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Solve the programming task below in a Python markdown code block.
Bob is a competitive programmer. He wants to become red, and for that he needs a strict training regime. He went to the annual meeting of grandmasters and asked $n$ of them how much effort they needed to reach red.
"Oh, I just spent $x_i$ hours solving... |
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Три брата договорились о встрече. Пронумеруем братьев следующим образом: пусть старший брат имеет номер 1, средний брат имеет номер 2, а младший брат — номер 3.
Когда пришло время встречи, один из братьев опоздал. По заданным номерам двух братьев, кот... |
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Omkar is building a waterslide in his water park, and he needs your help to ensure that he does it as efficiently as possible.
Omkar currently has $n$ supports arranged in a line, the $i$-th of which has height $a_i$. Omkar wants to build his waterslid... |
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You are given $n$ pairs of integers $(a_1, b_1), (a_2, b_2), \ldots, (a_n, b_n)$. All of the integers in the pairs are distinct and are in the range from $1$ to $2 \cdot n$ inclusive.
Let's call a sequence of integers $x_1, x_2, \ldots, x_{2k}$ good if... |
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You are given $n$ positive integers $a_1, \ldots, a_n$, and an integer $k \geq 2$. Count the number of pairs $i, j$ such that $1 \leq i < j \leq n$, and there exists an integer $x$ such that $a_i \cdot a_j = x^k$.
-----Input-----
The first line conta... |
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Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: A_{ij} ... |
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Egor is a famous Russian singer, rapper, actor and blogger, and finally he decided to give a concert in the sunny Republic of Dagestan.
There are $n$ cities in the republic, some of them are connected by $m$ directed roads without any additional condit... |
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You are given two integers $x$ and $y$. You can perform two types of operations: Pay $a$ dollars and increase or decrease any of these integers by $1$. For example, if $x = 0$ and $y = 7$ there are four possible outcomes after this operation: $x = 0... |
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Ivan has got an array of n non-negative integers a_1, a_2, ..., a_{n}. Ivan knows that the array is sorted in the non-decreasing order.
Ivan wrote out integers 2^{a}_1, 2^{a}_2, ..., 2^{a}_{n} on a piece of paper. Now he wonders, what minimum number o... |
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Dexterina and Womandark have been arch-rivals since they’ve known each other. Since both are super-intelligent teenage girls, they’ve always been trying to solve their disputes in a peaceful and nonviolent way. After god knows how many different challen... |
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Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrenc... |
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You are given a multiset S consisting of positive integers (initially empty). There are two kind of queries: Add a positive integer to S, the newly added integer is not less than any number in it. Find a subset s of the set S such that the value $\op... |
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Bimokh is Mashmokh's boss. For the following n days he decided to pay to his workers in a new way. At the beginning of each day he will give each worker a certain amount of tokens. Then at the end of each day each worker can give some of his tokens back... |
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Rebel spy Heidi has just obtained the plans for the Death Star from the Empire and, now on her way to safety, she is trying to break the encryption of the plans (of course they are encrypted – the Empire may be evil, but it is not stupid!). The encrypti... |
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Amr bought a new video game "Guess Your Way Out! II". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located... |
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Vladimir would like to prepare a present for his wife: they have an anniversary! He decided to buy her exactly $n$ flowers.
Vladimir went to a flower shop, and he was amazed to see that there are $m$ types of flowers being sold there, and there is unli... |
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People in the Tomskaya region like magic formulas very much. You can see some of them below.
Imagine you are given a sequence of positive integer numbers p_1, p_2, ..., p_{n}. Lets write down some magic formulas:$q_{i} = p_{i} \oplus(i \operatorname{mo... |
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There are n points marked on the plane. The points are situated in such a way that they form a regular polygon (marked points are its vertices, and they are numbered in counter-clockwise order). You can draw n - 1 segments, each connecting any two marke... |
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"The zombies are lurking outside. Waiting. Moaning. And when they come..."
"When they come?"
"I hope the Wall is high enough."
Zombie attacks have hit the Wall, our line of defense in the North. Its protection is failing, and cracks are showing. In p... |
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Mike and !Mike are old childhood rivals, they are opposite in everything they do, except programming. Today they have a problem they cannot solve on their own, but together (with you) — who knows?
Every one of them has an integer sequences a and b of ... |
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Ayush and Ashish play a game on an unrooted tree consisting of $n$ nodes numbered $1$ to $n$. Players make the following move in turns: Select any leaf node in the tree and remove it together with any edge which has this node as one of its endpoints. ... |
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Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is describ... |
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Find an n × n matrix with different numbers from 1 to n^2, so the sum in each row, column and both main diagonals are odd.
