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The winter in Berland lasts n days. For each day we know the forecast for the average air temperature that day. Vasya has a new set of winter tires which allows him to drive safely no more than k days at any average air temperature. After k days of using it (regardless of the temperature of these days) the set of winter tires wears down and cannot be used more. It is not necessary that these k days form a continuous segment of days.Before the first winter day Vasya still uses summer tires. It is possible to drive safely on summer tires any number of days when the average air temperature is non-negative. It is impossible to drive on summer tires at days when the average air temperature is negative. Vasya can change summer tires to winter tires and vice versa at the beginning of any day.Find the minimum number of times Vasya needs to change summer tires to winter tires and vice versa to drive safely during the winter. At the end of the winter the car can be with any set of tires. | Input: ['4 3-5 20 -3 0'] Output:['2'] | [
2
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A big company decided to launch a new series of rectangular displays, and decided that the display must have exactly n pixels. Your task is to determine the size of the rectangular display — the number of lines (rows) of pixels a and the number of columns of pixels b, so that: there are exactly n pixels on the display; the number of rows does not exceed the number of columns, it means a ≤ b; the difference b - a is as small as possible. | Input: ['8'] Output:['2 4'] | [
0,
3
] |
Sasha reaches the work by car. It takes exactly k minutes. On his way he listens to music. All songs in his playlist go one by one, after listening to the i-th song Sasha gets a pleasure which equals ai. The i-th song lasts for ti minutes. Before the beginning of his way Sasha turns on some song x and then he listens to the songs one by one: at first, the song x, then the song (x + 1), then the song number (x + 2), and so on. He listens to songs until he reaches the work or until he listens to the last song in his playlist. Sasha can listen to each song to the end or partly.In the second case he listens to the song for integer number of minutes, at least half of the song's length. Formally, if the length of the song equals d minutes, Sasha listens to it for no less than minutes, then he immediately switches it to the next song (if there is such). For example, if the length of the song which Sasha wants to partly listen to, equals 5 minutes, then he should listen to it for at least 3 minutes, if the length of the song equals 8 minutes, then he should listen to it for at least 4 minutes.It takes no time to switch a song.Sasha wants to listen partly no more than w songs. If the last listened song plays for less than half of its length, then Sasha doesn't get pleasure from it and that song is not included to the list of partly listened songs. It is not allowed to skip songs. A pleasure from a song does not depend on the listening mode, for the i-th song this value equals ai.Help Sasha to choose such x and no more than w songs for partial listening to get the maximum pleasure. Write a program to find the maximum pleasure Sasha can get from the listening to the songs on his way to the work. | Input: ['7 2 113 4 3 5 1 4 67 7 3 6 5 3 9'] Output:['12'] | [
2
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Eugeny has n cards, each of them has exactly one integer written on it. Eugeny wants to exchange some cards with Nikolay so that the number of even integers on his cards would equal the number of odd integers, and that all these numbers would be distinct. Nikolay has m cards, distinct numbers from 1 to m are written on them, one per card. It means that Nikolay has exactly one card with number 1, exactly one card with number 2 and so on. A single exchange is a process in which Eugeny gives one card to Nikolay and takes another one from those Nikolay has. Your task is to find the minimum number of card exchanges and determine which cards Eugeny should exchange. | Input: ['6 25 6 7 9 4 5'] Output:['15 6 7 9 4 2 '] | [
2,
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] |
Innokentiy likes tea very much and today he wants to drink exactly n cups of tea. He would be happy to drink more but he had exactly n tea bags, a of them are green and b are black.Innokentiy doesn't like to drink the same tea (green or black) more than k times in a row. Your task is to determine the order of brewing tea bags so that Innokentiy will be able to drink n cups of tea, without drinking the same tea more than k times in a row, or to inform that it is impossible. Each tea bag has to be used exactly once. | Input: ['5 1 3 2'] Output:['GBGBG'] | [
2,
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] |
The tram in Berland goes along a straight line from the point 0 to the point s and back, passing 1 meter per t1 seconds in both directions. It means that the tram is always in the state of uniform rectilinear motion, instantly turning around at points x = 0 and x = s.Igor is at the point x1. He should reach the point x2. Igor passes 1 meter per t2 seconds. Your task is to determine the minimum time Igor needs to get from the point x1 to the point x2, if it is known where the tram is and in what direction it goes at the moment Igor comes to the point x1.Igor can enter the tram unlimited number of times at any moment when his and the tram's positions coincide. It is not obligatory that points in which Igor enter and exit the tram are integers. Assume that any boarding and unboarding happens instantly. Igor can move arbitrary along the line (but not faster than 1 meter per t2 seconds). He can also stand at some point for some time. | Input: ['4 2 43 41 1'] Output:['8'] | [
3
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Nikolay has a lemons, b apples and c pears. He decided to cook a compote. According to the recipe the fruits should be in the ratio 1: 2: 4. It means that for each lemon in the compote should be exactly 2 apples and exactly 4 pears. You can't crumble up, break up or cut these fruits into pieces. These fruits — lemons, apples and pears — should be put in the compote as whole fruits.Your task is to determine the maximum total number of lemons, apples and pears from which Nikolay can cook the compote. It is possible that Nikolay can't use any fruits, in this case print 0. | Input: ['257'] Output:['7'] | [
3
] |
One day, Hongcow goes to the store and sees a brand new deck of n special cards. Each individual card is either red or blue. He decides he wants to buy them immediately. To do this, he needs to play a game with the owner of the store.This game takes some number of turns to complete. On a turn, Hongcow may do one of two things: Collect tokens. Hongcow collects 1 red token and 1 blue token by choosing this option (thus, 2 tokens in total per one operation). Buy a card. Hongcow chooses some card and spends tokens to purchase it as specified below. The i-th card requires ri red resources and bi blue resources. Suppose Hongcow currently has A red cards and B blue cards. Then, the i-th card will require Hongcow to spend max(ri - A, 0) red tokens, and max(bi - B, 0) blue tokens. Note, only tokens disappear, but the cards stay with Hongcow forever. Each card can be bought only once.Given a description of the cards and their costs determine the minimum number of turns Hongcow needs to purchase all cards. | Input: ['3R 0 1B 1 0R 1 1'] Output:['4'] | [
0
] |
Vladik was bored on his way home and decided to play the following game. He took n cards and put them in a row in front of himself. Every card has a positive integer number not exceeding 8 written on it. He decided to find the longest subsequence of cards which satisfies the following conditions: the number of occurrences of each number from 1 to 8 in the subsequence doesn't differ by more then 1 from the number of occurrences of any other number. Formally, if there are ck cards with number k on them in the subsequence, than for all pairs of integers the condition |ci - cj| ≤ 1 must hold. if there is at least one card with number x on it in the subsequence, then all cards with number x in this subsequence must form a continuous segment in it (but not necessarily a continuous segment in the original sequence). For example, the subsequence [1, 1, 2, 2] satisfies this condition while the subsequence [1, 2, 2, 1] doesn't. Note that [1, 1, 2, 2] doesn't satisfy the first condition. Please help Vladik to find the length of the longest subsequence that satisfies both conditions. | Input: ['31 1 1'] Output:['1'] | [
0,
4
] |
Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction as a sum of three distinct positive fractions in form .Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that . Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.If there is no such answer, print -1. | Input: ['3'] Output:['2 7 42'] | [
0,
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] |
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.Please help Chloe to solve the problem! | Input: ['3 2'] Output:['2'] | [
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Vladik is a competitive programmer. This year he is going to win the International Olympiad in Informatics. But it is not as easy as it sounds: the question Vladik face now is to find the cheapest way to get to the olympiad.Vladik knows n airports. All the airports are located on a straight line. Each airport has unique id from 1 to n, Vladik's house is situated next to the airport with id a, and the place of the olympiad is situated next to the airport with id b. It is possible that Vladik's house and the place of the olympiad are located near the same airport. To get to the olympiad, Vladik can fly between any pair of airports any number of times, but he has to start his route at the airport a and finish it at the airport b.Each airport belongs to one of two companies. The cost of flight from the airport i to the airport j is zero if both airports belong to the same company, and |i - j| if they belong to different companies.Print the minimum cost Vladik has to pay to get to the olympiad. | Input: ['4 1 41010'] Output:['1'] | [
2
] |
There are some beautiful girls in Arpa’s land as mentioned before.Once Arpa came up with an obvious problem:Given an array and a number x, count the number of pairs of indices i, j (1 ≤ i < j ≤ n) such that , where is bitwise xor operation (see notes for explanation). Immediately, Mehrdad discovered a terrible solution that nobody trusted. Now Arpa needs your help to implement the solution to that problem. | Input: ['2 31 2'] Output:['1'] | [
0,
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] |
There exists an island called Arpa’s land, some beautiful girls live there, as ugly ones do.Mehrdad wants to become minister of Arpa’s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n. Mehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat. | Input: ['1'] Output:['8'] | [
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As you have noticed, there are lovely girls in Arpa’s land.People in Arpa's land are numbered from 1 to n. Everyone has exactly one crush, i-th person's crush is person with the number crushi. Someday Arpa shouted Owf loudly from the top of the palace and a funny game started in Arpa's land. The rules are as follows.The game consists of rounds. Assume person x wants to start a round, he calls crushx and says: "Oww...wwf" (the letter w is repeated t times) and cuts off the phone immediately. If t > 1 then crushx calls crushcrushx and says: "Oww...wwf" (the letter w is repeated t - 1 times) and cuts off the phone immediately. The round continues until some person receives an "Owf" (t = 1). This person is called the Joon-Joon of the round. There can't be two rounds at the same time.Mehrdad has an evil plan to make the game more funny, he wants to find smallest t (t ≥ 1) such that for each person x, if x starts some round and y becomes the Joon-Joon of the round, then by starting from y, x would become the Joon-Joon of the round. Find such t for Mehrdad if it's possible.Some strange fact in Arpa's land is that someone can be himself's crush (i.e. crushi = i). | Input: ['42 3 1 4'] Output:['3'] | [
