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Solve the programming task below in a Python markdown code block.
After the fourth season Sherlock and Moriary have realized the whole foolishness of the battle between them and decided to continue their competitions in peaceful game of Credit Cards.
Rules of this game are simple: each player bring his favourite n-di... |
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You have decided to watch the best moments of some movie. There are two buttons on your player: Watch the current minute of the movie. By pressing this button, you watch the current minute of the movie and the player automatically proceeds to the next... |
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This is the easy version of the problem. The difference between versions is the constraints on $n$ and $a_i$. You can make hacks only if all versions of the problem are solved.
First, Aoi came up with the following idea for the competitive programming ... |
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Cucumber boy is fan of Kyubeat, a famous music game.
Kyubeat has 16 panels for playing arranged in 4 × 4 table. When a panel lights up, he has to press that panel.
Each panel has a timing to press (the preffered time when a player should press it), an... |
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To become the king of Codeforces, Kuroni has to solve the following problem.
He is given $n$ numbers $a_1, a_2, \dots, a_n$. Help Kuroni to calculate $\prod_{1\le i<j\le n} |a_i - a_j|$. As result can be very big, output it modulo $m$.
If you are not ... |
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You got a job as a marketer in a pet shop, and your current task is to boost sales of cat food. One of the strategies is to sell cans of food in packs with discounts.
Suppose you decided to sell packs with $a$ cans in a pack with a discount and some c... |
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Professor Dumbledore is helping Harry destroy the Horcruxes. He went to Gaunt Shack as he suspected a Horcrux to be present there. He saw Marvolo Gaunt's Ring and identified it as a Horcrux. Although he destroyed it, he is still affected by its curse. P... |
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Today, Wet Shark is given n bishops on a 1000 by 1000 grid. Both rows and columns of the grid are numbered from 1 to 1000. Rows are numbered from top to bottom, while columns are numbered from left to right.
Wet Shark thinks that two bishops attack eac... |
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Your search for Heidi is over – you finally found her at a library, dressed up as a human. In fact, she has spent so much time there that she now runs the place! Her job is to buy books and keep them at the library so that people can borrow and read the... |
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A classroom in a school has six rows with 3 desks in each row. Two people can use the same desk: one sitting on the left and one sitting on the right.
Some places are already occupied, and some places are vacant. Petya has just entered the class and w... |
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You are given a sequence $a_1, a_2, \dots, a_n$ consisting of $n$ integers.
You may perform the following operation on this sequence: choose any element and either increase or decrease it by one.
Calculate the minimum possible difference between the m... |
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We have a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i.
Consider painting each of these edges white or black. There are 2^{N-1} such ways to paint the edges. Among them, how many satisfy all of the... |
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There are N cities numbered 1 to N, connected by M railroads.
You are now at City 1, with 10^{100} gold coins and S silver coins in your pocket.
The i-th railroad connects City U_i and City V_i bidirectionally, and a one-way trip costs A_i silver coins ... |
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Given are a sequence of N positive integers A_1, A_2, \ldots, A_N and another positive integer S.
For a non-empty subset T of the set \{1, 2, \ldots , N \}, let us define f(T) as follows:
- f(T) is the number of different non-empty subsets \{x_1, x_2... |
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There are N boxes arranged in a row from left to right. The i-th box from the left contains A_i candies.
You will take out the candies from some consecutive boxes and distribute them evenly to M children.
Such being the case, find the number of the pair... |
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A tourist hiked along the mountain range. The hike lasted for n days, during each day the tourist noted height above the sea level. On the i-th day height was equal to some integer h_{i}. The tourist pick smooth enough route for his hike, meaning that t... |
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SaMer has written the greatest test case of all time for one of his problems. For a given array of integers, the problem asks to find the minimum number of groups the array can be divided into, such that the product of any pair of integers in the same g... |
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A super computer has been built in the Turtle Academy of Sciences. The computer consists of n·m·k CPUs. The architecture was the paralellepiped of size n × m × k, split into 1 × 1 × 1 cells, each cell contains exactly one CPU. Thus, each CPU can be simu... |
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Given two integers $n$ and $x$, construct an array that satisfies the following conditions: for any element $a_i$ in the array, $1 \le a_i<2^n$; there is no non-empty subsegment with bitwise XOR equal to $0$ or $x$, its length $l$ should be maximize... |
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Anton likes to play chess. Also he likes to do programming. No wonder that he decided to attend chess classes and programming classes.
