book. He wants to make as many distinct photobooks as possible, so he can make more money. He asks Haruhi, how many distinct photobooks can he make by inserting one extra photo into the photobook he already has?Please help Haruhi solve this problem. | Input: ['a'] Output:['51'] | [
0,
3
] |
Kyoya Ootori wants to take the train to get to school. There are n train stations and m one-way train lines going between various stations. Kyoya is currently at train station 1, and the school is at station n. To take a train, he must pay for a ticket, and the train also takes a certain amount of time. However, the trains are not perfect and take random amounts of time to arrive at their destination. If Kyoya arrives at school strictly after t time units, he will have to pay a fine of x.Each train line is described by a ticket price, and a probability distribution on the time the train takes. More formally, train line i has ticket cost ci, and a probability distribution pi,βk which denotes the probability that this train will take k time units for all 1ββ€βkββ€βt. Amounts of time that each of the trains used by Kyouya takes are mutually independent random values (moreover, if Kyoya travels along the same train more than once, it is possible for the train to take different amounts of time and those amounts are also independent one from another). Kyoya wants to get to school by spending the least amount of money in expectation (for the ticket price plus possible fine for being late). Of course, Kyoya has an optimal plan for how to get to school, and every time he arrives at a train station, he may recalculate his plan based on how much time he has remaining. What is the expected cost that Kyoya will pay to get to school if he moves optimally? | Input: ['4 4 5 11 2 050000 0 50000 0 02 3 010000 0 0 0 900003 4 0100000 0 0 0 02 4 00 0 0 50000 50000'] Output:['0.7000000000'] | [
3
] |
Nudist Beach is planning a military operation to attack the Life Fibers. In this operation, they will attack and capture several cities which are currently under the control of the Life Fibers.There are n cities, labeled from 1 to n, and m bidirectional roads between them. Currently, there are Life Fibers in every city. In addition, there are k cities that are fortresses of the Life Fibers that cannot be captured under any circumstances. So, the Nudist Beach can capture an arbitrary non-empty subset of cities with no fortresses.After the operation, Nudist Beach will have to defend the captured cities from counterattack. If they capture a city and it is connected to many Life Fiber controlled cities, it will be easily defeated. So, Nudist Beach would like to capture a set of cities such that for each captured city the ratio of Nudist Beach controlled neighbors among all neighbors of that city is as high as possible. More formally, they would like to capture a non-empty set of cities S with no fortresses of Life Fibers. The strength of a city is defined as (number of neighbors of x in S) / (total number of neighbors of x). Here, two cities are called neighbors if they are connnected with a road. The goal is to maximize the strength of the weakest city in S.Given a description of the graph, and the cities with fortresses, find a non-empty subset that maximizes the strength of the weakest city. | Input: ['9 8 43 9 6 81 21 31 41 52 62 72 82 9'] Output:['31 4 5'] | [
2,
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] |
Let's define the permutation of length n as an array pβ=β[p1,βp2,β...,βpn] consisting of n distinct integers from range from 1 to n. We say that this permutation maps value 1 into the value p1, value 2 into the value p2 and so on.Kyota Ootori has just learned about cyclic representation of a permutation. A cycle is a sequence of numbers such that each element of this sequence is being mapped into the next element of this sequence (and the last element of the cycle is being mapped into the first element of the cycle). The cyclic representation is a representation of p as a collection of cycles forming p. For example, permutation pβ=β[4,β1,β6,β2,β5,β3] has a cyclic representation that looks like (142)(36)(5) because 1 is replaced by 4, 4 is replaced by 2, 2 is replaced by 1, 3 and 6 are swapped, and 5 remains in place. Permutation may have several cyclic representations, so Kyoya defines the standard cyclic representation of a permutation as follows. First, reorder the elements within each cycle so the largest element is first. Then, reorder all of the cycles so they are sorted by their first element. For our example above, the standard cyclic representation of [4,β1,β6,β2,β5,β3] is (421)(5)(63).Now, Kyoya notices that if we drop the parenthesis in the standard cyclic representation, we get another permutation! For instance, [4,β1,β6,β2,β5,β3] will become [4,β2,β1,β5,β6,β3].Kyoya notices that some permutations don't change after applying operation described above at all. He wrote all permutations of length n that do not change in a list in lexicographic order. Unfortunately, his friend Tamaki Suoh lost this list. Kyoya wishes to reproduce the list and he needs your help. Given the integers n and k, print the permutation that was k-th on Kyoya's list. | Input: ['4 3'] Output:['1 3 2 4'] | [
2,
3,
4
] |
Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color iβ+β1 for all i from 1 to kβ-β1. Now he wonders how many different ways this can happen. | Input: ['3221'] Output:['3'] | [
3
] |
Vanya is doing his maths homework. He has an expression of form , where x1,βx2,β...,βxn are digits from 1 to 9, and sign represents either a plus '+' or the multiplication sign '*'. Vanya needs to add one pair of brackets in this expression so that to maximize the value of the resulting expression. | Input: ['3+5*7+8*4'] Output:['303'] | [
0,
2
] |
Vanya got bored and he painted n distinct points on the plane. After that he connected all the points pairwise and saw that as a result many triangles were formed with vertices in the painted points. He asks you to count the number of the formed triangles with the non-zero area. | Input: ['40 01 12 02 2'] Output:['3'] | [
0,
3
] |
Vanya has a scales for weighing loads and weights of masses w0,βw1,βw2,β...,βw100 grams where w is some integer not less than 2 (exactly one weight of each nominal value). Vanya wonders whether he can weight an item with mass m using the given weights, if the weights can be put on both pans of the scales. Formally speaking, your task is to determine whether it is possible to place an item of mass m and some weights on the left pan of the scales, and some weights on the right pan of the scales so that the pans of the scales were in balance. | Input: ['3 7'] Output:['YES'] | [
0,
2,
3
] |
Vanya got an important task β he should enumerate books in the library and label each book with its number. Each of the n books should be assigned with a number from 1 to n. Naturally, distinct books should be assigned distinct numbers.Vanya wants to know how many digits he will have to write down as he labels the books. | Input: ['13'] Output:['17'] | [
3
] |
Vanya has a table consisting of 100 rows, each row contains 100 cells. The rows are numbered by integers from 1 to 100 from bottom to top, the columns are numbered from 1 to 100 from left to right. In this table, Vanya chose n rectangles with sides that go along borders of squares (some rectangles probably occur multiple times). After that for each cell of the table he counted the number of rectangles it belongs to and wrote this number into it. Now he wants to find the sum of values in all cells of the table and as the table is too large, he asks you to help him find the result. | Input: ['21 1 2 32 2 3 3'] Output:['10'] | [
3
] |
Professor GukiZ was playing with arrays again and accidentally discovered new function, which he called GukiZiana. For given array a, indexed with integers from 1 to n, and number y, GukiZiana(a,βy) represents maximum value of jβ-βi, such that ajβ=βaiβ=βy. If there is no y as an element in a, then GukiZiana(a,βy) is equal to β-β1. GukiZ also prepared a problem for you. This time, you have two types of queries: First type has form 1 l r x and asks you to increase values of all ai such that lββ€βiββ€βr by the non-negative integer x. Second type has form 2 y and asks you to find value of GukiZiana(a,βy). For each query of type 2, print the answer and make GukiZ happy! | Input: ['4 31 2 3 41 1 2 11 1 1 12 3'] Output:['2'] | [
4
] |
We all know that GukiZ often plays with arrays. Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition: ? Here operation means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equivalent to &), operation means bitwise OR (in Pascal it is equivalent to , in C/C++/Java/Python it is equivalent to |). Because the answer can be quite large, calculate it modulo m. This time GukiZ hasn't come up with solution, and needs you to help him! | Input: ['2 1 2 10'] Output:['3'] | [
3
] |
