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Solve the programming task below in a Python markdown code block.
The process of mammoth's genome decoding in Berland comes to its end!
One of the few remaining tasks is to restore unrecognized nucleotides in a found chain s. Each nucleotide is coded with a capital letter of English alphabet: 'A', 'C', 'G' or 'T'. Un... |
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Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when the... |
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Vasya has an array a consisting of positive integer numbers. Vasya wants to divide this array into two non-empty consecutive parts (the prefix and the suffix) so that the sum of all elements in the first part equals to the sum of elements in the second ... |
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A few years ago, Hitagi encountered a giant crab, who stole the whole of her body weight. Ever since, she tried to avoid contact with others, for fear that this secret might be noticed.
To get rid of the oddity and recover her weight, a special integer... |
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The Duck song
For simplicity, we'll assume that there are only three types of grapes: green grapes, purple grapes and black grapes.
Andrew, Dmitry and Michal are all grapes' lovers, however their preferences of grapes are different. To make all of the... |
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While swimming at the beach, Mike has accidentally dropped his cellphone into the water. There was no worry as he bought a cheap replacement phone with an old-fashioned keyboard. The keyboard has only ten digital equal-sized keys, located in the followi... |
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Summer holidays! Someone is going on trips, someone is visiting grandparents, but someone is trying to get a part-time job. This summer Noora decided that she wants to earn some money, and took a job in a shop as an assistant.
Shop, where Noora is work... |
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It is a balmy spring afternoon, and Farmer John's n cows are ruminating about link-cut cacti in their stalls. The cows, labeled 1 through n, are arranged so that the i-th cow occupies the i-th stall from the left. However, Elsie, after realizing that sh... |
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Ivan is collecting coins. There are only $N$ different collectible coins, Ivan has $K$ of them. He will be celebrating his birthday soon, so all his $M$ freinds decided to gift him coins. They all agreed to three terms: Everyone must gift as many coins... |
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Polycarp has a checkered sheet of paper of size n × m. Polycarp painted some of cells with black, the others remained white. Inspired by Malevich's "Black Square", Polycarp wants to paint minimum possible number of white cells with black so that all bla... |
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There is a beautiful garden of stones in Innopolis.
Its most beautiful place is the $n$ piles with stones numbered from $1$ to $n$.
EJOI participants have visited this place twice.
When they first visited it, the number of stones in piles was $x_1, ... |
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Alice got many presents these days. So she decided to pack them into boxes and send them to her friends.
There are $n$ kinds of presents. Presents of one kind are identical (i.e. there is no way to distinguish two gifts of the same kind). Presents of d... |
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Katya studies in a fifth grade. Recently her class studied right triangles and the Pythagorean theorem. It appeared, that there are triples of positive integers such that you can construct a right triangle with segments of lengths corresponding to tripl... |
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Imp is watching a documentary about cave painting. [Image]
Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. U... |
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Kuro has recently won the "Most intelligent cat ever" contest. The three friends then decided to go to Katie's home to celebrate Kuro's winning. After a big meal, they took a small break then started playing games.
Kuro challenged Katie to create a gam... |
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The mayor of the Central Town wants to modernize Central Street, represented in this problem by the $(Ox)$ axis.
On this street, there are $n$ antennas, numbered from $1$ to $n$. The $i$-th antenna lies on the position $x_i$ and has an initial scope of... |
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You have a set of items, each having some integer weight not greater than $8$. You denote that a subset of items is good if total weight of items in the subset does not exceed $W$.
You want to calculate the maximum possible weight of a good subset of i... |
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Someone gave Alyona an array containing n positive integers a_1, a_2, ..., a_{n}. In one operation, Alyona can choose any element of the array and decrease it, i.e. replace with any positive integer that is smaller than the current one. Alyona can repea... |
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Recently Vasya found a golden ticket — a sequence which consists of $n$ digits $a_1a_2\dots a_n$. Vasya considers a ticket to be lucky if it can be divided into two or more non-intersecting segments with equal sums. For example, ticket $350178$ is lucky... |
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Those days, many boys use beautiful girls' photos as avatars in forums. So it is pretty hard to tell the gender of a user at the first glance. Last year, our hero went to a forum and had a nice chat with a beauty (he thought so). After that they talked ... |
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This morning, Roman woke up and opened the browser with $n$ opened tabs numbered from $1$ to $n$. There are two kinds of tabs: those with the information required for the test and those with social network sites. Roman decided that there are too many ta... |
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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 "Th... |
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The circle line of the Roflanpolis subway has $n$ stations.