Anton has n variants when he will attend chess classes, i-th variant is given by a period of time (l_{1, }i, r_{1, }i... |
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Sasha is a very happy guy, that's why he is always on the move. There are $n$ cities in the country where Sasha lives. They are all located on one straight line, and for convenience, they are numbered from $1$ to $n$ in increasing order. The distance be... |
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Once upon a time Petya and Gena gathered after another programming competition and decided to play some game. As they consider most modern games to be boring, they always try to invent their own games. They have only stickers and markers, but that won't... |
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Devu is a renowned classical singer. He is invited to many big functions/festivals. Recently he was invited to "All World Classical Singing Festival". Other than Devu, comedian Churu was also invited.
Devu has provided organizers a list of the songs an... |
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The Central Company has an office with a sophisticated security system. There are $10^6$ employees, numbered from $1$ to $10^6$.
The security system logs entrances and departures. The entrance of the $i$-th employee is denoted by the integer $i$, while... |
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The only difference between easy and hard versions is constraints.
The BerTV channel every day broadcasts one episode of one of the $k$ TV shows. You know the schedule for the next $n$ days: a sequence of integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le... |
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Vasya follows a basketball game and marks the distances from which each team makes a throw. He knows that each successful throw has value of either 2 or 3 points. A throw is worth 2 points if the distance it was made from doesn't exceed some value of d ... |
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You are given a string $s$ consisting only of lowercase Latin letters.
You can rearrange all letters of this string as you wish. Your task is to obtain a good string by rearranging the letters of the given string or report that it is impossible to do i... |
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Simon has a rectangular table consisting of n rows and m columns. Simon numbered the rows of the table from top to bottom starting from one and the columns — from left to right starting from one. We'll represent the cell on the x-th row and the y-th col... |
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Vasya decided to learn to play chess. Classic chess doesn't seem interesting to him, so he plays his own sort of chess.
The queen is the piece that captures all squares on its vertical, horizontal and diagonal lines. If the cell is located on the same ... |
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A lighthouse keeper Peter commands an army of $n$ battle lemmings. He ordered his army to stand in a line and numbered the lemmings from $1$ to $n$ from left to right. Some of the lemmings hold shields. Each lemming cannot hold more than one shield.
Th... |
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DZY loves chemistry, and he enjoys mixing chemicals.
DZY has n chemicals, and m pairs of them will react. He wants to pour these chemicals into a test tube, and he needs to pour them in one by one, in any order.
Let's consider the danger of a test tu... |
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Little Artem got n stones on his birthday and now wants to give some of them to Masha. He knows that Masha cares more about the fact of receiving the present, rather than the value of that present, so he wants to give her stones as many times as possibl... |
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Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction $\frac{a}{b}$ is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible if its ... |
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Grigory has $n$ magic stones, conveniently numbered from $1$ to $n$. The charge of the $i$-th stone is equal to $c_i$.
Sometimes Grigory gets bored and selects some inner stone (that is, some stone with index $i$, where $2 \le i \le n - 1$), and after ... |
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There are $n$ children numbered from $1$ to $n$ in a kindergarten. Kindergarten teacher gave $a_i$ ($1 \leq a_i \leq n$) candies to the $i$-th child. Children were seated in a row in order from $1$ to $n$ from left to right and started eating candies.
... |
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Arkady bought an air ticket from a city A to a city C. Unfortunately, there are no direct flights, but there are a lot of flights from A to a city B, and from B to C.
There are $n$ flights from A to B, they depart at time moments $a_1$, $a_2$, $a_3$, .... |
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You are given a permutation of integers from 1 to n. Exactly once you apply the following operation to this permutation: pick a random segment and shuffle its elements. Formally: Pick a random segment (continuous subsequence) from l to r. All $\frac{n(... |
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Tanya wants to go on a journey across the cities of Berland. There are $n$ cities situated along the main railroad line of Berland, and these cities are numbered from $1$ to $n$.
Tanya plans her journey as follows. First of all, she will choose some c... |
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Mancala is a game famous in the Middle East. It is played on a board that consists of 14 holes. [Image]
Initially, each hole has $a_i$ stones. When a player makes a move, he chooses a hole which contains a positive number of stones. He takes all the ... |
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George is a cat, so he really likes to play. Most of all he likes to play with his array of positive integers b. During the game, George modifies the array by using special changes. Let's mark George's current array as b_1, b_2, ..., b_{|}b| (record |b|... |
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User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this: << p - k p - k +... |
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This is the hard version of the problem. The difference between versions is the constraints on $n$ and $a_i$. You can make hacks only if all versions of the problem are solved.