-----Input-----
The only line contains odd integer n (1 ≤ n ≤ 49).
-----Output-----
Print n lines with n integers. All the i... |
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A binary matrix is called good if every even length square sub-matrix has an odd number of ones.
Given a binary matrix $a$ consisting of $n$ rows and $m$ columns, determine the minimum number of cells you need to change to make it good, or report that... |
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Sonya decided to organize an exhibition of flowers. Since the girl likes only roses and lilies, she decided that only these two kinds of flowers should be in this exhibition.
There are $n$ flowers in a row in the exhibition. Sonya can put either a rose... |
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Valera has got a rectangle table consisting of n rows and m columns. Valera numbered the table rows starting from one, from top to bottom and the columns – starting from one, from left to right. We will represent cell that is on the intersection of row ... |
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You are given a positive integer $D$. Let's build the following graph from it: each vertex is a divisor of $D$ (not necessarily prime, $1$ and $D$ itself are also included); two vertices $x$ and $y$ ($x > y$) have an undirected edge between them if $... |
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General Payne has a battalion of n soldiers. The soldiers' beauty contest is coming up, it will last for k days. Payne decided that his battalion will participate in the pageant. Now he has choose the participants.
All soldiers in the battalion have di... |
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You are given an integer $n$ and an integer $k$.
In one step you can do one of the following moves: decrease $n$ by $1$; divide $n$ by $k$ if $n$ is divisible by $k$.
For example, if $n = 27$ and $k = 3$ you can do the following steps: $27 \righta... |
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There are $n$ emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The $i$-th emote increases the opponent's happiness by $a_i$ units (we all know that emotes in this game are used to make opponents ... |
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You a captain of a ship. Initially you are standing in a point $(x_1, y_1)$ (obviously, all positions in the sea can be described by cartesian plane) and you want to travel to a point $(x_2, y_2)$.
You know the weather forecast — the string $s$ of len... |
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Now Serval is a junior high school student in Japari Middle School, and he is still thrilled on math as before.
As a talented boy in mathematics, he likes to play with numbers. This time, he wants to play with numbers on a rooted tree.
A tree is a co... |
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Paladin Manao caught the trail of the ancient Book of Evil in a swampy area. This area contains n settlements numbered from 1 to n. Moving through the swamp is very difficult, so people tramped exactly n - 1 paths. Each of these paths connects some pair... |
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Xenia the beginner programmer has a sequence a, consisting of 2^{n} non-negative integers: a_1, a_2, ..., a_2^{n}. Xenia is currently studying bit operations. To better understand how they work, Xenia decided to calculate some value v for a.
Namely, it... |
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You are given a simple weighted connected undirected graph, consisting of $n$ vertices and $m$ edges.
A path in the graph of length $k$ is a sequence of $k+1$ vertices $v_1, v_2, \dots, v_{k+1}$ such that for each $i$ $(1 \le i \le k)$ the edge $(v_i, ... |
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Volodya likes listening to heavy metal and (occasionally) reading. No wonder Volodya is especially interested in texts concerning his favourite music style.
Volodya calls a string powerful if it starts with "heavy" and ends with "metal". Finding all po... |
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During one of the space missions, humans have found an evidence of previous life at one of the planets. They were lucky enough to find a book with birth and death years of each individual that had been living at this planet. What's interesting is that t... |
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Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
b is lexicographically greater than or equal to a. b_{i} ≥ 2. b is pairwise coprime: for every 1 ≤ i < j ≤ n, b_{i} and b_{j} are c... |
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Gerald has n younger brothers and their number happens to be even. One day he bought n^2 candy bags. One bag has one candy, one bag has two candies, one bag has three candies and so on. In fact, for each integer k from 1 to n^2 he has exactly one bag wi... |
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You have $n$ sticks of the given lengths.
Your task is to choose exactly four of them in such a way that they can form a rectangle. No sticks can be cut to pieces, each side of the rectangle must be formed by a single stick. No stick can be chosen mult... |
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This problem is different from the hard version. In this version Ujan makes exactly one exchange. You can hack this problem only if you solve both problems.
