Split (1)

train · 10k rows

id stringlengths 11 14	content stringlengths 424 1.17M
apps_data_300	Translator's note: in Russia's most widespread grading system, there are four grades: 5, 4, 3, 2, the higher the better, roughly corresponding to A, B, C and F respectively in American grading system. The term is coming to an end and students start thinking about their grades. Today, a professor told his students that...
apps_data_301	Given 2 integers $u$ and $v$, find the shortest array such that bitwise-xor of its elements is $u$, and the sum of its elements is $v$. -----Input----- The only line contains 2 integers $u$ and $v$ $(0 \le u,v \le 10^{18})$. -----Output----- If there's no array that satisfies the condition, print "-1". Otherwise:...
apps_data_302	Prof. Vasechkin wants to represent positive integer n as a sum of addends, where each addends is an integer number containing only 1s. For example, he can represent 121 as 121=111+11+–1. Help him to find the least number of digits 1 in such sum. -----Input----- The first line of the input contains integer n (1 ≤ n <...
apps_data_303	Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure. Bottle with potion has two values x and y written on it. These values define four moves which can be performed...
apps_data_304	This night wasn't easy on Vasya. His favorite team lost, and he didn't find himself victorious either — although he played perfectly, his teammates let him down every time. He had to win at least one more time, but the losestreak only grew longer and longer... It's no wonder he didn't get any sleep this night at all. ...
apps_data_305	A new delivery of clothing has arrived today to the clothing store. This delivery consists of $a$ ties, $b$ scarves, $c$ vests and $d$ jackets. The store does not sell single clothing items — instead, it sells suits of two types: a suit of the first type consists of one tie and one jacket; a suit of the second type ...
apps_data_306	Given an integer $x$. Your task is to find out how many positive integers $n$ ($1 \leq n \leq x$) satisfy $$n \cdot a^n \equiv b \quad (\textrm{mod}\;p),$$ where $a, b, p$ are all known constants. -----Input----- The only line contains four integers $a,b,p,x$ ($2 \leq p \leq 10^6+3$, $1 \leq a,b < p$, $1 \leq x \leq...
apps_data_307	Recently Anton found a box with digits in his room. There are k_2 digits 2, k_3 digits 3, k_5 digits 5 and k_6 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 dig...
apps_data_308	Mr. Bender has a digital table of size n × n, each cell can be switched on or off. He wants the field to have at least c switched on squares. When this condition is fulfilled, Mr Bender will be happy. We'll consider the table rows numbered from top to bottom from 1 to n, and the columns — numbered from left to right f...
apps_data_309	A little girl loves problems on bitwise operations very much. Here's one of them. You are given two integers l and r. Let's consider the values of $a \oplus b$ for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones. Expression $x \oplus y$ means applying bi...
apps_data_310	You are given a set of $2n+1$ integer points on a Cartesian plane. Points are numbered from $0$ to $2n$ inclusive. Let $P_i$ be the $i$-th point. The $x$-coordinate of the point $P_i$ equals $i$. The $y$-coordinate of the point $P_i$ equals zero (initially). Thus, initially $P_i=(i,0)$. The given points are vertices o...
apps_data_311	Masha lives in a multi-storey building, where floors are numbered with positive integers. Two floors are called adjacent if their numbers differ by one. Masha decided to visit Egor. Masha lives on the floor $x$, Egor on the floor $y$ (not on the same floor with Masha). The house has a staircase and an elevator. If Mas...
apps_data_312	One day Misha and Andrew were playing a very simple game. First, each player chooses an integer in the range from 1 to n. Let's assume that Misha chose number m, and Andrew chose number a. Then, by using a random generator they choose a random integer c in the range between 1 and n (any integer from 1 to n is chosen w...
apps_data_313	Alena has successfully passed the entrance exams to the university and is now looking forward to start studying. One two-hour lesson at the Russian university is traditionally called a pair, it lasts for two academic hours (an academic hour is equal to 45 minutes). The University works in such a way that every day it...