First, Aoi came up with the following idea for the competitive programming ... |
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The Patisserie AtCoder sells cakes with number-shaped candles.
There are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively.
Each cake has an integer value called deliciousness, as follows:
- The deliciousness of the c... |
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Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?Definition of common divisor
An integer d is said to be... |
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To decide which is the strongest among Rock, Paper, and Scissors, we will hold an RPS tournament.
There are 2^k players in this tournament, numbered 0 through 2^k-1. Each player has his/her favorite hand, which he/she will use in every match.
A string s... |
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Let f(A, B) be the exclusive OR of A, A+1, ..., B. Find f(A, B).
What is exclusive OR?
The bitwise exclusive OR of integers c_1, c_2, ..., c_n (let us call it y) is defined as follows:
- When y is written in base two, the digit in the 2^k's place (k \g... |
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You are given a tree with N vertices.
Here, a tree is a kind of graph, and more specifically, a connected undirected graph with N-1 edges, where N is the number of its vertices.
The i-th edge (1≤i≤N-1) connects Vertices a_i and b_i, and has a length o... |
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Given is a string S of length N consisting of lowercase English letters.
Snuke can do this operation any number of times: remove fox occurring as a substring from s and concatenate the remaining parts of s.
What is the minimum possible length of s after... |
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n evenly spaced points have been marked around the edge of a circle. There is a number written at each point. You choose a positive real number k. Then you may repeatedly select a set of 2 or more points which are evenly spaced, and either increase all ... |
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Count the number of distinct sequences a_1, a_2, ..., a_{n} (1 ≤ a_{i}) consisting of positive integers such that gcd(a_1, a_2, ..., a_{n}) = x and $\sum_{i = 1}^{n} a_{i} = y$. As this number could be large, print the answer modulo 10^9 + 7.
gcd here ... |
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You are organizing a boxing tournament, where $n$ boxers will participate ($n$ is a power of $2$), and your friend is one of them. All boxers have different strength from $1$ to $n$, and boxer $i$ wins in the match against boxer $j$ if and only if $i$ i... |
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Peter Parker wants to play a game with Dr. Octopus. The game is about cycles. Cycle is a sequence of vertices, such that first one is connected with the second, second is connected with third and so on, while the last one is connected with the first one... |
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Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes... |
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Polycarpus is the director of a large corporation. There are n secretaries working for the corporation, each of them corresponds via the famous Spyke VoIP system during the day. We know that when two people call each other via Spyke, the Spyke network a... |
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A number is called quasibinary if its decimal representation contains only digits 0 or 1. For example, numbers 0, 1, 101, 110011 — are quasibinary and numbers 2, 12, 900 are not.
You are given a positive integer n. Represent it as a sum of minimum numb... |
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Arya has n opponents in the school. Each day he will fight with all opponents who are present this day. His opponents have some fighting plan that guarantees they will win, but implementing this plan requires presence of them all. That means if one day ... |
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Vus the Cossack holds a programming competition, in which $n$ people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly $m$ pens and $k$ notebooks.
Determine whether the Cossack can reward all participan... |
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This year, as in previous years, MemSQL is inviting the top 25 competitors from the Start[c]up qualification round to compete onsite for the final round. Not everyone who is eligible to compete onsite can afford to travel to the office, though. Initiall... |
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A permutation p of size n is an array such that every integer from 1 to n occurs exactly once in this array.
Let's call a permutation an almost identity permutation iff there exist at least n - k indices i (1 ≤ i ≤ n) such that p_{i} = i.
Your task is... |
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Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of n vertices numbered from 0 to n - 1. For all 0 ≤ u < v < n, vertex u and vertex v are connected ... |
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Many computer strategy games require building cities, recruiting army, conquering tribes, collecting resources. Sometimes it leads to interesting problems.
Let's suppose that your task is to build a square city. The world map uses the Cartesian coordi... |
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Thanos sort is a supervillain sorting algorithm, which works as follows: if the array is not sorted, snap your fingers* to remove the first or the second half of the items, and repeat the process.