3
] |
Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks.What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase. | Input: ['1 1 3 4'] Output:['3'] | [
0
] |
Gosha is hunting. His goal is to catch as many Pokemons as possible. Gosha has a Poke Balls and b Ultra Balls. There are n Pokemons. They are numbered 1 through n. Gosha knows that if he throws a Poke Ball at the i-th Pokemon he catches it with probability pi. If he throws an Ultra Ball at the i-th Pokemon he catches it with probability ui. He can throw at most one Ball of each type at any Pokemon.The hunting proceeds as follows: at first, Gosha chooses no more than a Pokemons at which he will throw Poke Balls and no more than b Pokemons at which he will throw Ultra Balls. After that, he throws the chosen Balls at the chosen Pokemons. If he throws both Ultra Ball and Poke Ball at some Pokemon, he is caught if and only if he is caught by any of these Balls. The outcome of a throw doesn't depend on the other throws.Gosha would like to know what is the expected number of the Pokemons he catches if he acts in an optimal way. In other words, he would like to know the maximum possible expected number of Pokemons can catch. | Input: ['3 2 21.000 0.000 0.5000.000 1.000 0.500'] Output:['2.75'] | [
0,
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] |
Alyona has a tree with n vertices. The root of the tree is the vertex 1. In each vertex Alyona wrote an positive integer, in the vertex i she wrote ai. Moreover, the girl wrote a positive integer to every edge of the tree (possibly, different integers on different edges).Let's define dist(v, u) as the sum of the integers written on the edges of the simple path from v to u.The vertex v controls the vertex u (v ≠ u) if and only if u is in the subtree of v and dist(v, u) ≤ au.Alyona wants to settle in some vertex. In order to do this, she wants to know for each vertex v what is the number of vertices u such that v controls u. | Input: ['52 5 1 4 61 71 13 53 6'] Output:['1 0 1 0 0'] | [
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Alyona's mother wants to present an array of n non-negative integers to Alyona. The array should be special. Alyona is a capricious girl so after she gets the array, she inspects m of its subarrays. Subarray is a set of some subsequent elements of the array. The i-th subarray is described with two integers li and ri, and its elements are a[li], a[li + 1], ..., a[ri].Alyona is going to find mex for each of the chosen subarrays. Among these m mexes the girl is going to find the smallest. She wants this minimum mex to be as large as possible. You are to find an array a of n elements so that the minimum mex among those chosen by Alyona subarrays is as large as possible.The mex of a set S is a minimum possible non-negative integer that is not in S. | Input: ['5 31 32 54 5'] Output:['21 0 2 1 0'] | [
2
] |
After one of celebrations there is a stack of dirty plates in Nikita's kitchen. Nikita has to wash them and put into a dryer. In dryer, the plates should be also placed in a stack also, and the plates sizes should increase down up. The sizes of all plates are distinct.Nikita has no so much free space, specifically, he has a place for only one more stack of plates. Therefore, he can perform only such two operations: Take any number of plates from 1 to a from the top of the dirty stack, wash them and put them to the intermediate stack. Take any number of plates from 1 to b from the top of the intermediate stack and put them to the stack in the dryer. Note that after performing each of the operations, the plates are put in the same order as they were before the operation.You are given the sizes of the plates s1, s2, ..., sn in the down up order in the dirty stack, and integers a and b. All the sizes are distinct. Write a program that determines whether or not Nikita can put the plates in increasing down up order in the dryer. If he is able to do so, the program should find some sequence of operations (not necessary optimal) to achieve it. | Input: ['6 2 32 3 6 4 1 5'] Output:['YES81 21 12 11 21 12 12 12 3'] | [
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Tanya is now five so all her friends gathered together to celebrate her birthday. There are n children on the celebration, including Tanya.The celebration is close to its end, and the last planned attraction is gaming machines. There are m machines in the hall, they are numbered 1 through m. Each of the children has a list of machines he wants to play on. Moreover, for each of the machines he knows the exact time he wants to play on it. For every machine, no more than one child can play on this machine at the same time.It is evening already, so every adult wants to go home. To speed up the process, you can additionally rent second copies of each of the machines. To rent the second copy of the j-th machine, you have to pay pj burles. After you rent a machine, you can use it for as long as you want.How long it will take to make every child play according to his plan, if you have a budget of b burles for renting additional machines? There is only one copy of each machine, so it's impossible to rent a third machine of the same type.The children can interrupt the game in any moment and continue it later. If the i-th child wants to play on the j-th machine, it is allowed after you rent the copy of the j-th machine that this child would play some part of the time on the j-th machine and some part of the time on its copy (each of these parts could be empty). The interruptions and changes take no time and can be performed in any integer moment of time. Of course, a child can't play on more than one machine at the same time.Remember, that it is not needed to save money (no one saves money at the expense of children happiness!), it is needed to minimize the latest moment of time some child ends his game. | Input: ['2 2 1003 72 1 3 2 12 1 3 2 1'] Output:['41081 1 0 12 2 0 11 1 1 12 1 1 12 1 2 11 1 2 11 2 3 12 1 3 1'] | [
2
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Ostap is preparing to play chess again and this time he is about to prepare. Thus, he was closely monitoring one recent chess tournament. There were m players participating and each pair of players played exactly one game. The victory gives 2 points, draw — 1 points, lose — 0 points.Ostap is lazy, so he never tries to remember the outcome of each game. Instead, he computes the total number of points earned by each of the players (the sum of his points in all games which he took part in), sort these value in non-ascending order and then remembers first n integers in this list.Now the Great Strategist Ostap wonders whether he remembers everything correct. He considers that he is correct if there exists at least one tournament results table such that it will produce the given integers. That means, if we count the sum of points for each player, sort them and take first n elements, the result will coincide with what Ostap remembers. Can you check if such table exists? | Input: ['5 58 6 4 2 0'] Output:['yesXWWWWLXWWWLLXWWLLLXWLLLLX'] | [
2,
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] |
Ostap Bender is worried that people started to forget that he is the Great Combinator. Now he wants to show them his skills in combinatorics. Now he studies the permutations of length n. He has a list of m valid pairs, pair ai and bi means that he is allowed to place integers bi at position ai.He knows that the number of permutations that use only valid pairs is odd. Now, for each pair he wants to find out, will the number of valid permutations be odd if he removes this pair (and only it) from the list. | Input: ['2 31 11 22 2'] Output:['NOYESNO'] | [
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Mr. Funt now lives in a country with a very specific tax laws. The total income of mr. Funt during this year is equal to n (n ≥ 2) burles and the amount of tax he has to pay is calculated as the maximum divisor of n (not equal to n, of course). For example, if n = 6 then Funt has to pay 3 burles, while for n = 25 he needs to pay 5 and if n = 2 he pays only 1 burle.As mr. Funt is a very opportunistic person he wants to cheat a bit. In particular, he wants to split the initial n in several parts n1 + n2 + ... + nk = n (here k is arbitrary, even k = 1 is allowed) and pay the taxes for each part separately. He can't make some part equal to 1 because it will reveal him. So, the condition ni ≥ 2 should hold for all i from 1 to k.Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts. | Input: ['4'] Output:['2'] | [
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Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help. | Input: ['2'] Output:['1'] | [
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Local authorities have heard a lot about combinatorial abilities of Ostap Bender so they decided to ask his help in the question of urbanization. There are n people who plan to move to the cities. The wealth of the i of them is equal to ai. Authorities plan to build two cities, first for n1 people and second for n2 people. Of course, each of n candidates can settle in only one of the cities. Thus, first some subset of candidates of size n1 settle in the first city and then some subset of size n2 is chosen among the remaining candidates and the move to the second city. All other candidates receive an official refuse and go back home.To make the statistic of local region look better in the eyes of their bosses, local authorities decided to pick subsets of candidates in such a way that the sum of arithmetic mean of wealth of people in each of the cities is as large as possible. Arithmetic mean of wealth in one city is the sum of wealth ai among all its residents divided by the number of them (n1 or n2 depending on the city). The division should be done in real numbers without any rounding.Please, help authorities find the optimal way to pick residents for two cities. | Input: ['2 1 11 5'] Output:['6.00000000'] | [
2
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Anton goes to school, his favorite lessons are arraystudying. He usually solves all the tasks pretty fast, but this time the teacher gave him a complicated one: given two arrays b and c of length n, find array a, such that:where a and b means bitwise AND, while a or b means bitwise OR.Usually Anton is good in arraystudying, but this problem is too hard, so Anton asks you to help. | Input: ['46 8 4 416 22 10 10'] Output:['3 5 1 1 '] | [
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Anton is playing a very interesting computer game, but now he is stuck at one of the levels. To pass to the next level he has to prepare n potions.Anton has a special kettle, that can prepare one potions in x seconds. Also, he knows spells of two types that can faster the process of preparing potions. Spells of this type speed up the preparation time of one potion. There are m spells of this type, the i-th of them costs bi manapoints and changes the preparation time of each potion to ai instead of x. Spells of this type immediately prepare some number of potions. There are k such spells, the i-th of them costs di manapoints and instantly create ci potions. Anton can use no more than one spell of the first type and no more than one spell of the second type, and the total number of manapoints spent should not exceed s. Consider that all spells are used instantly and right before Anton starts to prepare potions.Anton wants to get to the next level as fast as possible, so he is interested in the minimum number of time he needs to spent in order to prepare at least n potions. | Input: ['20 3 210 992 4 320 10 404 1510 80'] Output:['20'] | [
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Recently Anton found a box with digits in his room. There are k2 digits 2, k3 digits 3, k5 digits 5 and k6 digits 6.Anton's favorite integers are 32 and 256. He decided to compose this integers from digits he has. He wants to make the sum of these integers as large as possible. Help him solve this task!Each digit can be used no more than once, i.e. the composed integers should contain no more than k2 digits 2, k3 digits 3 and so on. Of course, unused digits are not counted in the sum. | Input: ['5 1 3 4'] Output:['800'] | [