Professor GukiZ is concerned about making his way to school, because massive piles of boxes are blocking his way. In total there are n piles of boxes, arranged in a line, from left to right, i-th pile (1ββ€βiββ€βn) containing ai boxes. Luckily, m students are willing to help GukiZ by removing all the boxes from his way. Students are working simultaneously. At time 0, all students are located left of the first pile. It takes one second for every student to move from this position to the first pile, and after that, every student must start performing sequence of two possible operations, each taking one second to complete. Possible operations are: If iββ βn, move from pile i to pile iβ+β1; If pile located at the position of student is not empty, remove one box from it.GukiZ's students aren't smart at all, so they need you to tell them how to remove boxes before professor comes (he is very impatient man, and doesn't want to wait). They ask you to calculate minumum time t in seconds for which they can remove all the boxes from GukiZ's way. Note that students can be positioned in any manner after t seconds, but all the boxes must be removed. | Input: ['2 11 1'] Output:['4'] | [
2,
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] |
Professor GukiZ doesn't accept string as they are. He likes to swap some letters in string to obtain a new one.GukiZ has strings a, b, and c. He wants to obtain string k by swapping some letters in a, so that k should contain as many non-overlapping substrings equal either to b or c as possible. Substring of string x is a string formed by consecutive segment of characters from x. Two substrings of string x overlap if there is position i in string x occupied by both of them.GukiZ was disappointed because none of his students managed to solve the problem. Can you help them and find one of possible strings k? | Input: ['aaaab'] Output:['aaa'] | [
0
] |
Professor GukiZ likes programming contests. He especially likes to rate his students on the contests he prepares. Now, he has decided to prepare a new contest. In total, n students will attend, and before the start, every one of them has some positive integer rating. Students are indexed from 1 to n. Let's denote the rating of i-th student as ai. After the contest ends, every student will end up with some positive integer position. GukiZ expects that his students will take places according to their ratings. He thinks that each student will take place equal to . In particular, if student A has rating strictly lower then student B, A will get the strictly better position than B, and if two students have equal ratings, they will share the same position. GukiZ would like you to reconstruct the results by following his expectations. Help him and determine the position after the end of the contest for each of his students if everything goes as expected. | Input: ['31 3 3'] Output:['3 1 1'] | [
0
] |
Implication is a function of two logical arguments, its value is false if and only if the value of the first argument is true and the value of the second argument is false. Implication is written by using character '', and the arguments and the result of the implication are written as '0' (false) and '1' (true). According to the definition of the implication: When a logical expression contains multiple implications, then when there are no brackets, it will be calculated from left to fight. For example,. When there are brackets, we first calculate the expression in brackets. For example,.For the given logical expression determine if it is possible to place there brackets so that the value of a logical expression is false. If it is possible, your task is to find such an arrangement of brackets. | Input: ['40 1 1 0'] Output:['YES(((0)->1)->(1->0))'] | [
2,
3
] |
You are given a non-negative integer n, its decimal representation consists of at most 100 digits and doesn't contain leading zeroes.Your task is to determine if it is possible in this case to remove some of the digits (possibly not remove any digit at all) so that the result contains at least one digit, forms a non-negative integer, doesn't have leading zeroes and is divisible by 8. After the removing, it is forbidden to rearrange the digits.If a solution exists, you should print it. | Input: ['3454'] Output:['YES344'] | [
0,
3
] |
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.Find the number of ways to choose a problemset for the contest. | Input: ['3 5 6 11 2 3'] Output:['2'] | [
0
] |
You are given string s. Your task is to determine if the given string s contains two non-overlapping substrings "AB" and "BA" (the substrings can go in any order). | Input: ['ABA'] Output:['NO'] | [
0,
2
] |
The determinant of a matrix 2βΓβ2 is defined as follows:A matrix is called degenerate if its determinant is equal to zero. The norm ||A|| of a matrix A is defined as a maximum of absolute values of its elements.You are given a matrix . Consider any degenerate matrix B such that norm ||Aβ-βB|| is minimum possible. Determine ||Aβ-βB||. | Input: ['1 23 4'] Output:['0.2000000000'] | [
3,
4
] |
Do you like summer? Residents of Berland do. They especially love eating ice cream in the hot summer. So this summer day a large queue of n Berland residents lined up in front of the ice cream stall. We know that each of them has a certain amount of berland dollars with them. The residents of Berland are nice people, so each person agrees to swap places with the person right behind him for just 1 dollar. More formally, if person a stands just behind person b, then person a can pay person b 1 dollar, then a and b get swapped. Of course, if person a has zero dollars, he can not swap places with person b.Residents of Berland are strange people. In particular, they get upset when there is someone with a strictly smaller sum of money in the line in front of them.Can you help the residents of Berland form such order in the line so that they were all happy? A happy resident is the one who stands first in the line or the one in front of who another resident stands with not less number of dollars. Note that the people of Berland are people of honor and they agree to swap places only in the manner described above. | Input: ['211 8'] Output:['9 10 '] | [
2
] |
Berlanders like to eat cones after a hard day. Misha Square and Sasha Circle are local authorities of Berland. Each of them controls its points of cone trade. Misha has n points, Sasha β m. Since their subordinates constantly had conflicts with each other, they decided to build a fence in the form of a circle, so that the points of trade of one businessman are strictly inside a circle, and points of the other one are strictly outside. It doesn't matter which of the two gentlemen will have his trade points inside the circle.Determine whether they can build a fence or not. | Input: ['2 2-1 01 00 -10 1'] Output:['NO'] | [
3
] |
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 nβΓβm. The table elements are integers that specify the brightness of each pixel in the image.A feature also is a rectangular table of size nβΓβm. 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 Wβ-βB, 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. | Input: ['6 8BBBBBBBBBBBBBBBBBBBBBBBBWWWWWWWWWWWWWWWWWWWWWWWW'] Output:['2'] | [
2
] |
The Looksery company, consisting of n staff members, is planning another big party. Every employee has his phone number and the phone numbers of his friends in the phone book. Everyone who comes to the party, sends messages to his contacts about how cool it is. At the same time everyone is trying to spend as much time on the fun as possible, so they send messages to everyone without special thinking, moreover, each person even sends a message to himself or herself.Igor and Max, Looksery developers, started a dispute on how many messages each person gets. Igor indicates n numbers, the i-th of which indicates how many messages, in his view, the i-th employee is going to take. If Igor guesses correctly at least one of these numbers, he wins, otherwise Max wins.You support Max in this debate, so you need, given the contact lists of the employees, to determine whether there is a situation where Igor loses. Specifically, you need to determine which employees should come to the party, and which should not, so after all the visitors send messages to their contacts, each employee received a number of messages that is different from what Igor stated. | Input: ['31010100010 1 2'] Output:['11 '] | [
2
] |
Mike and some bears are playing a game just for fun. Mike is the judge. All bears except Mike are standing in an nβΓβm grid, there's exactly one bear in each cell. We denote the bear standing in column number j of row number i by (i,βj). Mike's hands are on his ears (since he's the judge) and each bear standing in the grid has hands either on his mouth or his eyes. They play for q rounds. In each round, Mike chooses a bear (i,βj) and tells him to change his state i. e. if his hands are on his mouth, then he'll put his hands on his eyes or he'll put his hands on his mouth otherwise. After that, Mike wants to know the score of the bears.Score of the bears is the maximum over all rows of number of consecutive bears with hands on their eyes in that row.Since bears are lazy, Mike asked you for help. For each round, tell him the score of these bears after changing the state of a bear selected in that round. | Input: ['5 4 50 1 1 01 0 0 10 1 1 01 0 0 10 0 0 01 11 41 14 24 3'] Output:['34334'] | [