Given an input array, what is the size of the longest s... |
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Hyakugoku has just retired from being the resident deity of the South Black Snail Temple in order to pursue her dream of becoming a cartoonist. She spent six months in that temple just playing "Cat's Cradle" so now she wants to try a different game — "S... |
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You are given $n$ blocks, each of them is of the form [color$_1$|value|color$_2$], where the block can also be flipped to get [color$_2$|value|color$_1$].
A sequence of blocks is called valid if the touching endpoints of neighboring blocks have the sa... |
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Tom loves vowels, and he likes long words with many vowels. His favorite words are vowelly words. We say a word of length $k$ is vowelly if there are positive integers $n$ and $m$ such that $n\cdot m = k$ and when the word is written by using $n$ rows a... |
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Ford Prefect got a job as a web developer for a small company that makes towels. His current work task is to create a search engine for the website of the company. During the development process, he needs to write a subroutine for comparing strings S an... |
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Peter wrote on the board a strictly increasing sequence of positive integers a_1, a_2, ..., a_{n}. Then Vasil replaced some digits in the numbers of this sequence by question marks. Thus, each question mark corresponds to exactly one lost digit.
Restor... |
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Adilbek's house is located on a street which can be represented as the OX axis. This street is really dark, so Adilbek wants to install some post lamps to illuminate it. Street has $n$ positions to install lamps, they correspond to the integer numbers f... |
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$k$ people want to split $n$ candies between them. Each candy should be given to exactly one of them or be thrown away.
The people are numbered from $1$ to $k$, and Arkady is the first of them. To split the candies, Arkady will choose an integer $x$ an... |
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Being a nonconformist, Volodya is displeased with the current state of things, particularly with the order of natural numbers (natural number is positive integer number). He is determined to rearrange them. But there are too many natural numbers, so Vol... |
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You are given $n$ numbers $a_1, a_2, \dots, a_n$. With a cost of one coin you can perform the following operation:
Choose one of these numbers and add or subtract $1$ from it.
In particular, we can apply this operation to the same number several times... |
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A correct expression of the form a+b=c was written; a, b and c are non-negative integers without leading zeros. In this expression, the plus and equally signs were lost. The task is to restore the expression. In other words, one character '+' and one ch... |
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Fedya studies in a gymnasium. Fedya's maths hometask is to calculate the following expression:(1^{n} + 2^{n} + 3^{n} + 4^{n}) mod 5
for given value of n. Fedya managed to complete the task. Can you? Note that given number n can be extremely large (e.g.... |
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There are $n$ houses along the road where Anya lives, each one is painted in one of $k$ possible colors.
Anya likes walking along this road, but she doesn't like when two adjacent houses at the road have the same color. She wants to select a long segme... |
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Bizon the Champion is called the Champion for a reason.
Bizon the Champion has recently got a present — a new glass cupboard with n shelves and he decided to put all his presents there. All the presents can be divided into two types: medals and cups. ... |
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++++++++[>+>++>+++>++++>+++++>++++++>+++++++>++++++++>+++++++++>++++++++++>+
++++++++++>++++++++++++>+++++++++++++>++++++++++++++>+++++++++++++++>+++++++
+++++++++<<<<<<<<<<<<<<<<-]>>>>>>>>>>.<<<<<<<<<<>>>>>>>>>>>>>>++.--<<<<<<<<<
<<<<<>>>>>>>>>>>>>+.-<... |
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zscoder has a deck of $n+m$ custom-made cards, which consists of $n$ cards labelled from $1$ to $n$ and $m$ jokers. Since zscoder is lonely, he wants to play a game with himself using those cards.
Initially, the deck is shuffled uniformly randomly and... |
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Polycarp is a music editor at the radio station. He received a playlist for tomorrow, that can be represented as a sequence a_1, a_2, ..., a_{n}, where a_{i} is a band, which performs the i-th song. Polycarp likes bands with the numbers from 1 to m, but... |
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Another Codeforces Round has just finished! It has gathered $n$ participants, and according to the results, the expected rating change of participant $i$ is $a_i$. These rating changes are perfectly balanced — their sum is equal to $0$.
Unfortunately, ... |
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Valera considers a number beautiful, if it equals 2^{k} or -2^{k} for some integer k (k ≥ 0). Recently, the math teacher asked Valera to represent number n as the sum of beautiful numbers. As Valera is really greedy, he wants to complete the task using ... |
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You are given an array $a_1, a_2, \ldots, a_n$.