apps_data_314	Bran and his older sister Arya are from the same house. Bran like candies so much, so Arya is going to give him some Candies. At first, Arya and Bran have 0 Candies. There are n days, at the i-th day, Arya finds a_{i} candies in a box, that is given by the Many-Faced God. Every day she can give Bran at most 8 of her c...
apps_data_315	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...
apps_data_316	While playing with geometric figures Alex has accidentally invented a concept of a $n$-th order rhombus in a cell grid. A $1$-st order rhombus is just a square $1 \times 1$ (i.e just a cell). A $n$-th order rhombus for all $n \geq 2$ one obtains from a $n-1$-th order rhombus adding all cells which have a common side ...
apps_data_317	A word or a sentence in some language is called a pangram if all the characters of the alphabet of this language appear in it at least once. Pangrams are often used to demonstrate fonts in printing or test the output devices. You are given a string consisting of lowercase and uppercase Latin letters. Check whether thi...
apps_data_318	You are given the current time in 24-hour format hh:mm. Find and print the time after a minutes. Note that you should find only the time after a minutes, see the examples to clarify the problem statement. You can read more about 24-hour format here https://en.wikipedia.org/wiki/24-hour_clock. -----Input----- The f...
apps_data_319	You are given n switches and m lamps. The i-th switch turns on some subset of the lamps. This information is given as the matrix a consisting of n rows and m columns where a_{i}, j = 1 if the i-th switch turns on the j-th lamp and a_{i}, j = 0 if the i-th switch is not connected to the j-th lamp. Initially all m lamps...
apps_data_320	Valera has got n domino pieces in a row. Each piece consists of two halves — the upper one and the lower one. Each of the halves contains a number from 1 to 6. Valera loves even integers very much, so he wants the sum of the numbers on the upper halves and the sum of the numbers on the lower halves to be even. To do t...
apps_data_321	Alice has a lovely piece of cloth. It has the shape of a square with a side of length $a$ centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length $b$ centimeters (where $b < a$). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave ...
apps_data_322	You have n distinct points on a plane, none of them lie on OY axis. Check that there is a point after removal of which the remaining points are located on one side of the OY axis. -----Input----- The first line contains a single positive integer n (2 ≤ n ≤ 10^5). The following n lines contain coordinates of the poi...
apps_data_323	Holidays have finished. Thanks to the help of the hacker Leha, Noora managed to enter the university of her dreams which is located in a town Pavlopolis. It's well known that universities provide students with dormitory for the period of university studies. Consequently Noora had to leave Vičkopolis and move to Pavlopo...
apps_data_324	Let's call a positive integer composite if it has at least one divisor other than $1$ and itself. For example: the following numbers are composite: $1024$, $4$, $6$, $9$; the following numbers are not composite: $13$, $1$, $2$, $3$, $37$. You are given a positive integer $n$. Find two composite integers $a,b$ suc...
apps_data_325	There is a directed graph with N vertices numbered 1 to N and M edges. The i-th edge is directed from Vertex A_i to Vertex B_i, and there are C_i coins placed along that edge. Additionally, there is a button on Vertex N. We will play a game on this graph. You start the game on Vertex 1 with zero coins, and head for Ver...
apps_data_326	We have N strings of lowercase English letters: S_1, S_2, \cdots, S_N. Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice. The cost of using the string S_i once is C_i, and the...
apps_data_327	Since Grisha behaved well last year, at New Year's Eve he was visited by Ded Moroz who brought an enormous bag of gifts with him! The bag contains n sweet candies from the good ol' bakery, each labeled from 1 to n corresponding to its tastiness. No two candies have the same tastiness. The choice of candies has a direc...
apps_data_328	There are $n$ points on the plane, $(x_1,y_1), (x_2,y_2), \ldots, (x_n,y_n)$. You need to place an isosceles triangle with two sides on the coordinate axis to cover all points (a point is covered if it lies inside the triangle or on the side of the triangle). Calculate the minimum length of the shorter side of the tri...