0,
2
] |
While Mike was walking in the subway, all the stuff in his back-bag dropped on the ground. There were several fax messages among them. He concatenated these strings in some order and now he has string s. He is not sure if this is his own back-bag or someone else's. He remembered that there were exactly k messages in his own bag, each was a palindrome string and all those strings had the same length.He asked you to help him and tell him if he has worn his own back-bag. Check if the given string s is a concatenation of k palindromes of the same length. | Input: ['saba2'] Output:['NO'] | [
0
] |
Mike is a bartender at Rico's bar. At Rico's, they put beer glasses in a special shelf. There are n kinds of beer at Rico's numbered from 1 to n. i-th kind of beer has ai milliliters of foam on it. Maxim is Mike's boss. Today he told Mike to perform q queries. Initially the shelf is empty. In each request, Maxim gives him a number x. If beer number x is already in the shelf, then Mike should remove it from the shelf, otherwise he should put it in the shelf.After each query, Mike should tell him the score of the shelf. Bears are geeks. So they think that the score of a shelf is the number of pairs (i,βj) of glasses in the shelf such that iβ<βj and where is the greatest common divisor of numbers a and b.Mike is tired. So he asked you to help him in performing these requests. | Input: ['5 61 2 3 4 6123451'] Output:['013562'] | [
3
] |
Mike is the president of country What-The-Fatherland. There are n bears living in this country besides Mike. All of them are standing in a line and they are numbered from 1 to n from left to right. i-th bear is exactly ai feet high. A group of bears is a non-empty contiguous segment of the line. The size of a group is the number of bears in that group. The strength of a group is the minimum height of the bear in that group.Mike is a curious to know for each x such that 1ββ€βxββ€βn the maximum strength among all groups of size x. | Input: ['101 2 3 4 5 4 3 2 1 6'] Output:['6 4 4 3 3 2 2 1 1 1 '] | [
4
] |
Mike has a frog and a flower. His frog is named Xaniar and his flower is named Abol. Initially(at time 0), height of Xaniar is h1 and height of Abol is h2. Each second, Mike waters Abol and Xaniar. So, if height of Xaniar is h1 and height of Abol is h2, after one second height of Xaniar will become and height of Abol will become where x1,βy1,βx2 and y2 are some integer numbers and denotes the remainder of a modulo b.Mike is a competitive programmer fan. He wants to know the minimum time it takes until height of Xania is a1 and height of Abol is a2.Mike has asked you for your help. Calculate the minimum time or say it will never happen. | Input: ['54 21 10 12 3'] Output:['3'] | [
0,
2,
3
] |
In the country there are n cities and m bidirectional roads between them. Each city has an army. Army of the i-th city consists of ai soldiers. Now soldiers roam. After roaming each soldier has to either stay in his city or to go to the one of neighboring cities by at moving along at most one road.Check if is it possible that after roaming there will be exactly bi soldiers in the i-th city. | Input: ['4 41 2 6 33 5 3 11 22 33 44 2'] Output:['YES1 0 0 0 2 0 0 0 0 5 1 0 0 0 2 1 '] | [
3
] |
Two soldiers are playing a game. At the beginning first of them chooses a positive integer n and gives it to the second soldier. Then the second one tries to make maximum possible number of rounds. Each round consists of choosing a positive integer xβ>β1, such that n is divisible by x and replacing n with nβ/βx. When n becomes equal to 1 and there is no more possible valid moves the game is over and the score of the second soldier is equal to the number of rounds he performed.To make the game more interesting, first soldier chooses n of form a!β/βb! for some positive integer a and b (aββ₯βb). Here by k! we denote the factorial of k that is defined as a product of all positive integers not large than k.What is the maximum possible score of the second soldier? | Input: ['23 16 3'] Output:['25'] | [
3
] |
Two bored soldiers are playing card war. Their card deck consists of exactly n cards, numbered from 1 to n, all values are different. They divide cards between them in some manner, it's possible that they have different number of cards. Then they play a "war"-like card game. The rules are following. On each turn a fight happens. Each of them picks card from the top of his stack and puts on the table. The one whose card value is bigger wins this fight and takes both cards from the table to the bottom of his stack. More precisely, he first takes his opponent's card and puts to the bottom of his stack, and then he puts his card to the bottom of his stack. If after some turn one of the player's stack becomes empty, he loses and the other one wins. You have to calculate how many fights will happen and who will win the game, or state that game won't end. | Input: ['42 1 32 4 2'] Output:['6 2'] | [
0
] |
Colonel has n badges. He wants to give one badge to every of his n soldiers. Each badge has a coolness factor, which shows how much it's owner reached. Coolness factor can be increased by one for the cost of one coin. For every pair of soldiers one of them should get a badge with strictly higher factor than the second one. Exact values of their factors aren't important, they just need to have distinct factors. Colonel knows, which soldier is supposed to get which badge initially, but there is a problem. Some of badges may have the same factor of coolness. Help him and calculate how much money has to be paid for making all badges have different factors of coolness. | Input: ['41 3 1 4'] Output:['1'] | [
0,
2
] |
A soldier wants to buy w bananas in the shop. He has to pay k dollars for the first banana, 2k dollars for the second one and so on (in other words, he has to pay iΒ·k dollars for the i-th banana). He has n dollars. How many dollars does he have to borrow from his friend soldier to buy w bananas? | Input: ['3 17 4'] Output:['13'] | [
0,
3
] |
Little girl Susie accidentally found her elder brother's notebook. She has many things to do, more important than solving problems, but she found this problem too interesting, so she wanted to know its solution and decided to ask you about it. So, the problem statement is as follows.Let's assume that we are given a connected weighted undirected graph Gβ=β(V,βE) (here V is the set of vertices, E is the set of edges). The shortest-path tree from vertex u is such graph G1β=β(V,βE1) that is a tree with the set of edges E1 that is the subset of the set of edges of the initial graph E, and the lengths of the shortest paths from u to any vertex to G and to G1 are the same. You are given a connected weighted undirected graph G and vertex u. Your task is to find the shortest-path tree of the given graph from vertex u, the total weight of whose edges is minimum possible. | Input: ['3 31 2 12 3 11 3 23'] Output:['21 2 '] | [
2
] |
Little girl Susie went shopping with her mom and she wondered how to improve service quality. There are n people in the queue. For each person we know time ti needed to serve him. A person will be disappointed if the time he waits is more than the time needed to serve him. The time a person waits is the total time when all the people who stand in the queue in front of him are served. Susie thought that if we swap some people in the queue, then we can decrease the number of people who are disappointed. Help Susie find out what is the maximum number of not disappointed people can be achieved by swapping people in the queue. | Input: ['515 2 1 5 3'] Output:['4'] | [
2
] |
Little Susie listens to fairy tales before bed every day. Today's fairy tale was about wood cutters and the little girl immediately started imagining the choppers cutting wood. She imagined the situation that is described below.There are n trees located along the road at points with coordinates x1,βx2,β...,βxn. Each tree has its height hi. Woodcutters can cut down a tree and fell it to the left or to the right. After that it occupies one of the segments [xiβ-βhi,βxi] or [xi;xiβ+βhi]. The tree that is not cut down occupies a single point with coordinate xi. Woodcutters can fell a tree if the segment to be occupied by the fallen tree doesn't contain any occupied point. The woodcutters want to process as many trees as possible, so Susie wonders, what is the maximum number of trees to fell. | Input: ['51 22 15 1010 919 1'] Output:['3'] | [
2
] |