0,
2,
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] |
The academic year has just begun, but lessons and olympiads have already occupied all the free time. It is not a surprise that today Olga fell asleep on the Literature. She had a dream in which she was on a stairs. The stairs consists of n steps. The steps are numbered from bottom to top, it means that the lowest step has number 1, and the highest step has number n. Above each of them there is a pointer with the direction (up or down) Olga should move from this step. As soon as Olga goes to the next step, the direction of the pointer (above the step she leaves) changes. It means that the direction "up" changes to "down", the direction "down" — to the direction "up".Olga always moves to the next step in the direction which is shown on the pointer above the step. If Olga moves beyond the stairs, she will fall and wake up. Moving beyond the stairs is a moving down from the first step or moving up from the last one (it means the n-th) step. In one second Olga moves one step up or down according to the direction of the pointer which is located above the step on which Olga had been at the beginning of the second. For each step find the duration of the dream if Olga was at this step at the beginning of the dream.Olga's fall also takes one second, so if she was on the first step and went down, she would wake up in the next second. | Input: ['3UUD'] Output:['5 6 3 '] | [
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There was an epidemic in Monstropolis and all monsters became sick. To recover, all monsters lined up in queue for an appointment to the only doctor in the city.Soon, monsters became hungry and began to eat each other. One monster can eat other monster if its weight is strictly greater than the weight of the monster being eaten, and they stand in the queue next to each other. Monsters eat each other instantly. There are no monsters which are being eaten at the same moment. After the monster A eats the monster B, the weight of the monster A increases by the weight of the eaten monster B. In result of such eating the length of the queue decreases by one, all monsters after the eaten one step forward so that there is no empty places in the queue again. A monster can eat several monsters one after another. Initially there were n monsters in the queue, the i-th of which had weight ai.For example, if weights are [1, 2, 2, 2, 1, 2] (in order of queue, monsters are numbered from 1 to 6 from left to right) then some of the options are: the first monster can't eat the second monster because a1 = 1 is not greater than a2 = 2; the second monster can't eat the third monster because a2 = 2 is not greater than a3 = 2; the second monster can't eat the fifth monster because they are not neighbors; the second monster can eat the first monster, the queue will be transformed to [3, 2, 2, 1, 2]. After some time, someone said a good joke and all monsters recovered. At that moment there were k (k ≤ n) monsters in the queue, the j-th of which had weight bj. Both sequences (a and b) contain the weights of the monsters in the order from the first to the last.You are required to provide one of the possible orders of eating monsters which led to the current queue, or to determine that this could not happen. Assume that the doctor didn't make any appointments while monsters were eating each other. | Input: ['61 2 2 2 1 225 5'] Output:['YES2 L1 R4 L3 L'] | [
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Very soon there will be a parade of victory over alien invaders in Berland. Unfortunately, all soldiers died in the war and now the army consists of entirely new recruits, many of whom do not even know from which leg they should begin to march. The civilian population also poorly understands from which leg recruits begin to march, so it is only important how many soldiers march in step.There will be n columns participating in the parade, the i-th column consists of li soldiers, who start to march from left leg, and ri soldiers, who start to march from right leg.The beauty of the parade is calculated by the following formula: if L is the total number of soldiers on the parade who start to march from the left leg, and R is the total number of soldiers on the parade who start to march from the right leg, so the beauty will equal |L - R|.No more than once you can choose one column and tell all the soldiers in this column to switch starting leg, i.e. everyone in this columns who starts the march from left leg will now start it from right leg, and vice versa. Formally, you can pick no more than one index i and swap values li and ri. Find the index of the column, such that switching the starting leg for soldiers in it will maximize the the beauty of the parade, or determine, that no such operation can increase the current beauty. | Input: ['35 68 910 3'] Output:['3'] | [
3
] |
The ICM ACPC World Finals is coming! Unfortunately, the organizers of the competition were so busy preparing tasks that totally missed an important technical point — the organization of electricity supplement for all the participants workstations.There are n computers for participants, the i-th of which has power equal to positive integer pi. At the same time there are m sockets available, the j-th of which has power euqal to positive integer sj. It is possible to connect the i-th computer to the j-th socket if and only if their powers are the same: pi = sj. It is allowed to connect no more than one computer to one socket. Thus, if the powers of all computers and sockets are distinct, then no computer can be connected to any of the sockets. In order to fix the situation professor Puch Williams urgently ordered a wagon of adapters — power splitters. Each adapter has one plug and one socket with a voltage divider between them. After plugging an adapter to a socket with power x, the power on the adapter's socket becomes equal to , it means that it is equal to the socket's power divided by two with rounding up, for example and .Each adapter can be used only once. It is possible to connect several adapters in a chain plugging the first to a socket. For example, if two adapters are plugged one after enother to a socket with power 10, it becomes possible to connect one computer with power 3 to this socket.The organizers should install adapters so that it will be possible to supply with electricity the maximum number of computers c at the same time. If there are several possible connection configurations, they want to find the one that uses the minimum number of adapters u to connect c computers.Help organizers calculate the maximum number of connected computers c and the minimum number of adapters u needed for this.The wagon of adapters contains enough of them to do the task. It is guaranteed that it's possible to connect at least one computer. | Input: ['2 21 12 2'] Output:['2 21 11 2'] | [
2
] |
Vasiliy has an exam period which will continue for n days. He has to pass exams on m subjects. Subjects are numbered from 1 to m.About every day we know exam for which one of m subjects can be passed on that day. Perhaps, some day you can't pass any exam. It is not allowed to pass more than one exam on any day. On each day Vasiliy can either pass the exam of that day (it takes the whole day) or prepare all day for some exam or have a rest. About each subject Vasiliy know a number ai — the number of days he should prepare to pass the exam number i. Vasiliy can switch subjects while preparing for exams, it is not necessary to prepare continuously during ai days for the exam number i. He can mix the order of preparation for exams in any way.Your task is to determine the minimum number of days in which Vasiliy can pass all exams, or determine that it is impossible. Each exam should be passed exactly one time. | Input: ['7 20 1 0 2 1 0 22 1'] Output:['5'] | [
2,
4
] |
Vasiliy spent his vacation in a sanatorium, came back and found that he completely forgot details of his vacation! Every day there was a breakfast, a dinner and a supper in a dining room of the sanatorium (of course, in this order). The only thing that Vasiliy has now is a card from the dining room contaning notes how many times he had a breakfast, a dinner and a supper (thus, the card contains three integers). Vasiliy could sometimes have missed some meal, for example, he could have had a breakfast and a supper, but a dinner, or, probably, at some days he haven't been at the dining room at all.Vasiliy doesn't remember what was the time of the day when he arrived to sanatorium (before breakfast, before dinner, before supper or after supper), and the time when he left it (before breakfast, before dinner, before supper or after supper). So he considers any of these options. After Vasiliy arrived to the sanatorium, he was there all the time until he left. Please note, that it's possible that Vasiliy left the sanatorium on the same day he arrived.According to the notes in the card, help Vasiliy determine the minimum number of meals in the dining room that he could have missed. We shouldn't count as missed meals on the arrival day before Vasiliy's arrival and meals on the departure day after he left. | Input: ['3 2 1'] Output:['1'] | [
2,
3,
4
] |
Recently a dog was bought for Polycarp. The dog's name is Cormen. Now Polycarp has a lot of troubles. For example, Cormen likes going for a walk. Empirically Polycarp learned that the dog needs at least k walks for any two consecutive days in order to feel good. For example, if k = 5 and yesterday Polycarp went for a walk with Cormen 2 times, today he has to go for a walk at least 3 times. Polycarp analysed all his affairs over the next n days and made a sequence of n integers a1, a2, ..., an, where ai is the number of times Polycarp will walk with the dog on the i-th day while doing all his affairs (for example, he has to go to a shop, throw out the trash, etc.).Help Polycarp determine the minimum number of walks he needs to do additionaly in the next n days so that Cormen will feel good during all the n days. You can assume that on the day before the first day and on the day after the n-th day Polycarp will go for a walk with Cormen exactly k times. Write a program that will find the minumum number of additional walks and the appropriate schedule — the sequence of integers b1, b2, ..., bn (bi ≥ ai), where bi means the total number of walks with the dog on the i-th day. | Input: ['3 52 0 1'] Output:['42 3 2'] | [
2
] |
Polycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.In his pocket Polycarp has an unlimited number of "10-burle coins" and exactly one coin of r burles (1 ≤ r ≤ 9).What is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel. | Input: ['117 3'] Output:['9'] | [
0,
3
] |
Little Vlad is fond of popular computer game Bota-2. Recently, the developers announced the new add-on named Bota-3. Of course, Vlad immediately bought only to find out his computer is too old for the new game and needs to be updated.There are n video cards in the shop, the power of the i-th video card is equal to integer value ai. As Vlad wants to be sure the new game will work he wants to buy not one, but several video cards and unite their powers using the cutting-edge technology. To use this technology one of the cards is chosen as the leading one and other video cards are attached to it as secondary. For this new technology to work it's required that the power of each of the secondary video cards is divisible by the power of the leading video card. In order to achieve that the power of any secondary video card can be reduced to any integer value less or equal than the current power. However, the power of the leading video card should remain unchanged, i.e. it can't be reduced.Vlad has an infinite amount of money so he can buy any set of video cards. Help him determine which video cards he should buy such that after picking the leading video card and may be reducing some powers of others to make them work together he will get the maximum total value of video power. | Input: ['43 2 15 9'] Output:['27'] | [