apps_data_329	Alice likes word "nineteen" very much. She has a string s and wants the string to contain as many such words as possible. For that reason she can rearrange the letters of the string. For example, if she has string "xiineteenppnnnewtnee", she can get string "xnineteenppnineteenw", containing (the occurrences marked) tw...
apps_data_330	The weather is fine today and hence it's high time to climb the nearby pine and enjoy the landscape. The pine's trunk includes several branches, located one above another and numbered from 2 to y. Some of them (more precise, from 2 to p) are occupied by tiny vile grasshoppers which you're at war with. These grasshoppe...
apps_data_331	Zane the wizard had never loved anyone before, until he fell in love with a girl, whose name remains unknown to us. [Image] The girl lives in house m of a village. There are n houses in that village, lining in a straight line from left to right: house 1, house 2, ..., house n. The village is also well-structured: h...
apps_data_332	Nastya came to her informatics lesson, and her teacher who is, by the way, a little bit famous here gave her the following task. Two matrices $A$ and $B$ are given, each of them has size $n \times m$. Nastya can perform the following operation to matrix $A$ unlimited number of times: take any square square submatrix...
apps_data_333	While Mahmoud and Ehab were practicing for IOI, they found a problem which name was Longest common subsequence. They solved it, and then Ehab challenged Mahmoud with another problem. Given two strings a and b, find the length of their longest uncommon subsequence, which is the longest string that is a subsequence of o...
apps_data_334	A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, .... [Image] The Monster will catch them if at any point they scream at the same tim...
apps_data_335	Little C loves number «3» very much. He loves all things about it. Now he has a positive integer $n$. He wants to split $n$ into $3$ positive integers $a,b,c$, such that $a+b+c=n$ and none of the $3$ integers is a multiple of $3$. Help him to find a solution. -----Input----- A single line containing one integer $n$...
apps_data_336	Vasya works as a watchman in the gallery. Unfortunately, one of the most expensive paintings was stolen while he was on duty. He doesn't want to be fired, so he has to quickly restore the painting. He remembers some facts about it. The painting is a square 3 × 3, each cell contains a single integer from 1 to n, and di...
apps_data_337	Today's morning was exceptionally snowy. Meshanya decided to go outside and noticed a huge snowball rolling down the mountain! Luckily, there are two stones on that mountain. Initially, snowball is at height $h$ and it has weight $w$. Each second the following sequence of events happens: snowball's weights increases b...
apps_data_338	At the beginning of the school year Berland State University starts two city school programming groups, for beginners and for intermediate coders. The children were tested in order to sort them into groups. According to the results, each student got some score from 1 to m points. We know that c_1 schoolchildren got 1 p...
apps_data_339	Right now she actually isn't. But she will be, if you don't solve this problem. You are given integers n, k, A and B. There is a number x, which is initially equal to n. You are allowed to perform two types of operations: Subtract 1 from x. This operation costs you A coins. Divide x by k. Can be performed only if x...
apps_data_340	JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer $n$, you can perform the following operations zero or more times: mul $x$: multiplies $n$ by $x$ (where $x$ is an arbitrary positive integer). sqrt: replaces $n$ wi...
apps_data_341	At an arcade, Takahashi is playing a game called RPS Battle, which is played as follows: - The player plays N rounds of Rock Paper Scissors against the machine. (See Notes for the description of Rock Paper Scissors. A draw also counts as a round.) - Each time the player wins a round, depending on which hand he/she us...
apps_data_342	Let's call a string good if and only if it consists of only two types of letters — 'a' and 'b' and every two consecutive letters are distinct. For example "baba" and "aba" are good strings and "abb" is a bad string. You have $a$ strings "a", $b$ strings "b" and $c$ strings "ab". You want to choose some subset of these...