Little Susie loves strings. Today she calculates distances between them. As Susie is a small girl after all, her strings contain only digits zero and one. She uses the definition of Hamming distance:We will define the distance between two strings s and t of the same length consisting of digits zero and one as the number of positions i, such that si isn't equal to ti. As besides everything else Susie loves symmetry, she wants to find for two strings s and t of length n such string p of length n, that the distance from p to s was equal to the distance from p to t.It's time for Susie to go to bed, help her find such string p or state that it is impossible. | Input: ['00011011'] Output:['0011'] | [
2
] |
Polycarp is making a quest for his friends. He has already made n tasks, for each task the boy evaluated how interesting it is as an integer qi, and the time ti in minutes needed to complete the task. An interesting feature of his quest is: each participant should get the task that is best suited for him, depending on his preferences. The task is chosen based on an interactive quiz that consists of some questions. The player should answer these questions with "yes" or "no". Depending on the answer to the question, the participant either moves to another question or goes to one of the tasks that are in the quest. In other words, the quest is a binary tree, its nodes contain questions and its leaves contain tasks. We know that answering any of the questions that are asked before getting a task takes exactly one minute from the quest player. Polycarp knows that his friends are busy people and they can't participate in the quest for more than T minutes. Polycarp wants to choose some of the n tasks he made, invent the corresponding set of questions for them and use them to form an interactive quiz as a binary tree so that no matter how the player answers quiz questions, he spends at most T minutes on completing the whole quest (that is, answering all the questions and completing the task). Specifically, the quest can contain zero questions and go straight to the task. Each task can only be used once (i.e., the people who give different answers to questions should get different tasks).Polycarp wants the total "interest" value of the tasks involved in the quest to be as large as possible. Help him determine the maximum possible total interest value of the task considering that the quest should be completed in T minutes at any variant of answering questions. | Input: ['5 51 11 12 23 34 4'] Output:['11'] | [
2
] |
It's tough to be a superhero. And it's twice as tough to resist the supervillain who is cool at math. Suppose that you're an ordinary Batman in an ordinary city of Gotham. Your enemy Joker mined the building of the city administration and you only have several minutes to neutralize the charge. To do that you should enter the cancel code on the bomb control panel.However, that mad man decided to give you a hint. This morning the mayor found a playing card under his pillow. There was a line written on the card:The bomb has a note saying "J(x)β=βA", where A is some positive integer. You suspect that the cancel code is some integer x that meets the equation J(x)β=βA. Now in order to decide whether you should neutralize the bomb or run for your life, you've got to count how many distinct positive integers x meet this equation. | Input: ['3'] Output:['1'] | [
3
] |
Some time ago Leonid have known about idempotent functions. Idempotent function defined on a set {1,β2,β...,βn} is such function , that for any the formula g(g(x))β=βg(x) holds.Let's denote as f(k)(x) the function f applied k times to the value x. More formally, f(1)(x)β=βf(x), f(k)(x)β=βf(f(kβ-β1)(x)) for each kβ>β1.You are given some function . Your task is to find minimum positive integer k such that function f(k)(x) is idempotent. | Input: ['41 2 2 4'] Output:['1'] | [
3
] |
There is an infinite sequence consisting of all positive integers in the increasing order: pβ=β{1,β2,β3,β...}. We performed n swap operations with this sequence. A swap(a,βb) is an operation of swapping the elements of the sequence on positions a and b. Your task is to find the number of inversions in the resulting sequence, i.e. the number of such index pairs (i,βj), that iβ<βj and piβ>βpj. | Input: ['24 21 4'] Output:['4'] | [
4
] |
Little Vova studies programming in an elite school. Vova and his classmates are supposed to write n progress tests, for each test they will get a mark from 1 to p. Vova is very smart and he can write every test for any mark, but he doesn't want to stand out from the crowd too much. If the sum of his marks for all tests exceeds value x, then his classmates notice how smart he is and start distracting him asking to let them copy his homework. And if the median of his marks will be lower than y points (the definition of a median is given in the notes), then his mom will decide that he gets too many bad marks and forbid him to play computer games.Vova has already wrote k tests and got marks a1,β...,βak. He doesn't want to get into the first or the second situation described above and now he needs to determine which marks he needs to get for the remaining tests. Help him do that. | Input: ['5 3 5 18 43 5 4'] Output:['4 1'] | [
2
] |
T students applied into the ZPP class of Summer Irrelevant School. The organizing committee of the school may enroll any number of them, but at least t students must be enrolled. The enrolled students should be divided into two groups in any manner (it is possible that one of the groups will be empty!)During a shift the students from the ZPP grade are tutored by n teachers. Due to the nature of the educational process, each of the teachers should be assigned to exactly one of two groups (it is possible that no teacher will be assigned to some of the groups!). The i-th teacher is willing to work in a group as long as the group will have at least li and at most ri students (otherwise it would be either too boring or too hard). Besides, some pairs of the teachers don't like each other other and therefore can not work in the same group; in total there are m pairs of conflicting teachers.You, as the head teacher of Summer Irrelevant School, have got a difficult task: to determine how many students to enroll in each of the groups and in which group each teacher will teach. | Input: ['10 203 03 64 916 25'] Output:['POSSIBLE4 16112'] | [
2
] |
Help! A robot escaped our lab and we need help finding it. The lab is at the point (0,β0) of the coordinate plane, at time 0 the robot was there. The robot's movements are defined by a program β a string of length l, consisting of characters U, L, D, R. Each second the robot executes the next command in his program: if the current coordinates of the robot are (x,βy), then commands U, L, D, R move it to cells (x,βyβ+β1), (xβ-β1,βy), (x,βyβ-β1), (xβ+β1,βy) respectively. The execution of the program started at time 0. The program is looped, i.e. each l seconds of executing the program start again from the first character. Unfortunately, we don't know what program was loaded into the robot when he left the lab.Our radars managed to find out the position of the robot at n moments of time: we know that at the moment of time ti the robot is at the point (xi,βyi). Given this data, either help to determine what program could be loaded into the robot, or determine that no possible program meets the data and the robot must have broken down. | Input: ['3 31 1 02 1 -13 0 -1'] Output:['RDL'] | [
3
] |
Andrew skipped lessons on the subject 'Algorithms and Data Structures' for the entire term. When he came to the final test, the teacher decided to give him a difficult task as a punishment.The teacher gave Andrew an array of n numbers a1, ..., an. After that he asked Andrew for each k from 1 to nβ-β1 to build a k-ary heap on the array and count the number of elements for which the property of the minimum-rooted heap is violated, i.e. the value of an element is less than the value of its parent.Andrew looked up on the Wikipedia that a k-ary heap is a rooted tree with vertices in elements of the array. If the elements of the array are indexed from 1 to n, then the children of element v are elements with indices k(vβ-β1)β+β2, ..., kvβ+β1 (if some of these elements lie outside the borders of the array, the corresponding children are absent). In any k-ary heap every element except for the first one has exactly one parent; for the element 1 the parent is absent (this element is the root of the heap). Denote p(v) as the number of the parent of the element with the number v. Let's say that for a non-root element v the property of the heap is violated if avβ<βap(v).Help Andrew cope with the task! | Input: ['51 5 4 3 2'] Output:['3 2 1 0'] | [
0,
3
] |