0,
3
] |
Archeologists have found a secret pass in the dungeon of one of the pyramids of Cycleland. To enter the treasury they have to open an unusual lock on the door. The lock consists of n words, each consisting of some hieroglyphs. The wall near the lock has a round switch. Each rotation of this switch changes the hieroglyphs according to some rules. The instruction nearby says that the door will open only if words written on the lock would be sorted in lexicographical order (the definition of lexicographical comparison in given in notes section).The rule that changes hieroglyphs is the following. One clockwise rotation of the round switch replaces each hieroglyph with the next hieroglyph in alphabet, i.e. hieroglyph x (1 ≤ x ≤ c - 1) is replaced with hieroglyph (x + 1), and hieroglyph c is replaced with hieroglyph 1.Help archeologist determine, how many clockwise rotations they should perform in order to open the door, or determine that this is impossible, i.e. no cyclic shift of the alphabet will make the sequence of words sorted lexicographically. | Input: ['4 32 3 21 13 2 3 14 2 3 1 2'] Output:['1'] | [
0,
2
] |
Arseniy is already grown-up and independent. His mother decided to leave him alone for m days and left on a vacation. She have prepared a lot of food, left some money and washed all Arseniy's clothes. Ten minutes before her leave she realized that it would be also useful to prepare instruction of which particular clothes to wear on each of the days she will be absent. Arseniy's family is a bit weird so all the clothes is enumerated. For example, each of Arseniy's n socks is assigned a unique integer from 1 to n. Thus, the only thing his mother had to do was to write down two integers li and ri for each of the days — the indices of socks to wear on the day i (obviously, li stands for the left foot and ri for the right). Each sock is painted in one of k colors.When mother already left Arseniy noticed that according to instruction he would wear the socks of different colors on some days. Of course, that is a terrible mistake cause by a rush. Arseniy is a smart boy, and, by some magical coincidence, he posses k jars with the paint — one for each of k colors.Arseniy wants to repaint some of the socks in such a way, that for each of m days he can follow the mother's instructions and wear the socks of the same color. As he is going to be very busy these days he will have no time to change the colors of any socks so he has to finalize the colors now.The new computer game Bota-3 was just realised and Arseniy can't wait to play it. What is the minimum number of socks that need their color to be changed in order to make it possible to follow mother's instructions and wear the socks of the same color during each of m days. | Input: ['3 2 31 2 31 22 3'] Output:['2'] | [
2
] |
The programming competition season has already started and it's time to train for ICPC. Sereja coaches his teams for a number of year and he knows that to get ready for the training session it's not enough to prepare only problems and editorial. As the training sessions lasts for several hours, teams become hungry. Thus, Sereja orders a number of pizzas so they can eat right after the end of the competition.Teams plan to train for n times during n consecutive days. During the training session Sereja orders exactly one pizza for each team that is present this day. He already knows that there will be ai teams on the i-th day.There are two types of discounts in Sereja's favourite pizzeria. The first discount works if one buys two pizzas at one day, while the second is a coupon that allows to buy one pizza during two consecutive days (two pizzas in total).As Sereja orders really a lot of pizza at this place, he is the golden client and can use the unlimited number of discounts and coupons of any type at any days.Sereja wants to order exactly ai pizzas on the i-th day while using only discounts and coupons. Note, that he will never buy more pizzas than he need for this particular day. Help him determine, whether he can buy the proper amount of pizzas each day if he is allowed to use only coupons and discounts. Note, that it's also prohibited to have any active coupons after the end of the day n. | Input: ['41 2 1 2'] Output:['YES'] | [
2
] |
There are n students at Berland State University. Every student has two skills, each measured as a number: ai — the programming skill and bi — the sports skill.It is announced that an Olympiad in programming and sports will be held soon. That's why Berland State University should choose two teams: one to take part in the programming track and one to take part in the sports track.There should be exactly p students in the programming team and exactly s students in the sports team. A student can't be a member of both teams.The university management considers that the strength of the university on the Olympiad is equal to the sum of two values: the programming team strength and the sports team strength. The strength of a team is the sum of skills of its members in the corresponding area, so the strength of the programming team is the sum of all ai and the strength of the sports team is the sum of all bi over corresponding team members.Help Berland State University to compose two teams to maximize the total strength of the university on the Olympiad. | Input: ['5 2 21 3 4 5 25 3 2 1 4'] Output:['183 4 1 5 '] | [
2
] |
All-Berland programming contest comes to an end. In total, n teams participated in it. Like in ACM-ICPC, current results stopped refreshing one hour before the contest ends. So at the Award Ceremony, results are partially known. For each team the value ai is given — the number of points the i-th team has earned before the last hour of the contest. Besides that, the Jury has evaluated all submissions sent during the last hour and knows values di — the number of points earned by the i-th team during the last hour (these values can be negative, which means that a team can lose points).Before the contest, each team got unique id from 1 to n. According to the contest rules, a team with more points takes a higher place. If two or more teams have equal number of points, the team with lower id will take the higher place. So no two teams can share the same place.The Award Ceremony proceeds in the following way. At the beginning of the ceremony, a large screen shows the results for the time moment "one hour before the end", which means that the i-th team has ai points. Then the Jury unfreezes results of the teams one by one in some order. When result of the j-th team is unfrozen, its score changes from aj to aj + dj. At this time the table of results is modified and the place of the team can change. The unfreezing of the j-th team is followed by the applause from the audience with duration of |xj - yj| seconds, where xj is the place of the j-th team before unfreezing and yj is the place right after the unfreezing. For example, if the team does not change the place, there is no applause from the audience. As you can see, during the Award Ceremony, each team will be unfrozen exactly once.Your task is to find such an order to unfreeze all the teams that the total duration of applause is maximum possible. | Input: ['417 -1452 -51 526 0'] Output:['4'] | [
2
] |
Polycarp is playing a game called "Running Over The Bridges". In this game he has to run over n bridges from the left to the right. Bridges are arranged one after the other, so the i-th bridge begins where the (i - 1)-th bridge ends.You have the following data about bridges: li and ti — the length of the i-th bridge and the maximum allowed time which Polycarp can spend running over the i-th bridge. Thus, if Polycarp is in the beginning of the bridge i at the time T then he has to leave it at the time T + ti or earlier. It is allowed to reach the right end of a bridge exactly at the time T + ti.Polycarp can run from the left side to the right one with speed 0.5, so he will run over a bridge with length s in time 2·s. Besides, he has several magical drinks. If he uses one drink, his speed increases twice (i.e. to value 1) for r seconds. All magical drinks are identical. Please note that Polycarp can use a drink only at integer moments of time, and he drinks it instantly and completely. Additionally, if Polycarp uses a drink at the moment T he can use the next drink not earlier than at the moment T + r.What is the minimal number of drinks Polycarp has to use to run over all n bridges? If this number is not greater than 105, then you have to find out the moments of time when Polycarp has to use each magical drink. | Input: ['1 3710'] Output:['20 3'] | [
2,
3
] |
A new trade empire is rising in Berland. Bulmart, an emerging trade giant, decided to dominate the market of ... shovels! And now almost every city in Berland has a Bulmart store, and some cities even have several of them! The only problem is, at the moment sales are ... let's say a little below estimates. Some people even say that shovels retail market is too small for such a big company to make a profit. But the company management believes in the future of that market and seeks new ways to increase income. There are n cities in Berland connected with m bi-directional roads. All roads have equal lengths. It can happen that it is impossible to reach a city from another city using only roads. There is no road which connects a city to itself. Any pair of cities can be connected by at most one road.There are w Bulmart stores in Berland. Each of them is described by three numbers: ci — the number of city where the i-th store is located (a city can have no stores at all or have several of them), ki — the number of shovels in the i-th store, pi — the price of a single shovel in the i-th store (in burles). The latest idea of the Bulmart management is to create a program which will help customers get shovels as fast as possible for affordable budget. Formally, the program has to find the minimum amount of time needed to deliver rj shovels to the customer in the city gj for the total cost of no more than aj burles. The delivery time between any two adjacent cities is equal to 1. If shovels are delivered from several cities, the delivery time is equal to the arrival time of the last package. The delivery itself is free of charge.The program needs to find answers to q such queries. Each query has to be processed independently from others, i.e. a query does not change number of shovels in stores for the next queries. | Input: ['6 44 25 41 23 224 1 23 2 361 2 62 3 73 1 24 3 85 2 56 1 10'] Output:['2-1223-1'] | [
4
] |
A group of n friends enjoys playing popular video game Toda 2. There is a rating system describing skill level of each player, initially the rating of the i-th friend is ri.The friends decided to take part in the championship as a team. But they should have equal ratings to be allowed to compose a single team consisting of all n friends. So the friends are faced with the problem: how to make all their ratings equal.One way to change ratings is to willingly lose in some matches. Friends can form a party consisting of two to five (but not more than n) friends and play a match in the game. When the party loses, the rating of each of its members decreases by 1. A rating can't become negative, so ri = 0 doesn't change after losing.The friends can take part in multiple matches, each time making a party from any subset of friends (but remember about constraints on party size: from 2 to 5 members).The friends want to make their ratings equal but as high as possible.Help the friends develop a strategy of losing the matches so that all their ratings become equal and the resulting rating is maximum possible. | Input: ['54 5 1 7 4'] Output:['180101000011010101001000011110000001111000'] | [
2
] |