After struggling and failing many times, Ujan decided to try to clean up his house again. He de... |
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We have a point $A$ with coordinate $x = n$ on $OX$-axis. We'd like to find an integer point $B$ (also on $OX$-axis), such that the absolute difference between the distance from $O$ to $B$ and the distance from $A$ to $B$ is equal to $k$. [Image] The de... |
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A new innovative ticketing systems for public transport is introduced in Bytesburg. Now there is a single travel card for all transport. To make a trip a passenger scan his card and then he is charged according to the fare.
The fare is constructed in t... |
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There are n banks in the city where Vasya lives, they are located in a circle, such that any two banks are neighbouring if their indices differ by no more than 1. Also, bank 1 and bank n are neighbours if n > 1. No bank is a neighbour of itself.
Vasya ... |
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Kuro has just learned about permutations and he is really excited to create a new permutation type. He has chosen $n$ distinct positive integers and put all of them in a set $S$. Now he defines a magical permutation to be: A permutation of integers from... |
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Twilight Sparkle once got a crystal from the Crystal Mine. A crystal of size n (n is odd; n > 1) is an n × n matrix with a diamond inscribed into it.
You are given an odd integer n. You need to draw a crystal of size n. The diamond cells of the matrix ... |
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Mishka got a six-faced dice. It has integer numbers from $2$ to $7$ written on its faces (all numbers on faces are different, so this is an almost usual dice).
Mishka wants to get exactly $x$ points by rolling his dice. The number of points is just a s... |
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One of Arkady's friends works at a huge radio telescope. A few decades ago the telescope has sent a signal $s$ towards a faraway galaxy. Recently they've received a response $t$ which they believe to be a response from aliens! The scientists now want to... |
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Inna is a great piano player and Dima is a modest guitar player. Dima has recently written a song and they want to play it together. Of course, Sereja wants to listen to the song very much.
A song is a sequence of notes. Dima and Inna want to play eac... |
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Given is a string S consisting of digits from 1 through 9.
Find the number of pairs of integers (i,j) (1 ≤ i ≤ j ≤ |S|) that satisfy the following condition:
Condition: In base ten, the i-th through j-th characters of S form an integer that is a multipl... |
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Limak is a little polar bear. He loves connecting with other bears via social networks. He has n friends and his relation with the i-th of them is described by a unique integer t_{i}. The bigger this value is, the better the friendship is. No two friend... |
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The employees of the R1 company often spend time together: they watch football, they go camping, they solve contests. So, it's no big deal that sometimes someone pays for someone else.
Today is the day of giving out money rewards. The R1 company CEO wi... |
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There are n cities and n - 1 roads in the Seven Kingdoms, each road connects two cities and we can reach any city from any other by the roads.
Theon and Yara Greyjoy are on a horse in the first city, they are starting traveling through the roads. But t... |
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There is a special offer in Vasya's favourite supermarket: if the customer buys $a$ chocolate bars, he or she may take $b$ additional bars for free. This special offer can be used any number of times.
Vasya currently has $s$ roubles, and he wants to ge... |
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Further research on zombie thought processes yielded interesting results. As we know from the previous problem, the nervous system of a zombie consists of n brains and m brain connectors joining some pairs of brains together. It was observed that the in... |
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Since Sonya is interested in robotics too, she decided to construct robots that will read and recognize numbers.
Sonya has drawn $n$ numbers in a row, $a_i$ is located in the $i$-th position. She also has put a robot at each end of the row (to the left... |
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Omkar is playing his favorite pixelated video game, Bed Wars! In Bed Wars, there are $n$ players arranged in a circle, so that for all $j$ such that $2 \leq j \leq n$, player $j - 1$ is to the left of the player $j$, and player $j$ is to the right of pl... |
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Mr. Kitayuta has just bought an undirected graph consisting of n vertices and m edges. The vertices of the graph are numbered from 1 to n. Each edge, namely edge i, has a color c_{i}, connecting vertex a_{i} and b_{i}.
Mr. Kitayuta wants you to process... |
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Vladik had started reading a complicated book about algorithms containing n pages. To improve understanding of what is written, his friends advised him to read pages in some order given by permutation P = [p_1, p_2, ..., p_{n}], where p_{i} denotes the ... |
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We just discovered a new data structure in our research group: a suffix three!
It's very useful for natural language processing. Given three languages and three suffixes, a suffix three can determine which language a sentence is written in.
It's super... |
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Vasya has a sequence $a$ consisting of $n$ integers $a_1, a_2, \dots, a_n$. Vasya may pefrom the following operation: choose some number from the sequence and swap any pair of bits in its binary representation. For example, Vasya can transform number $6... |
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Lunar New Year is approaching, and Bob decides to take a wander in a nearby park.