apps_data_343	Little Vova studies programming in an elite school. Vova and his classmates are supposed to write n progress tests, for each test they will get a mark from 1 to p. Vova is very smart and he can write every test for any mark, but he doesn't want to stand out from the crowd too much. If the sum of his marks for all tests...
apps_data_344	Vitya has just started learning Berlanese language. It is known that Berlanese uses the Latin alphabet. Vowel letters are "a", "o", "u", "i", and "e". Other letters are consonant. In Berlanese, there has to be a vowel after every consonant, but there can be any letter after any vowel. The only exception is a consonant...
apps_data_345	Anadi has a set of dominoes. Every domino has two parts, and each part contains some dots. For every $a$ and $b$ such that $1 \leq a \leq b \leq 6$, there is exactly one domino with $a$ dots on one half and $b$ dots on the other half. The set contains exactly $21$ dominoes. Here is an exact illustration of his set: [...
apps_data_346	'Jeopardy!' is an intellectual game where players answer questions and earn points. Company Q conducts a simplified 'Jeopardy!' tournament among the best IT companies. By a lucky coincidence, the old rivals made it to the finals: company R1 and company R2. The finals will have n questions, m of them are auction quest...
apps_data_347	Kevin Sun has just finished competing in Codeforces Round #334! The round was 120 minutes long and featured five problems with maximum point values of 500, 1000, 1500, 2000, and 2500, respectively. Despite the challenging tasks, Kevin was uncowed and bulldozed through all of them, distinguishing himself from the herd a...
apps_data_348	Alice has got addicted to a game called Sirtet recently. In Sirtet, player is given an $n \times m$ grid. Initially $a_{i,j}$ cubes are stacked up in the cell $(i,j)$. Two cells are called adjacent if they share a side. Player can perform the following operations: stack up one cube in two adjacent cells; stack up t...
apps_data_349	You are given two $n \times m$ matrices containing integers. A sequence of integers is strictly increasing if each next number is greater than the previous one. A row is strictly increasing if all numbers from left to right are strictly increasing. A column is strictly increasing if all numbers from top to bottom are s...
apps_data_350	You are given an alphabet consisting of n letters, your task is to make a string of the maximum possible length so that the following conditions are satisfied: the i-th letter occurs in the string no more than a_{i} times; the number of occurrences of each letter in the string must be distinct for all the letters th...
apps_data_351	Makes solves problems on Decoforces and lots of other different online judges. Each problem is denoted by its difficulty — a positive integer number. Difficulties are measured the same across all the judges (the problem with difficulty d on Decoforces is as hard as the problem with difficulty d on any other judge). M...
apps_data_352	Soon a school Olympiad in Informatics will be held in Berland, n schoolchildren will participate there. At a meeting of the jury of the Olympiad it was decided that each of the n participants, depending on the results, will get a diploma of the first, second or third degree. Thus, each student will receive exactly one...
apps_data_353	Every summer Vitya comes to visit his grandmother in the countryside. This summer, he got a huge wart. Every grandma knows that one should treat warts when the moon goes down. Thus, Vitya has to catch the moment when the moon is down. Moon cycle lasts 30 days. The size of the visible part of the moon (in Vitya's units...
apps_data_354	We all know that a superhero can transform to certain other superheroes. But not all Superheroes can transform to any other superhero. A superhero with name $s$ can transform to another superhero with name $t$ if $s$ can be made equal to $t$ by changing any vowel in $s$ to any other vowel and any consonant in $s$ to an...
apps_data_355	Galois is one of the strongest chess players of Byteforces. He has even invented a new variant of chess, which he named «PawnChess». This new game is played on a board consisting of 8 rows and 8 columns. At the beginning of every game some black and white pawns are placed on the board. The number of black pawns placed...
apps_data_356	Vasya has two arrays $A$ and $B$ of lengths $n$ and $m$, respectively. He can perform the following operation arbitrary number of times (possibly zero): he takes some consecutive subsegment of the array and replaces it with a single element, equal to the sum of all elements on this subsegment. For example, from the ar...