There are n workers in a company, each of them has a unique id from 1 to n. Exaclty one of them is a chief, his id is s. Each worker except the chief has exactly one immediate superior.There was a request to each of the workers to tell how how many superiors (not only immediate). Worker's superiors are his immediate superior, the immediate superior of the his immediate superior, and so on. For example, if there are three workers in the company, from which the first is the chief, the second worker's immediate superior is the first, the third worker's immediate superior is the second, then the third worker has two superiors, one of them is immediate and one not immediate. The chief is a superior to all the workers except himself.Some of the workers were in a hurry and made a mistake. You are to find the minimum number of workers that could make a mistake. | Input: ['3 22 0 2'] Output:['1'] | [
2
] |
Galya is playing one-dimensional Sea Battle on a 1 × n grid. In this game a ships are placed on the grid. Each of the ships consists of b consecutive cells. No cell can be part of two ships, however, the ships can touch each other.Galya doesn't know the ships location. She can shoot to some cells and after each shot she is told if that cell was a part of some ship (this case is called "hit") or not (this case is called "miss").Galya has already made k shots, all of them were misses.Your task is to calculate the minimum number of cells such that if Galya shoot at all of them, she would hit at least one ship.It is guaranteed that there is at least one valid ships placement. | Input: ['5 1 2 100100'] Output:['24 2'] | [
2,
3
] |
Vasya is currently at a car rental service, and he wants to reach cinema. The film he has bought a ticket for starts in t minutes. There is a straight road of length s from the service to the cinema. Let's introduce a coordinate system so that the car rental service is at the point 0, and the cinema is at the point s.There are k gas stations along the road, and at each of them you can fill a car with any amount of fuel for free! Consider that this operation doesn't take any time, i.e. is carried out instantly.There are n cars in the rental service, i-th of them is characterized with two integers ci and vi — the price of this car rent and the capacity of its fuel tank in liters. It's not allowed to fuel a car with more fuel than its tank capacity vi. All cars are completely fueled at the car rental service.Each of the cars can be driven in one of two speed modes: normal or accelerated. In the normal mode a car covers 1 kilometer in 2 minutes, and consumes 1 liter of fuel. In the accelerated mode a car covers 1 kilometer in 1 minutes, but consumes 2 liters of fuel. The driving mode can be changed at any moment and any number of times.Your task is to choose a car with minimum price such that Vasya can reach the cinema before the show starts, i.e. not later than in t minutes. Assume that all cars are completely fueled initially. | Input: ['3 1 8 1010 85 711 93'] Output:['10'] | [
2,
4
] |
Polycarp is an experienced participant in Codehorses programming contests. Now he wants to become a problemsetter.He sent to the coordinator a set of n problems. Each problem has it's quality, the quality of the i-th problem is ai (ai can be positive, negative or equal to zero). The problems are ordered by expected difficulty, but the difficulty is not related to the quality in any way. The easiest problem has index 1, the hardest problem has index n.The coordinator's mood is equal to q now. After reading a problem, the mood changes by it's quality. It means that after the coordinator reads a problem with quality b, the value b is added to his mood. The coordinator always reads problems one by one from the easiest to the hardest, it's impossible to change the order of the problems.If after reading some problem the coordinator's mood becomes negative, he immediately stops reading and rejects the problemset.Polycarp wants to remove the minimum number of problems from his problemset to make the coordinator's mood non-negative at any moment of time. Polycarp is not sure about the current coordinator's mood, but he has m guesses "the current coordinator's mood q = bi".For each of m guesses, find the minimum number of problems Polycarp needs to remove so that the coordinator's mood will always be greater or equal to 0 while he reads problems from the easiest of the remaining problems to the hardest. | Input: ['6 38 -5 -4 1 -7 40 7 3'] Output:['201'] | [
2,
4
] |
The organizers of a programming contest have decided to present t-shirts to participants. There are six different t-shirts sizes in this problem: S, M, L, XL, XXL, XXXL (sizes are listed in increasing order). The t-shirts are already prepared. For each size from S to XXXL you are given the number of t-shirts of this size.During the registration, the organizers asked each of the n participants about the t-shirt size he wants. If a participant hesitated between two sizes, he could specify two neighboring sizes — this means that any of these two sizes suits him.Write a program that will determine whether it is possible to present a t-shirt to each participant of the competition, or not. Of course, each participant should get a t-shirt of proper size: the size he wanted, if he specified one size; any of the two neibouring sizes, if he specified two sizes. If it is possible, the program should find any valid distribution of the t-shirts. | Input: ['0 1 0 1 1 03XLS,MXL,XXL'] Output:['YESXLMXXL'] | [
2
] |
This is an interactive problem. You should use flush operation after each printed line. For example, in C++ you should use fflush(stdout), in Java you should use System.out.flush(), and in Pascal — flush(output).In this problem you should guess an array a which is unknown for you. The only information you have initially is the length n of the array a.The only allowed action is to ask the sum of two elements by their indices. Formally, you can print two indices i and j (the indices should be distinct). Then your program should read the response: the single integer equals to ai + aj.It is easy to prove that it is always possible to guess the array using at most n requests.Write a program that will guess the array a by making at most n requests. | Input: ['5\xa09\xa07\xa09\xa011\xa06\xa0'] Output:['\xa0? 1 5\xa0? 2 3\xa0? 4 1\xa0? 5 2\xa0? 3 4\xa0! 4 6 1 5 5'] | [
3
] |
Vasily has a number a, which he wants to turn into a number b. For this purpose, he can do two types of operations: multiply the current number by 2 (that is, replace the number x by 2·x); append the digit 1 to the right of current number (that is, replace the number x by 10·x + 1). You need to help Vasily to transform the number a into the number b using only the operations described above, or find that it is impossible.Note that in this task you are not required to minimize the number of operations. It suffices to find any way to transform a into b. | Input: ['2 162'] Output:['YES52 4 8 81 162 '] | [
0,
3
] |
Alice and Bonnie are sisters, but they don't like each other very much. So when some old family photos were found in the attic, they started to argue about who should receive which photos. In the end, they decided that they would take turns picking photos. Alice goes first.There are n stacks of photos. Each stack contains exactly two photos. In each turn, a player may take only a photo from the top of one of the stacks.Each photo is described by two non-negative integers a and b, indicating that it is worth a units of happiness to Alice and b units of happiness to Bonnie. Values of a and b might differ for different photos.It's allowed to pass instead of taking a photo. The game ends when all photos are taken or both players pass consecutively.The players don't act to maximize their own happiness. Instead, each player acts to maximize the amount by which her happiness exceeds her sister's. Assuming both players play optimal, find the difference between Alice's and Bonnie's happiness. That is, if there's a perfectly-played game such that Alice has x happiness and Bonnie has y happiness at the end, you should print x - y. | Input: ['212 3 4 71 15 9 1'] Output:['1'] | [
2
] |
Alfred wants to buy a toy moose that costs c dollars. The store doesn’t give change, so he must give the store exactly c dollars, no more and no less. He has n coins. To make c dollars from his coins, he follows the following algorithm: let S be the set of coins being used. S is initially empty. Alfred repeatedly adds to S the highest-valued coin he has such that the total value of the coins in S after adding the coin doesn’t exceed c. If there is no such coin, and the value of the coins in S is still less than c, he gives up and goes home. Note that Alfred never removes a coin from S after adding it.As a programmer, you might be aware that Alfred’s algorithm can fail even when there is a set of coins with value exactly c. For example, if Alfred has one coin worth 3, one coin worth 4, and two coins worth 5, and the moose costs 12, then Alfred will add both of the 5 coins to S and then give up, since adding any other coin would cause the value of the coins in S to exceed 12. Of course, Alfred could instead combine one 3 coin, one 4 coin, and one 5 coin to reach the total.Bob tried to convince Alfred that his algorithm was flawed, but Alfred didn’t believe him. Now Bob wants to give Alfred some coins (in addition to those that Alfred already has) such that Alfred’s algorithm fails. Bob can give Alfred any number of coins of any denomination (subject to the constraint that each coin must be worth a positive integer number of dollars). There can be multiple coins of a single denomination. He would like to minimize the total value of the coins he gives Alfred. Please find this minimum value. If there is no solution, print "Greed is good". You can assume that the answer, if it exists, is positive. In other words, Alfred's algorithm will work if Bob doesn't give him any coins. | Input: ['123534'] Output:['5'] | [
0,
2
] |
One tradition of ACM-ICPC contests is that a team gets a balloon for every solved problem. We assume that the submission time doesn't matter and teams are sorted only by the number of balloons they have. It means that one's place is equal to the number of teams with more balloons, increased by 1. For example, if there are seven teams with more balloons, you get the eight place. Ties are allowed.You should know that it's important to eat before a contest. If the number of balloons of a team is greater than the weight of this team, the team starts to float in the air together with their workstation. They eventually touch the ceiling, what is strictly forbidden by the rules. The team is then disqualified and isn't considered in the standings.A contest has just finished. There are n teams, numbered 1 through n. The i-th team has ti balloons and weight wi. It's guaranteed that ti doesn't exceed wi so nobody floats initially.Limak is a member of the first team. He doesn't like cheating and he would never steal balloons from other teams. Instead, he can give his balloons away to other teams, possibly making them float. Limak can give away zero or more balloons of his team. Obviously, he can't give away more balloons than his team initially has.What is the best place Limak can get? | Input: ['820 100032 3740 100045 5016 1616 1614 10002 1000'] Output:['3'] | [
2
] |
Let’s define a grid to be a set of tiles with 2 rows and 13 columns. Each tile has an English letter written in it. The letters don't have to be unique: there might be two or more tiles with the same letter written on them. Here is an example of a grid: ABCDEFGHIJKLMNOPQRSTUVWXYZ We say that two tiles are adjacent if they share a side or a corner. In the example grid above, the tile with the letter 'A' is adjacent only to the tiles with letters 'B', 'N', and 'O'. A tile is not adjacent to itself.A sequence of tiles is called a path if each tile in the sequence is adjacent to the tile which follows it (except for the last tile in the sequence, which of course has no successor). In this example, "ABC" is a path, and so is "KXWIHIJK". "MAB" is not a path because 'M' is not adjacent to 'A'. A single tile can be used more than once by a path (though the tile cannot occupy two consecutive places in the path because no tile is adjacent to itself).You’re given a string s which consists of 27 upper-case English letters. Each English letter occurs at least once in s. Find a grid that contains a path whose tiles, viewed in the order that the path visits them, form the string s. If there’s no solution, print "Impossible" (without the quotes). | Input: ['ABCDEFGHIJKLMNOPQRSGTUVWXYZ'] Output:['YXWVUTGHIJKLMZABCDEFSRQPON'] | [