Demiurges Shambambukli and Mazukta love to watch the games of ordinary people. Today, they noticed two men who play the following game.There is a rooted tree on n nodes, m of which are leaves (a leaf is a nodes that does not have any children), edges of the tree are directed from parent to children. In the leaves of the tree integers from 1 to m are placed in such a way that each number appears exactly in one leaf.Initially, the root of the tree contains a piece. Two players move this piece in turns, during a move a player moves the piece from its current nodes to one of its children; if the player can not make a move, the game ends immediately. The result of the game is the number placed in the leaf where a piece has completed its movement. The player who makes the first move tries to maximize the result of the game and the second player, on the contrary, tries to minimize the result. We can assume that both players move optimally well.Demiurges are omnipotent, so before the game they can arbitrarily rearrange the numbers placed in the leaves. Shambambukli wants to rearrange numbers so that the result of the game when both players play optimally well is as large as possible, and Mazukta wants the result to be as small as possible. What will be the outcome of the game, if the numbers are rearranged by Shambambukli, and what will it be if the numbers are rearranged by Mazukta? Of course, the Demiurges choose the best possible option of arranging numbers. | Input: ['51 21 32 42 5'] Output:['3 2'] | [
3
] |
Igor has been into chess for a long time and now he is sick of the game by the ordinary rules. He is going to think of new rules of the game and become world famous.Igor's chessboard is a square of size nβΓβn cells. Igor decided that simple rules guarantee success, that's why his game will have only one type of pieces. Besides, all pieces in his game are of the same color. The possible moves of a piece are described by a set of shift vectors. The next passage contains a formal description of available moves.Let the rows of the board be numbered from top to bottom and the columns be numbered from left to right from 1 to n. Let's assign to each square a pair of integers (x,βy) β the number of the corresponding column and row. Each of the possible moves of the piece is defined by a pair of integers (dx,βdy); using this move, the piece moves from the field (x,βy) to the field (xβ+βdx,βyβ+βdy). You can perform the move if the cell (xβ+βdx,βyβ+βdy) is within the boundaries of the board and doesn't contain another piece. Pieces that stand on the cells other than (x,βy) and (xβ+βdx,βyβ+βdy) are not important when considering the possibility of making the given move (for example, like when a knight moves in usual chess).Igor offers you to find out what moves his chess piece can make. He placed several pieces on the board and for each unoccupied square he told you whether it is attacked by any present piece (i.e. whether some of the pieces on the field can move to that cell). Restore a possible set of shift vectors of the piece, or else determine that Igor has made a mistake and such situation is impossible for any set of shift vectors. | Input: ['5oxxxxx...xx...xx...xxxxxo'] Output:['YES....x........x........x........x....xxxxoxxxx....x........x........x........x....'] | [
0
] |
A tourist hiked along the mountain range. The hike lasted for n days, during each day the tourist noted height above the sea level. On the i-th day height was equal to some integer hi. The tourist pick smooth enough route for his hike, meaning that the between any two consecutive days height changes by at most 1, i.e. for all i's from 1 to nβ-β1 the inequality |hiβ-βhiβ+β1|ββ€β1 holds.At the end of the route the tourist rafted down a mountain river and some notes in the journal were washed away. Moreover, the numbers in the notes could have been distorted. Now the tourist wonders what could be the maximum height during his hike. Help him restore the maximum possible value of the maximum height throughout the hike or determine that the notes were so much distorted that they do not represent any possible height values that meet limits |hiβ-βhiβ+β1|ββ€β1. | Input: ['8 22 07 0'] Output:['2'] | [
0,
2,
3,
4
] |
A number is called quasibinary if its decimal representation contains only digits 0 or 1. For example, numbers 0, 1, 101, 110011 β are quasibinary and numbers 2, 12, 900 are not.You are given a positive integer n. Represent it as a sum of minimum number of quasibinary numbers. | Input: ['9'] Output:['91 1 1 1 1 1 1 1 1 '] | [
2
] |
A large banner with word CODEFORCES was ordered for the 1000-th onsite round of CodeforcesΟ that takes place on the Miami beach. Unfortunately, the company that made the banner mixed up two orders and delivered somebody else's banner that contains someone else's word. The word on the banner consists only of upper-case English letters.There is very little time to correct the mistake. All that we can manage to do is to cut out some substring from the banner, i.e. several consecutive letters. After that all the resulting parts of the banner will be glued into a single piece (if the beginning or the end of the original banner was cut out, only one part remains); it is not allowed change the relative order of parts of the banner (i.e. after a substring is cut, several first and last letters are left, it is allowed only to glue the last letters to the right of the first letters). Thus, for example, for example, you can cut a substring out from string 'TEMPLATE' and get string 'TEMPLE' (if you cut out string AT), 'PLATE' (if you cut out TEM), 'T' (if you cut out EMPLATE), etc.Help the organizers of the round determine whether it is possible to cut out of the banner some substring in such a way that the remaining parts formed word CODEFORCES. | Input: ['CODEWAITFORITFORCES'] Output:['YES'] | [
0
] |
Tavas is a cheerleader in the new sports competition named "Pashmaks". This competition consists of two part: swimming and then running. People will immediately start running R meters after they finished swimming exactly S meters. A winner is a such person that nobody else finishes running before him/her (there may be more than one winner).Before the match starts, Tavas knows that there are n competitors registered for the match. Also, he knows that i-th person's swimming speed is si meters per second and his/her running speed is ri meters per second. Unfortunately, he doesn't know the values of R and S, but he knows that they are real numbers greater than 0.As a cheerleader, Tavas wants to know who to cheer up. So, he wants to know all people that might win. We consider a competitor might win if and only if there are some values of R and S such that with these values, (s)he will be a winner.Tavas isn't really familiar with programming, so he asked you to help him. | Input: ['31 32 23 1'] Output:['1 2 3 '] | [
3
] |
Tavas is a strange creature. Usually "zzz" comes out of people's mouth while sleeping, but string s of length n comes out from Tavas' mouth instead. Today Tavas fell asleep in Malekas' place. While he was sleeping, Malekas did a little process on s. Malekas has a favorite string p. He determined all positions x1β<βx2β<β...β<βxk where p matches s. More formally, for each xi (1ββ€βiββ€βk) he condition sxisxiβ+β1... sxiβ+β|p|β-β1β=βp is fullfilled.Then Malekas wrote down one of subsequences of x1,βx2,β... xk (possibly, he didn't write anything) on a piece of paper. Here a sequence b is a subsequence of sequence a if and only if we can turn a into b by removing some of its elements (maybe no one of them or all).After Tavas woke up, Malekas told him everything. He couldn't remember string s, but he knew that both p and s only contains lowercase English letters and also he had the subsequence he had written on that piece of paper.Tavas wonders, what is the number of possible values of s? He asked SaDDas, but he wasn't smart enough to solve this. So, Tavas asked you to calculate this number for him.Answer can be very large, so Tavas wants you to print the answer modulo 109β+β7. | Input: ['6 2ioi1 3'] Output:['26'] | [
2
] |
Karafs is some kind of vegetable in shape of an 1βΓβh rectangle. Tavaspolis people love Karafs and they use Karafs in almost any kind of food. Tavas, himself, is crazy about Karafs. Each Karafs has a positive integer height. Tavas has an infinite 1-based sequence of Karafses. The height of the i-th Karafs is siβ=βAβ+β(iβ-β1)βΓβB.For a given m, let's define an m-bite operation as decreasing the height of at most m distinct not eaten Karafses by 1. Karafs is considered as eaten when its height becomes zero.Now SaDDas asks you n queries. In each query he gives you numbers l, t and m and you should find the largest number r such that lββ€βr and sequence sl,βslβ+β1,β...,βsr can be eaten by performing m-bite no more than t times or print -1 if there is no such number r. | Input: ['2 1 41 5 33 3 107 10 26 4 8'] Output:['4-18-1'] | [
2,
3,
4
] |
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you." The problem is: You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.If we sort all lucky numbers in increasing order, what's the 1-based index of n? Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back. | Input: ['4'] Output:['1'] | [
0
] |
Today Tavas got his test result as an integer score and he wants to share it with his girlfriend, Nafas.His phone operating system is Tavdroid, and its keyboard doesn't have any digits! He wants to share his score with Nafas via text, so he has no choice but to send this number using words. He ate coffee mix without water again, so right now he's really messed up and can't think.Your task is to help him by telling him what to type. | Input: ['6'] Output:['six'] | [