apps_data_357	One day Alex was creating a contest about his friends, but accidentally deleted it. Fortunately, all the problems were saved, but now he needs to find them among other problems. But there are too many problems, to do it manually. Alex asks you to write a program, which will determine if a problem is from this contest ...
apps_data_358	You've decided to carry out a survey in the theory of prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer divisors. Consider positive integers a, a + 1, ..., b (a ≤ b). You want to find the minimum integer l (1 ≤ l ≤ b - a + 1) such that for any int...
apps_data_359	Arkadiy has lots square photos with size a × a. He wants to put some of them on a rectangular wall with size h × w. The photos which Arkadiy will put on the wall must form a rectangular grid and the distances between neighboring vertically and horizontally photos and also the distances between outside rows and column...
apps_data_360	After lessons Nastya decided to read a book. The book contains $n$ chapters, going one after another, so that one page of the book belongs to exactly one chapter and each chapter contains at least one page. Yesterday evening Nastya did not manage to finish reading the book, so she marked the page with number $k$ as th...
apps_data_361	A large banner with word CODEFORCES was ordered for the 1000-th onsite round of Codeforces^{ω} that takes place on the Miami beach. Unfortunately, the company that made the banner mixed up two orders and delivered somebody else's banner that contains someone else's word. The word on the banner consists only of upper-ca...
apps_data_362	You are given a regular polygon with $n$ vertices labeled from $1$ to $n$ in counter-clockwise order. The triangulation of a given polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon, there is no pair of triangles such that their intersection has non-zero area, and th...
apps_data_363	Vanya got an important task — he should enumerate books in the library and label each book with its number. Each of the n books should be assigned with a number from 1 to n. Naturally, distinct books should be assigned distinct numbers. Vanya wants to know how many digits he will have to write down as he labels the bo...
apps_data_364	Alice and Bob got very bored during a long car trip so they decided to play a game. From the window they can see cars of different colors running past them. Cars are going one after another. The game rules are like this. Firstly Alice chooses some color A, then Bob chooses some color B (A ≠ B). After each car they upd...
apps_data_365	A one-dimensional Japanese crossword can be represented as a binary string of length x. An encoding of this crossword is an array a of size n, where n is the number of segments formed completely of 1's, and a_{i} is the length of i-th segment. No two segments touch or intersect. For example: If x = 6 and the crosswo...
apps_data_366	You have unlimited number of coins with values $1, 2, \ldots, n$. You want to select some set of coins having the total value of $S$. It is allowed to have multiple coins with the same value in the set. What is the minimum number of coins required to get sum $S$? -----Input----- The only line of the input contains...
apps_data_367	A string is called palindrome if it reads the same from left to right and from right to left. For example "kazak", "oo", "r" and "mikhailrubinchikkihcniburliahkim" are palindroms, but strings "abb" and "ij" are not. You are given string s consisting of lowercase Latin letters. At once you can choose any position in th...
apps_data_368	A and B are preparing themselves for programming contests. To train their logical thinking and solve problems better, A and B decided to play chess. During the game A wondered whose position is now stronger. For each chess piece we know its weight: the queen's weight is 9, the rook's weight is 5, the bishop's wei...
apps_data_369	Takahashi is playing a board game called Sugoroku. On the board, there are N + 1 squares numbered 0 to N. Takahashi starts at Square 0, and he has to stop exactly at Square N to win the game. The game uses a roulette with the M numbers from 1 to M. In each turn, Takahashi spins the roulette. If the number x comes up wh...
apps_data_370	Jumbo Takahashi will play golf on an infinite two-dimensional grid. The ball is initially at the origin (0, 0), and the goal is a grid point (a point with integer coordinates) (X, Y). In one stroke, Jumbo Takahashi can perform the following operation: - Choose a grid point whose Manhattan distance from the current pos...