0
] |
A new airplane SuperPuperJet has an infinite number of rows, numbered with positive integers starting with 1 from cockpit to tail. There are six seats in each row, denoted with letters from 'a' to 'f'. Seats 'a', 'b' and 'c' are located to the left of an aisle (if one looks in the direction of the cockpit), while seats 'd', 'e' and 'f' are located to the right. Seats 'a' and 'f' are located near the windows, while seats 'c' and 'd' are located near the aisle. It's lunch time and two flight attendants have just started to serve food. They move from the first rows to the tail, always maintaining a distance of two rows from each other because of the food trolley. Thus, at the beginning the first attendant serves row 1 while the second attendant serves row 3. When both rows are done they move one row forward: the first attendant serves row 2 while the second attendant serves row 4. Then they move three rows forward and the first attendant serves row 5 while the second attendant serves row 7. Then they move one row forward again and so on.Flight attendants work with the same speed: it takes exactly 1 second to serve one passenger and 1 second to move one row forward. Each attendant first serves the passengers on the seats to the right of the aisle and then serves passengers on the seats to the left of the aisle (if one looks in the direction of the cockpit). Moreover, they always serve passengers in order from the window to the aisle. Thus, the first passenger to receive food in each row is located in seat 'f', and the last one — in seat 'c'. Assume that all seats are occupied.Vasya has seat s in row n and wants to know how many seconds will pass before he gets his lunch. | Input: ['1f'] Output:['1'] | [
3
] |
You are given an undirected graph, constisting of n vertices and m edges. Each edge of the graph has some non-negative integer written on it.Let's call a triple (u, v, s) interesting, if 1 ≤ u < v ≤ n and there is a path (possibly non-simple, i.e. it can visit the same vertices and edges multiple times) between vertices u and v such that xor of all numbers written on the edges of this path is equal to s. When we compute the value s for some path, each edge is counted in xor as many times, as it appear on this path. It's not hard to prove that there are finite number of such triples.Calculate the sum over modulo 109 + 7 of the values of s over all interesting triples. | Input: ['4 41 2 11 3 22 3 33 4 1'] Output:['12'] | [
3
] |
There are n cities located along the one-way road. Cities are numbered from 1 to n in the direction of the road.The i-th city had produced pi units of goods. No more than si units of goods can be sold in the i-th city.For each pair of cities i and j such that 1 ≤ i < j ≤ n you can no more than once transport no more than c units of goods from the city i to the city j. Note that goods can only be transported from a city with a lesser index to the city with a larger index. You can transport goods between cities in any order.Determine the maximum number of produced goods that can be sold in total in all the cities after a sequence of transportations. | Input: ['3 01 2 33 2 1'] Output:['4'] | [
2
] |
You are given a string s, consisting of lowercase English letters, and the integer m.One should choose some symbols from the given string so that any contiguous subsegment of length m has at least one selected symbol. Note that here we choose positions of symbols, not the symbols themselves.Then one uses the chosen symbols to form a new string. All symbols from the chosen position should be used, but we are allowed to rearrange them in any order.Formally, we choose a subsequence of indices 1 ≤ i1 < i2 < ... < it ≤ |s|. The selected sequence must meet the following condition: for every j such that 1 ≤ j ≤ |s| - m + 1, there must be at least one selected index that belongs to the segment [j, j + m - 1], i.e. there should exist a k from 1 to t, such that j ≤ ik ≤ j + m - 1.Then we take any permutation p of the selected indices and form a new string sip1sip2... sipt.Find the lexicographically smallest string, that can be obtained using this procedure. | Input: ['3cbabc'] Output:['a'] | [
2
] |
There are k sensors located in the rectangular room of size n × m meters. The i-th sensor is located at point (xi, yi). All sensors are located at distinct points strictly inside the rectangle. Opposite corners of the room are located at points (0, 0) and (n, m). Walls of the room are parallel to coordinate axes.At the moment 0, from the point (0, 0) the laser ray is released in the direction of point (1, 1). The ray travels with a speed of meters per second. Thus, the ray will reach the point (1, 1) in exactly one second after the start.When the ray meets the wall it's reflected by the rule that the angle of incidence is equal to the angle of reflection. If the ray reaches any of the four corners, it immediately stops.For each sensor you have to determine the first moment of time when the ray will pass through the point where this sensor is located. If the ray will never pass through this point, print - 1 for such sensors. | Input: ['3 3 41 11 22 12 2'] Output:['1-1-12'] | [
2,
3
] |
You are given a table consisting of n rows and m columns.Numbers in each row form a permutation of integers from 1 to m.You are allowed to pick two elements in one row and swap them, but no more than once for each row. Also, no more than once you are allowed to pick two columns and swap them. Thus, you are allowed to perform from 0 to n + 1 actions in total. Operations can be performed in any order.You have to check whether it's possible to obtain the identity permutation 1, 2, ..., m in each row. In other words, check if one can perform some of the operation following the given rules and make each row sorted in increasing order. | Input: ['2 41 3 2 41 3 4 2'] Output:['YES'] | [
0,
2,
3
] |
You are given an undirected connected graph consisting of n vertices and m edges. There are no loops and no multiple edges in the graph.You are also given two distinct vertices s and t, and two values ds and dt. Your task is to build any spanning tree of the given graph (note that the graph is not weighted), such that the degree of the vertex s doesn't exceed ds, and the degree of the vertex t doesn't exceed dt, or determine, that there is no such spanning tree.The spanning tree of the graph G is a subgraph which is a tree and contains all vertices of the graph G. In other words, it is a connected graph which contains n - 1 edges and can be obtained by removing some of the edges from G.The degree of a vertex is the number of edges incident to this vertex. | Input: ['3 31 22 33 11 2 1 1'] Output:['Yes3 21 3'] | [
2
] |
There are n cities and m two-way roads in Berland, each road connects two cities. It is known that there is no more than one road connecting each pair of cities, and there is no road which connects the city with itself. It is possible that there is no way to get from one city to some other city using only these roads.The road minister decided to make a reform in Berland and to orient all roads in the country, i.e. to make each road one-way. The minister wants to maximize the number of cities, for which the number of roads that begins in the city equals to the number of roads that ends in it. | Input: ['25 52 14 52 31 33 57 23 74 2'] Output:['31 33 55 43 22 132 43 7'] | [
2
] |
The map of Berland is a rectangle of the size n × m, which consists of cells of size 1 × 1. Each cell is either land or water. The map is surrounded by the ocean. Lakes are the maximal regions of water cells, connected by sides, which are not connected with the ocean. Formally, lake is a set of water cells, such that it's possible to get from any cell of the set to any other without leaving the set and moving only to cells adjacent by the side, none of them is located on the border of the rectangle, and it's impossible to add one more water cell to the set such that it will be connected with any other cell.You task is to fill up with the earth the minimum number of water cells so that there will be exactly k lakes in Berland. Note that the initial number of lakes on the map is not less than k. | Input: ['5 4 1*****..*******.*..**'] Output:['1*****..*********..**'] | [
2
] |
Polycarp is a music editor at the radio station. He received a playlist for tomorrow, that can be represented as a sequence a1, a2, ..., an, where ai is a band, which performs the i-th song. Polycarp likes bands with the numbers from 1 to m, but he doesn't really like others. We define as bj the number of songs the group j is going to perform tomorrow. Polycarp wants to change the playlist in such a way that the minimum among the numbers b1, b2, ..., bm will be as large as possible.Find this maximum possible value of the minimum among the bj (1 ≤ j ≤ m), and the minimum number of changes in the playlist Polycarp needs to make to achieve it. One change in the playlist is a replacement of the performer of the i-th song with any other group. | Input: ['4 21 2 3 2'] Output:['2 11 2 1 2 '] | [
2
] |
There are three friend living on the straight line Ox in Lineland. The first friend lives at the point x1, the second friend lives at the point x2, and the third friend lives at the point x3. They plan to celebrate the New Year together, so they need to meet at one point. What is the minimum total distance they have to travel in order to meet at some point and celebrate the New Year?It's guaranteed that the optimal answer is always integer. | Input: ['7 1 4'] Output:['6'] | [
3
] |
You are given a set Y of n distinct positive integers y1, y2, ..., yn.Set X of n distinct positive integers x1, x2, ..., xn is said to generate set Y if one can transform X to Y by applying some number of the following two operation to integers in X: Take any integer xi and multiply it by two, i.e. replace xi with 2·xi. Take any integer xi, multiply it by two and add one, i.e. replace xi with 2·xi + 1. Note that integers in X are not required to be distinct after each operation.Two sets of distinct integers X and Y are equal if they are equal as sets. In other words, if we write elements of the sets in the array in the increasing order, these arrays would be equal.Note, that any set of integers (or its permutation) generates itself.You are given a set Y and have to find a set X that generates Y and the maximum element of X is mininum possible. | Input: ['51 2 3 4 5'] Output:['4 5 2 3 1 '] | [
2,
4
] |
You are given a broken clock. You know, that it is supposed to show time in 12- or 24-hours HH:MM format. In 12-hours format hours change from 1 to 12, while in 24-hours it changes from 0 to 23. In both formats minutes change from 0 to 59.You are given a time in format HH:MM that is currently displayed on the broken clock. Your goal is to change minimum number of digits in order to make clocks display the correct time in the given format.For example, if 00:99 is displayed, it is enough to replace the second 9 with 3 in order to get 00:39 that is a correct time in 24-hours format. However, to make 00:99 correct in 12-hours format, one has to change at least two digits. Additionally to the first change one can replace the second 0 with 1 and obtain 01:39. | Input: ['2417:30'] Output:['17:30'] | [
0
] |