0
] |
In Berland a bus travels along the main street of the capital. The street begins from the main square and looks like a very long segment. There are n bus stops located along the street, the i-th of them is located at the distance ai from the central square, all distances are distinct, the stops are numbered in the order of increasing distance from the square, that is, aiβ<βaiβ+β1 for all i from 1 to nβ-β1. The bus starts its journey from the first stop, it passes stops 2, 3 and so on. It reaches the stop number n, turns around and goes in the opposite direction to stop 1, passing all the intermediate stops in the reverse order. After that, it again starts to move towards stop n. During the day, the bus runs non-stop on this route.The bus is equipped with the Berland local positioning system. When the bus passes a stop, the system notes down its number.One of the key features of the system is that it can respond to the queries about the distance covered by the bus for the parts of its path between some pair of stops. A special module of the system takes the input with the information about a set of stops on a segment of the path, a stop number occurs in the set as many times as the bus drove past it. This module returns the length of the traveled segment of the path (or -1 if it is impossible to determine the length uniquely). The operation of the module is complicated by the fact that stop numbers occur in the request not in the order they were visited but in the non-decreasing order.For example, if the number of stops is 6, and the part of the bus path starts at the bus stop number 5, ends at the stop number 3 and passes the stops as follows: , then the request about this segment of the path will have form: 3,β4,β5,β5,β6. If the bus on the segment of the path from stop 5 to stop 3 has time to drive past the 1-th stop (i.e., if we consider a segment that ends with the second visit to stop 3 on the way from 5), then the request will have form: 1,β2,β2,β3,β3,β4,β5,β5,β6.You will have to repeat the Berland programmers achievement and implement this function. | Input: ['62 3 5 7 11 1353 4 5 5 6'] Output:['10'] | [
2
] |
On February, 30th n students came in the Center for Training Olympiad Programmers (CTOP) of the Berland State University. They came one by one, one after another. Each of them went in, and before sitting down at his desk, greeted with those who were present in the room by shaking hands. Each of the students who came in stayed in CTOP until the end of the day and never left.At any time any three students could join together and start participating in a team contest, which lasted until the end of the day. The team did not distract from the contest for a minute, so when another student came in and greeted those who were present, he did not shake hands with the members of the contest writing team. Each team consisted of exactly three students, and each student could not become a member of more than one team. Different teams could start writing contest at different times.Given how many present people shook the hands of each student, get a possible order in which the students could have come to CTOP. If such an order does not exist, then print that this is impossible.Please note that some students could work independently until the end of the day, without participating in a team contest. | Input: ['52 1 3 0 1'] Output:['Possible4 5 1 3 2 '] | [
2,
4
] |
Polycarp has n dice d1,βd2,β...,βdn. The i-th dice shows numbers from 1 to di. Polycarp rolled all the dice and the sum of numbers they showed is A. Agrippina didn't see which dice showed what number, she knows only the sum A and the values d1,βd2,β...,βdn. However, she finds it enough to make a series of statements of the following type: dice i couldn't show number r. For example, if Polycarp had two six-faced dice and the total sum is Aβ=β11, then Agrippina can state that each of the two dice couldn't show a value less than five (otherwise, the remaining dice must have a value of at least seven, which is impossible).For each dice find the number of values for which it can be guaranteed that the dice couldn't show these values if the sum of the shown values is A. | Input: ['2 84 4'] Output:['3 3 '] | [
3
] |
The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals v1 meters per second, and in the end it is v2 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. | Input: ['5 64 2'] Output:['26'] | [
2,
3
] |
An exam for n students will take place in a long and narrow room, so the students will sit in a line in some order. The teacher suspects that students with adjacent numbers (i and iβ+β1) always studied side by side and became friends and if they take an exam sitting next to each other, they will help each other for sure.Your task is to choose the maximum number of students and make such an arrangement of students in the room that no two students with adjacent numbers sit side by side. | Input: ['6'] Output:['61 5 3 6 2 4'] | [
3
] |
Analyzing the mistakes people make while typing search queries is a complex and an interesting work. As there is no guaranteed way to determine what the user originally meant by typing some query, we have to use different sorts of heuristics.Polycarp needed to write a code that could, given two words, check whether they could have been obtained from the same word as a result of typos. Polycarpus suggested that the most common typo is skipping exactly one letter as you type a word.Implement a program that can, given two distinct words S and T of the same length n determine how many words W of length nβ+β1 are there with such property that you can transform W into both S, and T by deleting exactly one character. Words S and T consist of lowercase English letters. Word W also should consist of lowercase English letters. | Input: ['7readingtrading'] Output:['1'] | [
2
] |
Polycarp and Vasiliy love simple logical games. Today they play a game with infinite chessboard and one pawn for each player. Polycarp and Vasiliy move in turns, Polycarp starts. In each turn Polycarp can move his pawn from cell (x,βy) to (xβ-β1,βy) or (x,βyβ-β1). Vasiliy can move his pawn from (x,βy) to one of cells: (xβ-β1,βy),β(xβ-β1,βyβ-β1) and (x,βyβ-β1). Both players are also allowed to skip move. There are some additional restrictions β a player is forbidden to move his pawn to a cell with negative x-coordinate or y-coordinate or to the cell containing opponent's pawn The winner is the first person to reach cell (0,β0). You are given the starting coordinates of both pawns. Determine who will win if both of them play optimally well. | Input: ['2 1 2 2'] Output:['Polycarp'] | [
2,
3
] |
The biggest gold mine in Berland consists of n caves, connected by nβ-β1 transitions. The entrance to the mine leads to the cave number 1, it is possible to go from it to any remaining cave of the mine by moving along the transitions. The mine is being developed by the InMine Inc., k miners work for it. Each day the corporation sorts miners into caves so that each cave has at most one miner working there. For each cave we know the height of its ceiling hi in meters, and for each miner we know his height sj, also in meters. If a miner's height doesn't exceed the height of the cave ceiling where he is, then he can stand there comfortably, otherwise, he has to stoop and that makes him unhappy.Unfortunately, miners typically go on strike in Berland, so InMine makes all the possible effort to make miners happy about their work conditions. To ensure that no miner goes on strike, you need make sure that no miner has to stoop at any moment on his way from the entrance to the mine to his cave (in particular, he must be able to stand comfortably in the cave where he works). To reach this goal, you can choose exactly one cave and increase the height of its ceiling by several meters. However enlarging a cave is an expensive and complex procedure. That's why InMine Inc. asks you either to determine the minimum number of meters you should raise the ceiling of some cave so that it is be possible to sort the miners into the caves and keep all miners happy with their working conditions or to determine that it is impossible to achieve by raising ceiling in exactly one cave. | Input: ['65 8 4 6 3 121 21 34 22 56 367 4 2 5 3 11'] Output:['6'] | [
2,
4
] |
Many years have passed, and n friends met at a party again. Technologies have leaped forward since the last meeting, cameras with timer appeared and now it is not obligatory for one of the friends to stand with a camera, and, thus, being absent on the photo.Simply speaking, the process of photographing can be described as follows. Each friend occupies a rectangle of pixels on the photo: the i-th of them in a standing state occupies a wi pixels wide and a hi pixels high rectangle. But also, each person can lie down for the photo, and then he will occupy a hi pixels wide and a wi pixels high rectangle.The total photo will have size WβΓβH, where W is the total width of all the people rectangles, and H is the maximum of the heights. The friends want to determine what minimum area the group photo can they obtain if no more than nβ/β2 of them can lie on the ground (it would be strange if more than nβ/β2 gentlemen lie on the ground together, isn't it?..)Help them to achieve this goal. | Input: ['310 120 230 3'] Output:['180'] | [