apps_data_371	Bad news came to Mike's village, some thieves stole a bunch of chocolates from the local factory! Horrible! Aside from loving sweet things, thieves from this area are known to be very greedy. So after a thief takes his number of chocolates for himself, the next thief will take exactly k times more than the previous o...
apps_data_372	You are given two circles. Find the area of their intersection. -----Input----- The first line contains three integers x_1, y_1, r_1 ( - 10^9 ≤ x_1, y_1 ≤ 10^9, 1 ≤ r_1 ≤ 10^9) — the position of the center and the radius of the first circle. The second line contains three integers x_2, y_2, r_2 ( - 10^9 ≤ x_2, y_2 ...
apps_data_373	Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games. He came up with the following game. The player has a positive integer $n$. Initially the value of $n$ equals to $v$ and the player is able to do the following op...
apps_data_374	Bandits appeared in the city! One of them is trying to catch as many citizens as he can. The city consists of $n$ squares connected by $n-1$ roads in such a way that it is possible to reach any square from any other square. The square number $1$ is the main square. After Sunday walk all the roads were changed to one-...
apps_data_375	Analyzing the mistakes people make while typing search queries is a complex and an interesting work. As there is no guaranteed way to determine what the user originally meant by typing some query, we have to use different sorts of heuristics. Polycarp needed to write a code that could, given two words, check whether t...
apps_data_376	Although Inzane successfully found his beloved bone, Zane, his owner, has yet to return. To search for Zane, he would need a lot of money, of which he sadly has none. To deal with the problem, he has decided to hack the banks. [Image] There are n banks, numbered from 1 to n. There are also n - 1 wires connecting the ...
apps_data_377	The three friends, Kuro, Shiro, and Katie, met up again! It's time for a party... What the cats do when they unite? Right, they have a party. Since they wanted to have as much fun as possible, they invited all their friends. Now $n$ cats are at the party, sitting in a circle and eating soup. The rules are simple: anyo...
apps_data_378	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 ...
apps_data_379	Hongcow likes solving puzzles. One day, Hongcow finds two identical puzzle pieces, with the instructions "make a rectangle" next to them. The pieces can be described by an n by m grid of characters, where the character 'X' denotes a part of the puzzle and '.' denotes an empty part of the grid. It is guaranteed that th...
apps_data_380	There are three points marked on the coordinate plane. The goal is to make a simple polyline, without self-intersections and self-touches, such that it passes through all these points. Also, the polyline must consist of only segments parallel to the coordinate axes. You are to find the minimum number of segments this p...
apps_data_381	An undirected graph is called k-regular, if the degrees of all its vertices are equal k. An edge of a connected graph is called a bridge, if after removing it the graph is being split into two connected components. Build a connected undirected k-regular graph containing at least one bridge, or else state that such gra...
apps_data_382	You are given two strings $s$ and $t$, both consisting only of lowercase Latin letters. The substring $s[l..r]$ is the string which is obtained by taking characters $s_l, s_{l + 1}, \dots, s_r$ without changing the order. Each of the occurrences of string $a$ in a string $b$ is a position $i$ ($1 \le i \le \|b\| - \|a\| ...
apps_data_383	Quite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a k-tree. A k-tree is an infinite rooted tree where: each vertex has exactly k children; each edge has some weight; if we look at the edges that goes from some ...
apps_data_384	Recently Adaltik discovered japanese crosswords. Japanese crossword is a picture, represented as a table sized a × b squares, and each square is colored white or black. There are integers to the left of the rows and to the top of the columns, encrypting the corresponding row or column. The number of integers represents...
apps_data_385	Recently Polycarp started to develop a text editor that works only with correct bracket sequences (abbreviated as CBS). Note that a bracket sequence is correct if it is possible to get a correct mathematical expression by adding "+"-s and "1"-s to it. For example, sequences "(())()", "()" and "(()(()))" are correct, ...