There are two parallel routes in the subway. The first one visits stations in order $1 \to 2 \to \ldots \to n \to 1 \to 2 \to \ldots$ (so the next stop after station $x$ is equal to $(x+1)$ if... |
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Unlucky year in Berland is such a year that its number n can be represented as n = x^{a} + y^{b}, where a and b are non-negative integer numbers.
For example, if x = 2 and y = 3 then the years 4 and 17 are unlucky (4 = 2^0 + 3^1, 17 = 2^3 + 3^2 = 2^4 ... |
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Beroffice text editor has a wide range of features that help working with text. One of the features is an automatic search for typos and suggestions of how to fix them.
Beroffice works only with small English letters (i.e. with 26 letters from a to z).... |
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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 type... |
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Recall that a binary search tree is a rooted binary tree, whose nodes each store a key and each have at most two distinguished subtrees, left and right. The key in each node must be greater than any key stored in the left subtree, and less than any key ... |
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You might have heard about the next game in Lara Croft series coming out this year. You also might have watched its trailer. Though you definitely missed the main idea about its plot, so let me lift the veil of secrecy.
Lara is going to explore yet ano... |
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Today, Osama gave Fadi an integer $X$, and Fadi was wondering about the minimum possible value of $max(a, b)$ such that $LCM(a, b)$ equals $X$. Both $a$ and $b$ should be positive integers.
$LCM(a, b)$ is the smallest positive integer that is divisible... |
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Berland annual chess tournament is coming!
Organizers have gathered 2·n chess players who should be divided into two teams with n people each. The first team is sponsored by BerOil and the second team is sponsored by BerMobile. Obviously, organizers sh... |
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You are given an array of n elements, you must make it a co-prime array in as few moves as possible.
In each move you can insert any positive integral number you want not greater than 10^9 in any place in the array.
An array is co-prime if any two adj... |
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We have a sequence of N integers: A_1, A_2, \cdots, A_N.
You can perform the following operation between 0 and K times (inclusive):
- Choose two integers i and j such that i \neq j, each between 1 and N (inclusive). Add 1 to A_i and -1 to A_j, possibly... |
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Cat Furrier Transform is a popular algorithm among cat programmers to create longcats. As one of the greatest cat programmers ever exist, Neko wants to utilize this algorithm to create the perfect longcat.
Assume that we have a cat with a number $x$. A... |
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Luba thinks about watering her garden. The garden can be represented as a segment of length k. Luba has got n buckets, the i-th bucket allows her to water some continuous subsegment of garden of length exactly a_{i} each hour. Luba can't water any parts... |
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On the way to Rio de Janeiro Ostap kills time playing with a grasshopper he took with him in a special box. Ostap builds a line of length n such that some cells of this line are empty and some contain obstacles. Then, he places his grasshopper to one of... |
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It's a beautiful April day and Wallace is playing football with his friends. But his friends do not know that Wallace actually stayed home with Gromit and sent them his robotic self instead. Robo-Wallace has several advantages over the other guys. For e... |
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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 tha... |
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You are given two strings a and b. You have to remove the minimum possible number of consecutive (standing one after another) characters from string b in such a way that it becomes a subsequence of string a. It can happen that you will not need to remov... |
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Vasya has a pile, that consists of some number of stones. $n$ times he either took one stone from the pile or added one stone to the pile. The pile was non-empty before each operation of taking one stone from the pile.
You are given $n$ operations whic... |
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Kolya Gerasimov loves kefir very much. He lives in year 1984 and knows all the details of buying this delicious drink. One day, as you probably know, he found himself in year 2084, and buying kefir there is much more complicated.