0,
2
] |
Leonid works for a small and promising start-up that works on decoding the human genome. His duties include solving complex problems of finding certain patterns in long strings consisting of letters 'A', 'T', 'G' and 'C'.Let's consider the following scenario. There is a fragment of a human DNA chain, recorded as a string S. To analyze the fragment, you need to find all occurrences of string T in a string S. However, the matter is complicated by the fact that the original chain fragment could contain minor mutations, which, however, complicate the task of finding a fragment. Leonid proposed the following approach to solve this problem.Let's write down integer kββ₯β0 β the error threshold. We will say that string T occurs in string S on position i (1ββ€βiββ€β|S|β-β|T|β+β1), if after putting string T along with this position, each character of string T corresponds to the some character of the same value in string S at the distance of at most k. More formally, for any j (1ββ€βjββ€β|T|) there must exist such p (1ββ€βpββ€β|S|), that |(iβ+βjβ-β1)β-βp|ββ€βk and S[p]β=βT[j].For example, corresponding to the given definition, string "ACAT" occurs in string "AGCAATTCAT" in positions 2, 3 and 6. Note that at kβ=β0 the given definition transforms to a simple definition of the occurrence of a string in a string.Help Leonid by calculating in how many positions the given string T occurs in the given string S with the given error threshold. | Input: ['10 4 1AGCAATTCATACAT'] Output:['3'] | [
0
] |
The clique problem is one of the most well-known NP-complete problems. Under some simplification it can be formulated as follows. Consider an undirected graph G. It is required to find a subset of vertices C of the maximum size such that any two of them are connected by an edge in graph G. Sounds simple, doesn't it? Nobody yet knows an algorithm that finds a solution to this problem in polynomial time of the size of the graph. However, as with many other NP-complete problems, the clique problem is easier if you consider a specific type of a graph.Consider n distinct points on a line. Let the i-th point have the coordinate xi and weight wi. Let's form graph G, whose vertices are these points and edges connect exactly the pairs of points (i,βj), such that the distance between them is not less than the sum of their weights, or more formally: |xiβ-βxj|ββ₯βwiβ+βwj.Find the size of the maximum clique in such graph. | Input: ['42 33 16 10 2'] Output:['3'] | [
2
] |
Leonid wants to become a glass carver (the person who creates beautiful artworks by cutting the glass). He already has a rectangular w mm βΓβ h mm sheet of glass, a diamond glass cutter and lots of enthusiasm. What he lacks is understanding of what to carve and how.In order not to waste time, he decided to practice the technique of carving. To do this, he makes vertical and horizontal cuts through the entire sheet. This process results in making smaller rectangular fragments of glass. Leonid does not move the newly made glass fragments. In particular, a cut divides each fragment of glass that it goes through into smaller fragments.After each cut Leonid tries to determine what area the largest of the currently available glass fragments has. Since there appear more and more fragments, this question takes him more and more time and distracts him from the fascinating process.Leonid offers to divide the labor β he will cut glass, and you will calculate the area of the maximum fragment after each cut. Do you agree? | Input: ['4 3 4H 2V 2V 3V 1'] Output:['8442'] | [
4
] |
Ford Prefect got a job as a web developer for a small company that makes towels. His current work task is to create a search engine for the website of the company. During the development process, he needs to write a subroutine for comparing strings S and T of equal length to be "similar". After a brief search on the Internet, he learned about the Hamming distance between two strings S and T of the same length, which is defined as the number of positions in which S and T have different characters. For example, the Hamming distance between words "permanent" and "pergament" is two, as these words differ in the fourth and sixth letters.Moreover, as he was searching for information, he also noticed that modern search engines have powerful mechanisms to correct errors in the request to improve the quality of search. Ford doesn't know much about human beings, so he assumed that the most common mistake in a request is swapping two arbitrary letters of the string (not necessarily adjacent). Now he wants to write a function that determines which two letters should be swapped in string S, so that the Hamming distance between a new string S and string T would be as small as possible, or otherwise, determine that such a replacement cannot reduce the distance between the strings.Help him do this! | Input: ['9pergamentpermanent'] Output:['14 6'] | [
2
] |
One day Vasya was sitting on a not so interesting Maths lesson and making an origami from a rectangular a mm βΓβ b mm sheet of paper (aβ>βb). Usually the first step in making an origami is making a square piece of paper from the rectangular sheet by folding the sheet along the bisector of the right angle, and cutting the excess part. After making a paper ship from the square piece, Vasya looked on the remaining (aβ-βb) mm βΓβ b mm strip of paper. He got the idea to use this strip of paper in the same way to make an origami, and then use the remainder (if it exists) and so on. At the moment when he is left with a square piece of paper, he will make the last ship from it and stop.Can you determine how many ships Vasya will make during the lesson? | Input: ['2 1'] Output:['2'] | [
3
] |
Spiders are Om Nom's old enemies. They love eating candies as much as he does and that's why they keep trying to keep the monster away from his favorite candies. They came up with an evil plan to trap Om Nom. Let's consider a rope structure consisting of n nodes and nβ-β1 ropes connecting the nodes. The structure is connected, thus, the ropes and the nodes form a tree. Each rope of the formed structure is associated with its length. A candy is tied to node x of the structure. Om Nom really wants to eat this candy.The y spiders are trying to stop him from doing it. They decided to entangle the candy and some part of the structure into a web, thus attaching the candy to as large as possible part of the rope structure. Each spider can use his web to cover all ropes on the path between two arbitrary nodes a and b. Thus, y spiders can cover the set of ropes which is a union of y paths in the given tree. These y paths can arbitrarily intersect each other. The spiders want the following conditions to be hold: the node containing the candy is adjacent to at least one rope covered with a web the ropes covered with the web form a connected structure (what's the idea of covering with a web the ropes that are not connected with the candy?) the total length of the ropes covered with web is as large as possible The spiders haven't yet decided to what node of the structure they will tie the candy and how many spiders will cover the structure with web, so they asked you to help them. Help them calculate the optimal plan for multiple values of x and y. | Input: ['6 31 2 22 3 23 4 24 6 13 5 103 12 51 1'] Output:['141317'] | [
2
] |
A sweet little monster Om Nom loves candies very much. One day he found himself in a rather tricky situation that required him to think a bit in order to enjoy candies the most. Would you succeed with the same task if you were on his place? One day, when he came to his friend Evan, Om Nom didn't find him at home but he found two bags with candies. The first was full of blue candies and the second bag was full of red candies. Om Nom knows that each red candy weighs Wr grams and each blue candy weighs Wb grams. Eating a single red candy gives Om Nom Hr joy units and eating a single blue candy gives Om Nom Hb joy units.Candies are the most important thing in the world, but on the other hand overeating is not good. Om Nom knows if he eats more than C grams of candies, he will get sick. Om Nom thinks that it isn't proper to leave candy leftovers, so he can only eat a whole candy. Om Nom is a great mathematician and he quickly determined how many candies of what type he should eat in order to get the maximum number of joy units. Can you repeat his achievement? You can assume that each bag contains more candies that Om Nom can eat. | Input: ['10 3 5 2 3'] Output:['16'] | [
0,
2,
3
] |