Once Danil the student was returning home from tram stop lately by straight road of length L. The stop is located at the point x = 0, but the Danil's home — at the point x = L. Danil goes from x = 0 to x = L with a constant speed and does not change direction of movement.There are n street lights at the road, each of which lights some continuous segment of the road. All of the n lightened segments do not share common points.Danil loves to sing, thus he wants to sing his favourite song over and over again during his walk. As soon as non-lightened segments of the road scare him, he sings only when he goes through the lightened segments.Danil passes distance p while performing his favourite song once. Danil can't start another performance if the segment passed while performing is not fully lightened. Moreover, if Danil has taken a pause between two performances, he is not performing while not having passed a segment of length at least t. Formally, Danil can start single performance at a point x only if every point of segment [x, x + p] is lightened; If Danil has finished performing at a point x + p, then the next performance can be started only at a point y such that y = x + p or y ≥ x + p + t satisfying the statement under the point 1. Blue half-circles denote performances. Please note that just after Danil has taken a pause in performing, he has not sang for a path of length of at least t. Determine how many times Danil can perform his favourite song during his walk from x = 0 to x = L.Please note that Danil does not break a single performance, thus, started singing another time, he finishes singing when having a segment of length of p passed from the performance start point. | Input: ['17 2 2 60 913 17'] Output:['5'] | [
4
] |
Recently Maxim has found an array of n integers, needed by no one. He immediately come up with idea of changing it: he invented positive integer x and decided to add or subtract it from arbitrary array elements. Formally, by applying single operation Maxim chooses integer i (1 ≤ i ≤ n) and replaces the i-th element of array ai either with ai + x or with ai - x. Please note that the operation may be applied more than once to the same position.Maxim is a curious minimalis, thus he wants to know what is the minimum value that the product of all array elements (i.e. ) can reach, if Maxim would apply no more than k operations to it. Please help him in that. | Input: ['5 3 15 4 3 5 2'] Output:['5 4 3 5 -1 '] | [
2,
3
] |
Vanya is managed to enter his favourite site Codehorses. Vanya uses n distinct passwords for sites at all, however he can't remember which one exactly he specified during Codehorses registration.Vanya will enter passwords in order of non-decreasing their lengths, and he will enter passwords of same length in arbitrary order. Just when Vanya will have entered the correct password, he is immediately authorized on the site. Vanya will not enter any password twice.Entering any passwords takes one second for Vanya. But if Vanya will enter wrong password k times, then he is able to make the next try only 5 seconds after that. Vanya makes each try immediately, that is, at each moment when Vanya is able to enter password, he is doing that.Determine how many seconds will Vanya need to enter Codehorses in the best case for him (if he spends minimum possible number of second) and in the worst case (if he spends maximum possible amount of seconds). | Input: ['5 2cbaabcbb1abCABCabc'] Output:['1 15'] | [
3
] |
The closing ceremony of Squanch Code Cup is held in the big hall with n × m seats, arranged in n rows, m seats in a row. Each seat has two coordinates (x, y) (1 ≤ x ≤ n, 1 ≤ y ≤ m). There are two queues of people waiting to enter the hall: k people are standing at (0, 0) and n·m - k people are standing at (0, m + 1). Each person should have a ticket for a specific seat. If person p at (x, y) has ticket for seat (xp, yp) then he should walk |x - xp| + |y - yp| to get to his seat.Each person has a stamina — the maximum distance, that the person agrees to walk. You should find out if this is possible to distribute all n·m tickets in such a way that each person has enough stamina to get to their seat. | Input: ['2 23 3 3 21 3'] Output:['YES'] | [
2
] |
Anatoly lives in the university dorm as many other students do. As you know, cockroaches are also living there together with students. Cockroaches might be of two colors: black and red. There are n cockroaches living in Anatoly's room.Anatoly just made all his cockroaches to form a single line. As he is a perfectionist, he would like the colors of cockroaches in the line to alternate. He has a can of black paint and a can of red paint. In one turn he can either swap any two cockroaches, or take any single cockroach and change it's color.Help Anatoly find out the minimum number of turns he needs to make the colors of cockroaches in the line alternate. | Input: ['5rbbrr'] Output:['1'] | [
2
] |
Sasha has an array of integers a1, a2, ..., an. You have to perform m queries. There might be queries of two types: 1 l r x — increase all integers on the segment from l to r by values x; 2 l r — find , where f(x) is the x-th Fibonacci number. As this number may be large, you only have to find it modulo 109 + 7. In this problem we define Fibonacci numbers as follows: f(1) = 1, f(2) = 1, f(x) = f(x - 1) + f(x - 2) for all x > 2.Sasha is a very talented boy and he managed to perform all queries in five seconds. Will you be able to write the program that performs as well as Sasha? | Input: ['5 41 1 2 1 12 1 51 2 4 22 2 42 1 5'] Output:['579'] | [
3
] |
Efim just received his grade for the last test. He studies in a special school and his grade can be equal to any positive decimal fraction. First he got disappointed, as he expected a way more pleasant result. Then, he developed a tricky plan. Each second, he can ask his teacher to round the grade at any place after the decimal point (also, he can ask to round to the nearest integer). There are t seconds left till the end of the break, so Efim has to act fast. Help him find what is the maximum grade he can get in no more than t seconds. Note, that he can choose to not use all t seconds. Moreover, he can even choose to not round the grade at all.In this problem, classic rounding rules are used: while rounding number to the n-th digit one has to take a look at the digit n + 1. If it is less than 5 than the n-th digit remain unchanged while all subsequent digits are replaced with 0. Otherwise, if the n + 1 digit is greater or equal to 5, the digit at the position n is increased by 1 (this might also change some other digits, if this one was equal to 9) and all subsequent digits are replaced with 0. At the end, all trailing zeroes are thrown away.For example, if the number 1.14 is rounded to the first decimal place, the result is 1.1, while if we round 1.5 to the nearest integer, the result is 2. Rounding number 1.299996121 in the fifth decimal place will result in number 1.3. | Input: ['6 110.245'] Output:['10.25'] | [
3
] |
Welcome to the world of Pokermon, yellow little mouse-like creatures, who absolutely love playing poker! Yeah, right… In the ensuing Pokermon League, there are n registered Pokermon trainers, and t existing trainer teams each of which belongs to one of two conferences. Since there is a lot of jealousy between trainers, there are e pairs of trainers who hate each other. Their hate is mutual, there are no identical pairs among these, and no trainer hates himself (the world of Pokermon is a joyful place!). Each trainer has a wish-list of length li of teams he’d like to join.Your task is to divide players into teams and the teams into two conferences, so that: each trainer belongs to exactly one team; no team is in both conferences; total hate between conferences is at least e / 2; every trainer is in a team from his wish-list. Total hate between conferences is calculated as the number of pairs of trainers from teams from different conferences who hate each other. | Input: ['4 31 22 34 1161 2 3 4 5 6 7 8 9 10 11 12 13 14 16 15162 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18162 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19161 2 3 4 5 6 7 8 9 10 11 12 13 14 16 19'] Output:['16 15 19 14 2 2 2 1 1 1 2 1 1 2 1 1 1 2 2 1 1 1 1 '] | [
3
] |
R3D3 spent some time on an internship in MDCS. After earning enough money, he decided to go on a holiday somewhere far, far away. He enjoyed suntanning, drinking alcohol-free cocktails and going to concerts of popular local bands. While listening to "The White Buttons" and their hit song "Dacan the Baker", he met another robot for whom he was sure is the love of his life. Well, his summer, at least. Anyway, R3D3 was too shy to approach his potential soulmate, so he decided to write her a love letter. However, he stumbled upon a problem. Due to a terrorist threat, the Intergalactic Space Police was monitoring all letters sent in the area. Thus, R3D3 decided to invent his own alphabet, for which he was sure his love would be able to decipher.There are n letters in R3D3’s alphabet, and he wants to represent each letter as a sequence of '0' and '1', so that no letter’s sequence is a prefix of another letter's sequence. Since the Intergalactic Space Communications Service has lately introduced a tax for invented alphabets, R3D3 must pay a certain amount of money for each bit in his alphabet’s code (check the sample test for clarifications). He is too lovestruck to think clearly, so he asked you for help.Given the costs c0 and c1 for each '0' and '1' in R3D3’s alphabet, respectively, you should come up with a coding for the alphabet (with properties as above) with minimum total cost. | Input: ['4 1 2'] Output:['12'] | [
2
] |
The Prodiggers are quite a cool band and for this reason, they have been the surprise guest at the ENTER festival for the past 80 years. At the beginning of their careers, they weren’t so successful, so they had to spend time digging channels to earn money; hence the name. Anyway, they like to tour a lot and have surprising amounts of energy to do extremely long tours. However, they hate spending two consecutive days without having a concert, so they would like to avoid it.A tour is defined by a sequence of concerts and days-off. You need to count in how many ways The Prodiggers can select k different tours of the same length between l and r.For example if k = 2, l = 1 and r = 2, if we define concert day as {1} and day-off as {0}, here are all possible tours: {0}, {1}, {00}, {01}, {10}, {11}. But tour 00 can not be selected because it has 2 days-off in a row. Now, we need to count in how many ways we can select k = 2 tours of the same length in range [1;2]. Here they are: {0,1}; {01,10}; {01,11}; {10,11}.Since their schedule is quite busy, they want you to tell them in how many ways can do that, modulo 1 000 000 007 (109 + 7). | Input: ['1 1 2'] Output:['5'] | [
3
] |
ZS the Coder loves to read the dictionary. He thinks that a word is nice if there exists a substring (contiguous segment of letters) of it of length 26 where each letter of English alphabet appears exactly once. In particular, if the string has length strictly less than 26, no such substring exists and thus it is not nice.Now, ZS the Coder tells you a word, where some of its letters are missing as he forgot them. He wants to determine if it is possible to fill in the missing letters so that the resulting word is nice. If it is possible, he needs you to find an example of such a word as well. Can you help him? | Input: ['ABC??FGHIJK???OPQR?TUVWXY?'] Output:['ABCDEFGHIJKLMNOPQRZTUVWXYS'] | [
2
] |
ZS the Coder is given two permutations p and q of {1, 2, ..., n}, but some of their elements are replaced with 0. The distance between two permutations p and q is defined as the minimum number of moves required to turn p into q. A move consists of swapping exactly 2 elements of p.ZS the Coder wants to determine the number of ways to replace the zeros with positive integers from the set {1, 2, ..., n} such that p and q are permutations of {1, 2, ..., n} and the distance between p and q is exactly k.ZS the Coder wants to find the answer for all 0 ≤ k ≤ n - 1. Can you help him? | Input: ['31 0 00 2 0'] Output:['1 2 1 '] | [
3
] |
ZS the Coder has drawn an undirected graph of n vertices numbered from 0 to n - 1 and m edges between them. Each edge of the graph is weighted, each weight is a positive integer.The next day, ZS the Coder realized that some of the weights were erased! So he wants to reassign positive integer weight to each of the edges which weights were erased, so that the length of the shortest path between vertices s and t in the resulting graph is exactly L. Can you help him? | Input: ['5 5 13 0 40 1 52 1 23 2 31 4 04 3 4'] Output:['YES0 1 52 1 23 2 31 4 84 3 4'] | [