Kolya is hungry, so he... |
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Two bored soldiers are playing card war. Their card deck consists of exactly n cards, numbered from 1 to n, all values are different. They divide cards between them in some manner, it's possible that they have different number of cards. Then they play a... |
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You have probably registered on Internet sites many times. And each time you should enter your invented password. Usually the registration form automatically checks the password's crypt resistance. If the user's password isn't complex enough, a message ... |
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In Berland each high school student is characterized by academic performance — integer value between 1 and 5.
In high school 0xFF there are two groups of pupils: the group A and the group B. Each group consists of exactly n students. An academic perfor... |
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Imagine a city with n horizontal streets crossing m vertical streets, forming an (n - 1) × (m - 1) grid. In order to increase the traffic flow, mayor of the city has decided to make each street one way. This means in each horizontal street, the traffic ... |
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Implication is a function of two logical arguments, its value is false if and only if the value of the first argument is true and the value of the second argument is false.
Implication is written by using character '$\rightarrow$', and the arguments a... |
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You have two variables a and b. Consider the following sequence of actions performed with these variables: If a = 0 or b = 0, end the process. Otherwise, go to step 2; If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to s... |
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Find the number of k-divisible numbers on the segment [a, b]. In other words you need to find the number of such integer values x that a ≤ x ≤ b and x is divisible by k.
-----Input-----
The only line contains three space-separated integers k, a and b... |
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Let's write all the positive integer numbers one after another from $1$ without any delimiters (i.e. as a single string). It will be the infinite sequence starting with 123456789101112131415161718192021222324252627282930313233343536...
Your task is to ... |
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A telephone number is a sequence of exactly $11$ digits such that its first digit is 8.
Vasya and Petya are playing a game. Initially they have a string $s$ of length $n$ ($n$ is odd) consisting of digits. Vasya makes the first move, then players alter... |
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Andrey thinks he is truly a successful developer, but in reality he didn't know about the binary search algorithm until recently. After reading some literature Andrey understood that this algorithm allows to quickly find a certain number $x$ in an array... |
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Andrey received a postcard from Irina. It contained only the words "Hello, Andrey!", and a strange string consisting of lowercase Latin letters, snowflakes and candy canes. Andrey thought that this string is an encrypted message, and decided to decrypt ... |
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Vasya started working in a machine vision company of IT City. Vasya's team creates software and hardware for identification of people by their face.
One of the project's know-how is a camera rotating around its optical axis on shooting. People see an e... |
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Carl is a beginner magician. He has a blue, b violet and c orange magic spheres. In one move he can transform two spheres of the same color into one sphere of any other color. To make a spell that has never been seen before, he needs at least x blue, y ... |
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Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.
First he gave Amr two positive integers n and k. Then h... |
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Students in a class are making towers of blocks. Each student makes a (non-zero) tower by stacking pieces lengthwise on top of each other. n of the students use pieces made of two blocks and m of the students use pieces made of three blocks.
The studen... |
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Petya and Vasya decided to play a game. They have n cards (n is an even number). A single integer is written on each card.
Before the game Petya will choose an integer and after that Vasya will choose another integer (different from the number that Pet... |
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Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains a_{i} soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the... |
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Salem gave you $n$ sticks with integer positive lengths $a_1, a_2, \ldots, a_n$.
For every stick, you can change its length to any other positive integer length (that is, either shrink or stretch it). The cost of changing the stick's length from $a$ to... |
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Карта звёздного неба представляет собой прямоугольное поле, состоящее из n строк по m символов в каждой строке. Каждый символ — это либо «.» (означает пустой участок неба), либо «*» (означает то, что в этом месте на небе есть звезда).
Новое издание ка... |
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A girl named Sonya is studying in the scientific lyceum of the Kingdom of Kremland. The teacher of computer science (Sonya's favorite subject!) invented a task for her.
Given an array $a$ of length $n$, consisting only of the numbers $0$ and $1$, and t... |
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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... |
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The determinant of a matrix 2 × 2 is defined as follows:$\operatorname{det} \left(\begin{array}{ll}{a} & {b} \\{c} & {d} \end{array} \right) = a d - b c$
A matrix is called degenerate if its determinant is equal to zero.