Om Nom is the main character of a game "Cut the Rope". He is a bright little monster who likes visiting friends living at the other side of the park. However the dark old parks can scare even somebody as fearless as Om Nom, so he asks you to help him. The park consists of 2nβ+β1β-β1 squares connected by roads so that the scheme of the park is a full binary tree of depth n. More formally, the entrance to the park is located at the square 1. The exits out of the park are located at squares 2n,β2nβ+β1,β...,β2nβ+β1β-β1 and these exits lead straight to the Om Nom friends' houses. From each square i (2ββ€βiβ<β2nβ+β1) there is a road to the square . Thus, it is possible to go from the park entrance to each of the exits by walking along exactly n roads. To light the path roads in the evening, the park keeper installed street lights along each road. The road that leads from square i to square has ai lights.Om Nom loves counting lights on the way to his friend. Om Nom is afraid of spiders who live in the park, so he doesn't like to walk along roads that are not enough lit. What he wants is that the way to any of his friends should have in total the same number of lights. That will make him feel safe. He asked you to help him install additional lights. Determine what minimum number of lights it is needed to additionally place on the park roads so that a path from the entrance to any exit of the park contains the same number of street lights. You may add an arbitrary number of street lights to each of the roads. | Input: ['21 2 3 4 5 6'] Output:['5'] | [
2
] |
In this problem you will meet the simplified model of game King of Thieves.In a new ZeptoLab game called "King of Thieves" your aim is to reach a chest with gold by controlling your character, avoiding traps and obstacles on your way. An interesting feature of the game is that you can design your own levels that will be available to other players. Let's consider the following simple design of a level.A dungeon consists of n segments located at a same vertical level, each segment is either a platform that character can stand on, or a pit with a trap that makes player lose if he falls into it. All segments have the same length, platforms on the scheme of the level are represented as '*' and pits are represented as '.'. One of things that affects speedrun characteristics of the level is a possibility to perform a series of consecutive jumps of the same length. More formally, when the character is on the platform number i1, he can make a sequence of jumps through the platforms i1β<βi2β<β...β<βik, if i2β-βi1β=βi3β-βi2β=β...β=βikβ-βikβ-β1. Of course, all segments i1,βi2,β... ik should be exactly the platforms, not pits. Let's call a level to be good if you can perform a sequence of four jumps of the same length or in the other words there must be a sequence i1,βi2,β...,βi5, consisting of five platforms so that the intervals between consecutive platforms are of the same length. Given the scheme of the level, check if it is good. | Input: ['16.**.*..*.***.**.'] Output:['yes'] | [
0
] |
Anya loves to fold and stick. Today she decided to do just that.Anya has n cubes lying in a line and numbered from 1 to n from left to right, with natural numbers written on them. She also has k stickers with exclamation marks. We know that the number of stickers does not exceed the number of cubes.Anya can stick an exclamation mark on the cube and get the factorial of the number written on the cube. For example, if a cube reads 5, then after the sticking it reads 5!, which equals 120.You need to help Anya count how many ways there are to choose some of the cubes and stick on some of the chosen cubes at most k exclamation marks so that the sum of the numbers written on the chosen cubes after the sticking becomes equal to S. Anya can stick at most one exclamation mark on each cube. Can you do it?Two ways are considered the same if they have the same set of chosen cubes and the same set of cubes with exclamation marks. | Input: ['2 2 304 3'] Output:['1'] | [
0,
3,
4
] |
Finally it is a day when Arthur has enough money for buying an apartment. He found a great option close to the center of the city with a nice price.Plan of the apartment found by Arthur looks like a rectangle nβΓβm consisting of squares of size 1βΓβ1. Each of those squares contains either a wall (such square is denoted by a symbol "*" on the plan) or a free space (such square is denoted on the plan by a symbol ".").Room in an apartment is a maximal connected area consisting of free squares. Squares are considered adjacent if they share a common side.The old Arthur dream is to live in an apartment where all rooms are rectangles. He asks you to calculate minimum number of walls you need to remove in order to achieve this goal. After removing a wall from a square it becomes a free square. While removing the walls it is possible that some rooms unite into a single one. | Input: ['5 5.*.*.*****.*.*.*****.*.*.'] Output:['.*.*.*****.*.*.*****.*.*.'] | [
2
] |
In the evening, after the contest Ilya was bored, and he really felt like maximizing. He remembered that he had a set of n sticks and an instrument. Each stick is characterized by its length li.Ilya decided to make a rectangle from the sticks. And due to his whim, he decided to make rectangles in such a way that maximizes their total area. Each stick is used in making at most one rectangle, it is possible that some of sticks remain unused. Bending sticks is not allowed.Sticks with lengths a1, a2, a3 and a4 can make a rectangle if the following properties are observed: a1ββ€βa2ββ€βa3ββ€βa4 a1β=βa2 a3β=βa4 A rectangle can be made of sticks with lengths of, for example, 3 3 3 3 or 2 2 4 4. A rectangle cannot be made of, for example, sticks 5 5 5 7.Ilya also has an instrument which can reduce the length of the sticks. The sticks are made of a special material, so the length of each stick can be reduced by at most one. For example, a stick with length 5 can either stay at this length or be transformed into a stick of length 4.You have to answer the question β what maximum total area of the rectangles can Ilya get with a file if makes rectangles from the available sticks? | Input: ['42 4 4 2'] Output:['8'] | [
2,
3
] |
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 string β each day he chose integer ai and reversed a piece of string (a segment) from position ai to position |s|β-βaiβ+β1. It is guaranteed that 2Β·aiββ€β|s|.You face the following task: determine what Pasha's string will look like after m days. | Input: ['abcdef12'] Output:['aedcbf'] | [
2,
3
] |
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (nβ-β1)-th room to the n-th room. Thus, you can go to room x only from room xβ-β1.The potato pie is located in the n-th room and Vitaly needs to go there. Each pair of consecutive rooms has a door between them. In order to go to room x from room xβ-β1, you need to open the door between the rooms with the corresponding key. In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.Each of the first nβ-β1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number. | Input: ['3aAbB'] Output:['0'] | [
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Polycarpus has a finite sequence of opening and closing brackets. In order not to fall asleep in a lecture, Polycarpus is having fun with his sequence. He is able to perform two operations: adding any bracket in any position (in the beginning, the end, or between any two existing brackets); cyclic shift β moving the last bracket from the end of the sequence to the beginning. Polycarpus can apply any number of operations to his sequence and adding a cyclic shift in any order. As a result, he wants to get the correct bracket sequence of the minimum possible length. If there are several such sequences, Polycarpus is interested in the lexicographically smallest one. Help him find such a sequence.Acorrect bracket sequence is a sequence of opening and closing brackets, from which you can get a correct arithmetic expression by adding characters "1" and "+" . Each opening bracket must correspond to a closed one. For example, the sequences "(())()", "()", "(()(()))" are correct and ")(", "(()" and "(()))(" are not.The sequence a1 a2... an is lexicographically smaller than sequence b1 b2... bn, if there is such number i from 1 to n, thatakβ=βbk for 1ββ€βkβ<βi and aiβ<βbi. Consider that "(" β<β ")". | Input: ['()(())'] Output:['(())()'] | [
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Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, sβ+β1, sβ+β2, ..., sβ+βTβ-β1. So, the user's time online can be calculated as the union of time intervals of the form [s,βsβ+βTβ-β1] over all times s of requests from him.Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that: the number of different users online did not exceed M at any moment, at some second the number of distinct users online reached value M, the total number of users (the number of distinct identifiers) was as much as possible. Help Polycarpus cope with the test. | Input: ['4 2 1017:05:5317:05:5817:06:0122:39:47'] Output:['31223'] | [
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