In one operation you can choose two elements $a_i$ and $a_j$ ($i \ne j$) and decrease each of them by one.
You need to check whether it is possible to make all the elements equal to zero or not.
-----I... |
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-----Input-----
The input contains a single integer $a$ ($1 \le a \le 99$).
-----Output-----
Output "YES" or "NO".
-----Examples-----
Input
5
Output
YES
Input
13
Output
NO
Input
24
Output
NO
Input
46
Output
YES
Read the inputs from stdin ... |
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Petya was late for the lesson too. The teacher gave him an additional task. For some array a Petya should find the number of different ways to select non-empty subset of elements from it in such a way that their product is equal to a square of some inte... |
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There is a rectangular grid of n rows of m initially-white cells each.
Arkady performed a certain number (possibly zero) of operations on it. In the i-th operation, a non-empty subset of rows R_{i} and a non-empty subset of columns C_{i} are chosen. Fo... |
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Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
- Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many cho... |
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We have a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.
The square (i, j) has two numbers A_{ij} and B_{ij} written on it.
First, for each square, Takahash... |
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You are given N non-negative integers A_1, A_2, ..., A_N and another non-negative integer K.
For a integer X between 0 and K (inclusive), let f(X) = (X XOR A_1) + (X XOR A_2) + ... + (X XOR A_N).
Here, for non-negative integers a and b, a XOR b denotes ... |
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Given are an N \times N matrix and an integer K. The entry in the i-th row and j-th column of this matrix is denoted as a_{i, j}. This matrix contains each of 1, 2, \dots, N^2 exactly once.
Sigma can repeat the following two kinds of operation arbitrari... |
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We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them.
If we place the K pieces on squares (x_1, y_1)... |
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There are N people standing in a queue from west to east.
Given is a string S of length N representing the directions of the people.
The i-th person from the west is facing west if the i-th character of S is L, and east if that character of S is R.
A pe... |
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In this problem we consider a special type of an auction, which is called the second-price auction. As in regular auction n bidders place a bid which is price a bidder ready to pay. The auction is closed, that is, each bidder secretly informs the organi... |
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Профиль горного хребта схематично задан в виде прямоугольной таблицы из символов «.» (пустое пространство) и «*» (часть горы). Каждый столбец таблицы содержит хотя бы одну «звёздочку». Гарантируется, что любой из символов «*» либо находится в нижней стр... |
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Polycarp is a big lover of killing time in social networks. A page with a chatlist in his favourite network is made so that when a message is sent to some friend, his friend's chat rises to the very top of the page. The relative order of the other chats... |
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You are given a tube which is reflective inside represented as two non-coinciding, but parallel to $Ox$ lines. Each line has some special integer points — positions of sensors on sides of the tube.
You are going to emit a laser ray in the tube. To do s... |
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The only king stands on the standard chess board. You are given his position in format "cd", where c is the column from 'a' to 'h' and d is the row from '1' to '8'. Find the number of moves permitted for the king.
Check the king's moves here https://en... |
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There are n cities in Berland, each of them has a unique id — an integer from 1 to n, the capital is the one with id 1. Now there is a serious problem in Berland with roads — there are no roads.
That is why there was a decision to build n - 1 roads so ... |
Solve the programming task below in a Python markdown code block.
Polycarp has a strict daily schedule. He has n alarms set for each day, and the i-th alarm rings each day at the same time during exactly one minute.
Determine the longest time segment when Polycarp can sleep, i. e. no alarm rings in that period. It is... |
Solve the programming task below in a Python markdown code block.
You are given a tree with $n$ vertices. You are allowed to modify the structure of the tree through the following multi-step operation: Choose three vertices $a$, $b$, and $c$ such that $b$ is adjacent to both $a$ and $c$. For every vertex $d$ other t... |
Solve the programming task below in a Python markdown code block.
In an attempt to escape the Mischievous Mess Makers' antics, Farmer John has abandoned his farm and is traveling to the other side of Bovinia. During the journey, he and his k cows have decided to stay at the luxurious Grand Moo-dapest Hotel. The hotel ... |
Solve the programming task below in a Python markdown code block.
There are n cities in Bearland, numbered 1 through n. Cities are arranged in one long row. The distance between cities i and j is equal to |i - j|.
Limak is a police officer. He lives in a city a. His job is to catch criminals. It's hard because he doe... |
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