4
] |
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.When ZS the Coder is at level k, he can : Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k. Press the '' button. Let the number on the screen be x. After pressing this button, the number becomes . After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m. Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.ZS the Coder needs your help in beating the game — he wants to reach level n + 1. In other words, he needs to press the '' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '' button at each level. Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses. | Input: ['3'] Output:['141646'] | [
3
] |
Today an outstanding event is going to happen in the forest — hedgehog Filya will come to his old fried Sonya!Sonya is an owl and she sleeps during the day and stay awake from minute l1 to minute r1 inclusive. Also, during the minute k she prinks and is unavailable for Filya.Filya works a lot and he plans to visit Sonya from minute l2 to minute r2 inclusive.Calculate the number of minutes they will be able to spend together. | Input: ['1 10 9 20 1'] Output:['2'] | [
3
] |
Owl Sonya decided to become a partymaker. To train for this role she gather all her owl friends in the country house. There are m chairs located in a circle and consequently numbered with integers from 1 to m. Thus, chairs i and i + 1 are neighbouring for all i from 1 to m - 1. Chairs 1 and m are also neighbouring. Some chairs are occupied by her friends. There are n friends in total. No two friends occupy the same chair. Rules are the following: Each participant removes from the game the chair he is currently sitting on. Each of the participants choose a direction that she will follow: clockwise (indices increase, from m goes to 1) and counter-clockwise (indices decrease, from 1 goes to m). This direction may coincide or be different for any pair of owls. Each turn all guests move one step in the chosen directions. If some guest move to the position with a chair there, he removes this chair from the game. Game ends if there are no more chairs left in the game. Owls are very busy and want to get rid of the game as soon as possible. They cooperate to pick the direction. Your goal is to find the minimum number o moves required to finish the game. | Input: ['631 3 5'] Output:['1'] | [
4
] |
Owl Sonya gave a huge lake puzzle of size n × m to hedgehog Filya as a birthday present. Friends immediately started to assemble the puzzle, but some parts of it turned out to be empty — there was no picture on them. Parts with picture on it are denoted by 1, while empty parts are denoted by 0. Rows of the puzzle are numbered from top to bottom with integers from 1 to n, while columns are numbered from left to right with integers from 1 to m.Animals decided to complete the picture and play with it, as it might be even more fun! Owl and hedgehog ask each other some queries. Each query is provided by four integers x1, y1, x2, y2 which define the rectangle, where (x1, y1) stands for the coordinates of the up left cell of the rectangle, while (x2, y2) stands for the coordinates of the bottom right cell. The answer to the query is the size of the maximum square consisting of picture parts only (only parts denoted by 1) and located fully inside the query rectangle.Help Sonya and Filya answer t queries. | Input: ['3 41 1 0 10 1 1 00 1 1 051 1 2 32 1 3 23 2 3 41 1 3 41 2 3 4'] Output:['11122'] | [
4
] |
Filya just learned new geometry object — rectangle. He is given a field consisting of n × n unit cells. Rows are numbered from bottom to top with integer from 1 to n. Columns are numbered from left to right with integers from 1 to n. Cell, located at the intersection of the row r and column c is denoted as (r, c). Filya has painted two rectangles, such that their sides are parallel to coordinate axes and each cell lies fully inside or fully outside each of them. Moreover, no cell lies in both rectangles.Later, hedgehog Filya became interested in the location of his rectangles but was unable to find the sheet of paper they were painted on. They were taken by Sonya and now she wants to play a little game with Filya. He tells her a query rectangle and she replies with the number of initial rectangles that lie fully inside the given query rectangle. The query rectangle should match the same conditions as initial rectangles. Rectangle lies fully inside the query if each o its cells lies inside the query.Filya knows Sonya really well, so is sure that if he asks more than 200 questions she will stop to reply. | Input: ['521011101'] Output:['? 1 1 5 5? 1 1 3 3? 1 1 3 1? 2 2 2 2? 3 3 5 5? 3 3 3 5? 3 3 3 4? 3 4 3 5! 2 2 2 2 3 4 3 5'] | [
4
] |
There are n casinos lined in a row. If Memory plays at casino i, he has probability pi to win and move to the casino on the right (i + 1) or exit the row (if i = n), and a probability 1 - pi to lose and move to the casino on the left (i - 1) or also exit the row (if i = 1). We say that Memory dominates on the interval i... j if he completes a walk such that, He starts on casino i. He never looses in casino i. He finishes his walk by winning in casino j. Note that Memory can still walk left of the 1-st casino and right of the casino n and that always finishes the process.Now Memory has some requests, in one of the following forms: 1 i a b: Set . 2 l r: Print the probability that Memory will dominate on the interval l... r, i.e. compute the probability that Memory will first leave the segment l... r after winning at casino r, if she starts in casino l. It is guaranteed that at any moment of time p is a non-decreasing sequence, i.e. pi ≤ pi + 1 for all i from 1 to n - 1.Please help Memory by answering all his requests! | Input: ['3 131 31 22 32 1 12 1 22 1 32 2 22 2 32 3 31 2 2 32 1 12 1 22 1 32 2 22 2 32 3 3'] Output:['0.33333333330.20000000000.16666666670.50000000000.40000000000.66666666670.33333333330.25000000000.22222222220.66666666670.57142857140.6666666667'] | [
3
] |
Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among - k, - k + 1, - k + 2, ..., - 2, - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)2t games in total. Since the answer can be very large, you should print it modulo 109 + 7. Please solve this problem for Memory. | Input: ['1 2 2 1'] Output:['6'] | [
3
] |
Memory is now interested in the de-evolution of objects, specifically triangles. He starts with an equilateral triangle of side length x, and he wishes to perform operations to obtain an equilateral triangle of side length y.In a single second, he can modify the length of a single side of the current triangle such that it remains a non-degenerate triangle (triangle of positive area). At any moment of time, the length of each side should be integer.What is the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y? | Input: ['6 3'] Output:['4'] | [
2,
3
] |
There are n integers b1, b2, ..., bn written in a row. For all i from 1 to n, values ai are defined by the crows performing the following procedure: The crow sets ai initially 0. The crow then adds bi to ai, subtracts bi + 1, adds the bi + 2 number, and so on until the n'th number. Thus, ai = bi - bi + 1 + bi + 2 - bi + 3.... Memory gives you the values a1, a2, ..., an, and he now wants you to find the initial numbers b1, b2, ..., bn written in the row? Can you do it? | Input: ['56 -4 8 -2 3'] Output:['2 4 6 1 3 '] | [
3
] |
ZS the Coder has recently found an interesting concept called the Birthday Paradox. It states that given a random set of 23 people, there is around 50% chance that some two of them share the same birthday. ZS the Coder finds this very interesting, and decides to test this with the inhabitants of Udayland.In Udayland, there are 2n days in a year. ZS the Coder wants to interview k people from Udayland, each of them has birthday in one of 2n days (each day with equal probability). He is interested in the probability of at least two of them have the birthday at the same day. ZS the Coder knows that the answer can be written as an irreducible fraction . He wants to find the values of A and B (he does not like to deal with floating point numbers). Can you help him? | Input: ['3 2'] Output:['1 8'] | [
3
] |
ZS the Coder and Chris the Baboon has explored Udayland for quite some time. They realize that it consists of n towns numbered from 1 to n. There are n directed roads in the Udayland. i-th of them goes from town i to some other town ai (ai ≠ i). ZS the Coder can flip the direction of any road in Udayland, i.e. if it goes from town A to town B before the flip, it will go from town B to town A after.ZS the Coder considers the roads in the Udayland confusing, if there is a sequence of distinct towns A1, A2, ..., Ak (k > 1) such that for every 1 ≤ i < k there is a road from town Ai to town Ai + 1 and another road from town Ak to town A1. In other words, the roads are confusing if some of them form a directed cycle of some towns.Now ZS the Coder wonders how many sets of roads (there are 2n variants) in initial configuration can he choose to flip such that after flipping each road in the set exactly once, the resulting network will not be confusing.Note that it is allowed that after the flipping there are more than one directed road from some town and possibly some towns with no roads leading out of it, or multiple roads between any pair of cities. | Input: ['32 3 1'] Output:['6'] | [
3
] |
ZS the Coder and Chris the Baboon are travelling to Udayland! To get there, they have to get on the special IOI bus. The IOI bus has n rows of seats. There are 4 seats in each row, and the seats are separated into pairs by a walkway. When ZS and Chris came, some places in the bus was already occupied.ZS and Chris are good friends. They insist to get a pair of neighbouring empty seats. Two seats are considered neighbouring if they are in the same row and in the same pair. Given the configuration of the bus, can you help ZS and Chris determine where they should sit? | Input: ['6OO|OXXO|XXOX|OOXX|OXOO|OOOO|XX'] Output:['YES++|OXXO|XXOX|OOXX|OXOO|OOOO|XX'] | [
0
] |
You should process m queries over a set D of strings. Each query is one of three kinds: Add a string s to the set D. It is guaranteed that the string s was not added before. Delete a string s from the set D. It is guaranteed that the string s is in the set D. For the given string s find the number of occurrences of the strings from the set D. If some string p from D has several occurrences in s you should count all of them. Note that you should solve the problem in online mode. It means that you can't read the whole input at once. You can read each query only after writing the answer for the last query of the third type. Use functions fflush in C++ and BufferedWriter.flush in Java languages after each writing in your program. | Input: ['51 abc3 abcabc2 abc1 aba3 abababc'] Output:['22'] | [
0
] |
You are given two arithmetic progressions: a1k + b1 and a2l + b2. Find the number of integers x such that L ≤ x ≤ R and x = a1k' + b1 = a2l' + b2, for some integers k', l' ≥ 0. | Input: ['2 0 3 3 5 21'] Output:['3'] | [
3
] |
Find an n × n matrix with different numbers from 1 to n2, so the sum in each row, column and both main diagonals are odd. | Input: ['1'] Output:['1'] | [
3
] |
You are given n points on a line with their coordinates xi. Find the point x so the sum of distances to the given points is minimal. | Input: ['41 2 3 4'] Output:['2'] | [
0
] |
Vasya takes part in the orienteering competition. There are n checkpoints located along the line at coordinates x1, x2, ..., xn. Vasya starts at the point with coordinate a. His goal is to visit at least n - 1 checkpoint in order to finish the competition. Participant are allowed to visit checkpoints in arbitrary order.Vasya wants to pick such checkpoints and the order of visiting them that the total distance travelled is minimized. He asks you to calculate this minimum possible value. | Input: ['3 101 7 12'] Output:['7'] | [
2
] |
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