apps_data_386	A TV show called "Guess a number!" is gathering popularity. The whole Berland, the old and the young, are watching the show. The rules are simple. The host thinks of an integer y and the participants guess it by asking questions to the host. There are four types of acceptable questions: Is it true that y is strictly ...
apps_data_387	You are given $a$ uppercase Latin letters 'A' and $b$ letters 'B'. The period of the string is the smallest such positive integer $k$ that $s_i = s_{i~mod~k}$ ($0$-indexed) for each $i$. Note that this implies that $k$ won't always divide $a+b = \|s\|$. For example, the period of string "ABAABAA" is $3$, the period of ...
apps_data_388	In the army, it isn't easy to form a group of soldiers that will be effective on the battlefield. The communication is crucial and thus no two soldiers should share a name (what would happen if they got an order that Bob is a scouter, if there are two Bobs?). A group of soldiers is effective if and only if their names...
apps_data_389	Two little greedy bears have found two pieces of cheese in the forest of weight a and b grams, correspondingly. The bears are so greedy that they are ready to fight for the larger piece. That's where the fox comes in and starts the dialog: "Little bears, wait a little, I want to make your pieces equal" "Come off it fox...
apps_data_390	A group of $n$ dancers rehearses a performance for the closing ceremony. The dancers are arranged in a row, they've studied their dancing moves and can't change positions. For some of them, a white dancing suit is already bought, for some of them — a black one, and for the rest the suit will be bought in the future. O...
apps_data_391	You are given a cube of size k × k × k, which consists of unit cubes. Two unit cubes are considered neighbouring, if they have common face. Your task is to paint each of k^3 unit cubes one of two colours (black or white), so that the following conditions must be satisfied: each white cube has exactly 2 neighbouring c...
apps_data_392	Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a^2 is a divisor of x. [Image] Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to ...
apps_data_393	You're given a row with $n$ chairs. We call a seating of people "maximal" if the two following conditions hold: There are no neighbors adjacent to anyone seated. It's impossible to seat one more person without violating the first rule. The seating is given as a string consisting of zeros and ones ($0$ means that th...
apps_data_394	Bajtek, known for his unusual gifts, recently got an integer array $x_0, x_1, \ldots, x_{k-1}$. Unfortunately, after a huge array-party with his extraordinary friends, he realized that he'd lost it. After hours spent on searching for a new toy, Bajtek found on the arrays producer's website another array $a$ of length ...
apps_data_395	In a small but very proud high school it was decided to win ACM ICPC. This goal requires to compose as many teams of three as possible, but since there were only 6 students who wished to participate, the decision was to build exactly two teams. After practice competition, participant number i got a score of a_{i}. Tea...
apps_data_396	A positive integer is called a 2-3-integer, if it is equal to 2^{x}·3^{y} for some non-negative integers x and y. In other words, these integers are such integers that only have 2 and 3 among their prime divisors. For example, integers 1, 6, 9, 16 and 108 — are 2-3 integers, while 5, 10, 21 and 120 are not. Print the ...
apps_data_397	Each evening after the dinner the SIS's students gather together to play the game of Sport Mafia. For the tournament, Alya puts candies into the box, which will serve as a prize for a winner. To do that, she performs $n$ actions. The first action performed is to put a single candy into the box. For each of the remain...
apps_data_398	Mahmoud has n line segments, the i-th of them has length a_{i}. Ehab challenged him to use exactly 3 line segments to form a non-degenerate triangle. Mahmoud doesn't accept challenges unless he is sure he can win, so he asked you to tell him if he should accept the challenge. Given the lengths of the line segments, che...
apps_data_399	Imp likes his plush toy a lot. [Image] Recently, he found a machine that can clone plush toys. Imp knows that if he applies the machine to an original toy, he additionally gets one more original toy and one copy, and if he applies the machine to a copied toy, he gets two additional copies. Initially, Imp has only ...

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