The park can be represented as a connected graph with $n$ nodes and $m$ bidirectional edges. Initially Bob is at the node $1$ and he records $1$ on his notebook. He can w... |
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You are the gym teacher in the school.
There are $n$ students in the row. And there are two rivalling students among them. The first one is in position $a$, the second in position $b$. Positions are numbered from $1$ to $n$ from left to right.
Since t... |
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Madeline has an array $a$ of $n$ integers. A pair $(u, v)$ of integers forms an inversion in $a$ if:
$1 \le u < v \le n$. $a_u > a_v$.
Madeline recently found a magical paper, which allows her to write two indices $u$ and $v$ and swap the values $... |
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Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a_1, a_2, ..., a_{n} in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially ... |
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The HR manager was disappointed again. The last applicant failed the interview the same way as 24 previous ones. "Do I give such a hard task?" — the HR manager thought. "Just raise number 5 to the power of n and get last two digits of the number. Yes, o... |
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The semester is already ending, so Danil made an effort and decided to visit a lesson on harmony analysis to know how does the professor look like, at least. Danil was very bored on this lesson until the teacher gave the group a simple task: find 4 vect... |
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In Aramic language words can only represent objects.
Words in Aramic have special properties: A word is a root if it does not contain the same letter more than once. A root and all its permutations represent the same object. The root $x$ of a word ... |
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New Year is coming in Tree World! In this world, as the name implies, there are n cities connected by n - 1 roads, and for any two distinct cities there always exists a path between them. The cities are numbered by integers from 1 to n, and the roads ar... |
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Your math teacher gave you the following problem:
There are $n$ segments on the $x$-axis, $[l_1; r_1], [l_2; r_2], \ldots, [l_n; r_n]$. The segment $[l; r]$ includes the bounds, i.e. it is a set of such $x$ that $l \le x \le r$. The length of the segme... |
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Vus the Cossack has two binary strings, that is, strings that consist only of "0" and "1". We call these strings $a$ and $b$. It is known that $|b| \leq |a|$, that is, the length of $b$ is at most the length of $a$.
The Cossack considers every substrin... |
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Inzane finally found Zane with a lot of money to spare, so they together decided to establish a country of their own.
Ruling a country is not an easy job. Thieves and terrorists are always ready to ruin the country's peace. To fight back, Zane and Inza... |
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The name of one small but proud corporation consists of n lowercase English letters. The Corporation has decided to try rebranding — an active marketing strategy, that includes a set of measures to change either the brand (both for the company and the g... |
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You are given a string $s$ such that each its character is either 1, 2, or 3. You have to choose the shortest contiguous substring of $s$ such that it contains each of these three characters at least once.
A contiguous substring of string $s$ is a stri... |
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This year in Equestria was a year of plenty, so Applejack has decided to build some new apple storages. According to the advice of the farm designers, she chose to build two storages with non-zero area: one in the shape of a square and another one in th... |
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Heidi has finally found the mythical Tree of Life – a legendary combinatorial structure which is said to contain a prophecy crucially needed to defeat the undead armies.
On the surface, the Tree of Life is just a regular undirected tree well-known from... |
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In this problem at each moment you have a set of intervals. You can move from interval (a, b) from our set to interval (c, d) from our set if and only if c < a < d or c < b < d. Also there is a path from interval I_1 from our set to interval I_2 from ou... |
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You have a simple undirected graph consisting of $n$ vertices and $m$ edges. The graph doesn't contain self-loops, there is at most one edge between a pair of vertices. The given graph can be disconnected.
Let's make a definition.
Let $v_1$ and $v_2$ ... |
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Consider a conveyor belt represented using a grid consisting of $n$ rows and $m$ columns. The cell in the $i$-th row from the top and the $j$-th column from the left is labelled $(i,j)$.
Every cell, except $(n,m)$, has a direction R (Right) or D (Down... |
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It's a walking tour day in SIS.Winter, so $t$ groups of students are visiting Torzhok. Streets of Torzhok are so narrow that students have to go in a row one after another.
Initially, some students are angry. Let's describe a group of students by a str... |
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Vasya has a string $s$ of length $n$ consisting only of digits 0 and 1. Also he has an array $a$ of length $n$.
Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from... |
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A permutation of size n is an array of size n such that each integer from 1 to n occurs exactly once in this array. An inversion in a permutation p is a pair of indices (i, j) such that i > j and a_{i} < a_{j}. For example, a permutation [4, 1, 3, 2] co... |
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Given a positive integer $m$, we say that a sequence $x_1, x_2, \dots, x_n$ of positive integers is $m$-cute if for every index $i$ such that $2 \le i \le n$ it holds that $x_i = x_{i - 1} + x_{i - 2} + \dots + x_1 + r_i$ for some positive integer $r_i$... |
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There is a programing contest named SnakeUp, 2n people want to compete for it. In order to attend this contest, people need to form teams of exactly two people. You are given the strength of each possible combination of two people. All the values of the... |
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Let's denote a $k$-step ladder as the following structure: exactly $k + 2$ wooden planks, of which
two planks of length at least $k+1$ — the base of the ladder; $k$ planks of length at least $1$ — the steps of the ladder;
Note that neither the bas... |
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You have array a that contains all integers from 1 to n twice. You can arbitrary permute any numbers in a.
Let number i be in positions x_{i}, y_{i} (x_{i} < y_{i}) in the permuted array a. Let's define the value d_{i} = y_{i} - x_{i} — the distance be... |
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Today, Mezo is playing a game. Zoma, a character in that game, is initially at position $x = 0$. Mezo starts sending $n$ commands to Zoma. There are two possible commands: 'L' (Left) sets the position $x: =x - 1$; 'R' (Right) sets the position $x: =x ... |
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The marmots need to prepare k problems for HC^2 over n days. Each problem, once prepared, also has to be printed.
The preparation of a problem on day i (at most one per day) costs a_{i} CHF, and the printing of a problem on day i (also at most one per ... |
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An IPv6-address is a 128-bit number. For convenience, this number is recorded in blocks of 16 bits in hexadecimal record, the blocks are separated by colons — 8 blocks in total, each block has four hexadecimal digits. Here is an example of the correct r... |
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This is the easy version of the problem. The difference is constraints on the number of wise men and the time limit. You can make hacks only if all versions of this task are solved.
$n$ wise men live in a beautiful city. Some of them know each other.
... |
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You are given a string $s$. Each character is either 0 or 1.
You want all 1's in the string to form a contiguous subsegment. For example, if the string is 0, 1, 00111 or 01111100, then all 1's form a contiguous subsegment, and if the string is 0101, 10... |
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Ashish has $n$ elements arranged in a line.
These elements are represented by two integers $a_i$ — the value of the element and $b_i$ — the type of the element (there are only two possible types: $0$ and $1$). He wants to sort the elements in non-decr... |
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Ivar the Boneless is a great leader. He is trying to capture Kattegat from Lagertha. The war has begun and wave after wave Ivar's warriors are falling in battle.
Ivar has $n$ warriors, he places them on a straight line in front of the main gate, in a w... |
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You're given an undirected graph with $n$ nodes and $m$ edges. Nodes are numbered from $1$ to $n$.
The graph is considered harmonious if and only if the following property holds: For every triple of integers $(l, m, r)$ such that $1 \le l < m < r \le ... |
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Today, as a friendship gift, Bakry gave Badawy $n$ integers $a_1, a_2, \dots, a_n$ and challenged him to choose an integer $X$ such that the value $\underset{1 \leq i \leq n}{\max} (a_i \oplus X)$ is minimum possible, where $\oplus$ denotes the bitwise ... |
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Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid.
Each test case consists of an integer $n$ and two arrays $a$ and $b$, of size $n$. If after some (possibly zero... |
Solve the programming task below in a Python markdown code block.
Dora the explorer has decided to use her money after several years of juicy royalties to go shopping. What better place to shop than Nlogonia?
There are $n$ stores numbered from $1$ to $n$ in Nlogonia. The $i$-th of these stores offers a positive integ... |
Solve the programming task below in a Python markdown code block.
Little Artem has invented a time machine! He could go anywhere in time, but all his thoughts of course are with computer science. He wants to apply this time machine to a well-known data structure: multiset.
Artem wants to create a basic multiset of in... |
Solve the programming task below in a Python markdown code block.
You are given an array a consisting of n positive integers. You pick two integer numbers l and r from 1 to n, inclusive (numbers are picked randomly, equiprobably and independently). If l > r, then you swap values of l and r. You have to calculate the e... |
Solve the programming task below in a Python markdown code block.
Hag is a very talented person. He has always had an artist inside him but his father forced him to study mechanical engineering.
Yesterday he spent all of his time cutting a giant piece of wood trying to make it look like a goose. Anyway, his dad found... |
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