The norm ||A|| of a matrix A ... |
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In a small restaurant there are a tables for one person and b tables for two persons.
It it known that n groups of people come today, each consisting of one or two people.
If a group consist of one person, it is seated at a vacant one-seater table. ... |
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Each student eagerly awaits the day he would pass the exams successfully. Thus, Vasya was ready to celebrate, but, alas, he didn't pass it. However, many of Vasya's fellow students from the same group were more successful and celebrated after the exam.
... |
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Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n.
Pasha likes rectangle... |
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The Fair Nut likes kvass very much. On his birthday parents presented him $n$ kegs of kvass. There are $v_i$ liters of kvass in the $i$-th keg. Each keg has a lever. You can pour your glass by exactly $1$ liter pulling this lever. The Fair Nut likes thi... |
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The 9-th grade student Gabriel noticed a caterpillar on a tree when walking around in a forest after the classes. The caterpillar was on the height h_1 cm from the ground. On the height h_2 cm (h_2 > h_1) on the same tree hung an apple and the caterpill... |
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A sweet little monster Om Nom loves candies very much. One day he found himself in a rather tricky situation that required him to think a bit in order to enjoy candies the most. Would you succeed with the same task if you were on his place? [Image]
On... |
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There are n employees in Alternative Cake Manufacturing (ACM). They are now voting on some very important question and the leading world media are trying to predict the outcome of the vote.
Each of the employees belongs to one of two fractions: depubli... |
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Monocarp has decided to buy a new TV set and hang it on the wall in his flat. The wall has enough free space so Monocarp can buy a TV set with screen width not greater than $a$ and screen height not greater than $b$. Monocarp is also used to TV sets wit... |
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The number "zero" is called "love" (or "l'oeuf" to be precise, literally means "egg" in French), for example when denoting the zero score in a game of tennis.
Aki is fond of numbers, especially those with trailing zeros. For example, the number $9200$... |
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A frog is initially at position $0$ on the number line. The frog has two positive integers $a$ and $b$. From a position $k$, it can either jump to position $k+a$ or $k-b$.
Let $f(x)$ be the number of distinct integers the frog can reach if it never jum... |
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Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?
Given an integer sequence a_1, a_2, ..., a_{n} of length n. Decide whether it is possible to divide it into an odd number of non-empty subsegments, the each o... |
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One spring day on his way to university Lesha found an array A. Lesha likes to split arrays into several parts. This time Lesha decided to split the array A into several, possibly one, new arrays so that the sum of elements in each of the new arrays is ... |
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You are given a non-negative integer n, its decimal representation consists of at most 100 digits and doesn't contain leading zeroes.
Your task is to determine if it is possible in this case to remove some of the digits (possibly not remove any digit a... |
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In a building where Polycarp lives there are equal number of flats on each floor. Unfortunately, Polycarp don't remember how many flats are on each floor, but he remembers that the flats are numbered from 1 from lower to upper floors. That is, the first... |
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Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states:
XX XX .X X.
X. .X XX XX
Bishwocks don't attack any squares a... |
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Polycarp loves lowercase letters and dislikes uppercase ones. Once he got a string s consisting only of lowercase and uppercase Latin letters.
Let A be a set of positions in the string. Let's call it pretty if following conditions are met: letters on ... |
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You are given a sequence a consisting of n integers. You may partition this sequence into two sequences b and c in such a way that every element belongs exactly to one of these sequences.
Let B be the sum of elements belonging to b, and C be the sum o... |
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A bus moves along the coordinate line Ox from the point x = 0 to the point x = a. After starting from the point x = 0, it reaches the point x = a, immediately turns back and then moves to the point x = 0. After returning to the point x = 0 it immediatel... |
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You are given the string s of length n and the numbers p, q. Split the string s to pieces of length p and q.
For example, the string "Hello" for p = 2, q = 3 can be split to the two strings "Hel" and "lo" or to the two strings "He" and "llo".
Note it ... |
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A sportsman starts from point x_{start} = 0 and runs to point with coordinate x_{finish} = m (on a straight line). Also, the sportsman can jump — to jump, he should first take a run of length of not less than s meters (in this case for these s meters hi... |
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Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?
-----Input-----
The first line of the input contains two integers s and x (2 ≤ s ≤ 10^12, 0 ≤ x ≤ 10^12), the sum an... |
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Long story short, shashlik is Miroslav's favorite food. Shashlik is prepared on several skewers simultaneously. There are two states for each skewer: initial and turned over.
This time Miroslav laid out $n$ skewers parallel to each other, and enumerate... |
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Let's define a function $f(p)$ on a permutation $p$ as follows. Let $g_i$ be the greatest common divisor (GCD) of elements $p_1$, $p_2$, ..., $p_i$ (in other words, it is the GCD of the prefix of length $i$). Then $f(p)$ is the number of distinct elemen... |
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One day, the Grasshopper was jumping on the lawn and found a piece of paper with a string. Grasshopper became interested what is the minimum jump ability he should have in order to be able to reach the far end of the string, jumping only on vowels of th... |
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You may have heard of the pie rule before. It states that if two people wish to fairly share a slice of pie, one person should cut the slice in half, and the other person should choose who gets which slice. Alice and Bob have many slices of pie, and rat... |
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You've got a positive integer sequence a_1, a_2, ..., a_{n}. All numbers in the sequence are distinct. Let's fix the set of variables b_1, b_2, ..., b_{m}. Initially each variable b_{i} (1 ≤ i ≤ m) contains the value of zero. Consider the following sequ... |
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Today, hedgehog Filya went to school for the very first time! Teacher gave him a homework which Filya was unable to complete without your help.
Filya is given an array of non-negative integers a_1, a_2, ..., a_{n}. First, he pick an integer x and then ... |
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The main street of Berland is a straight line with n houses built along it (n is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to n - 1 in the order... |
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There is unrest in the Galactic Senate. Several thousand solar systems have declared their intentions to leave the Republic. Master Heidi needs to select the Jedi Knights who will go on peacekeeping missions throughout the galaxy. It is well-known that ... |
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Mishka is a little polar bear. As known, little bears loves spending their free time playing dice for chocolates. Once in a wonderful sunny morning, walking around blocks of ice, Mishka met her friend Chris, and they started playing the game.
Rules of ... |
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One day Alex decided to remember childhood when computers were not too powerful and lots of people played only default games. Alex enjoyed playing Minesweeper that time. He imagined that he saved world from bombs planted by terrorists, but he rarely won... |
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After passing a test, Vasya got himself a box of $n$ candies. He decided to eat an equal amount of candies each morning until there are no more candies. However, Petya also noticed the box and decided to get some candies for himself.
This means the pro... |
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A necklace can be described as a string of links ('-') and pearls ('o'), with the last link or pearl connected to the first one. $0$
You can remove a link or a pearl and insert it between two other existing links or pearls (or between a link and a pea... |
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n hobbits are planning to spend the night at Frodo's house. Frodo has n beds standing in a row and m pillows (n ≤ m). Each hobbit needs a bed and at least one pillow to sleep, however, everyone wants as many pillows as possible. Of course, it's not alwa... |
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You are given an array $a_1, a_2, \dots , a_n$ and two integers $m$ and $k$.
You can choose some subarray $a_l, a_{l+1}, \dots, a_{r-1}, a_r$.
The cost of subarray $a_l, a_{l+1}, \dots, a_{r-1}, a_r$ is equal to $\sum\limits_{i=l}^{r} a_i - k \lceil ... |
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You are given a rectangular grid of lattice points from (0, 0) to (n, m) inclusive. You have to choose exactly 4 different points to build a polyline possibly with self-intersections and self-touching. This polyline should be as long as possible.
A pol... |
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Not so long ago company R2 bought company R1 and consequently, all its developments in the field of multicore processors. Now the R2 laboratory is testing one of the R1 processors.
The testing goes in n steps, at each step the processor gets some instr... |
Solve the programming task below in a Python markdown code block.
Mr. Santa asks all the great programmers of the world to solve a trivial problem. He gives them an integer m and asks for the number of positive integers n, such that the factorial of n ends with exactly m zeroes. Are you among those great programmers w... |
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