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Sasha lives in a big happy family. At the Man's Day all the men of the family gather to celebrate it following their own traditions. There are n men in Sasha's family, so let's number them with integers from 1 to n.
Each man has at most one father but ... |
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You are given a string, consisting of lowercase Latin letters.
A pair of neighbouring letters in a string is considered ugly if these letters are also neighbouring in a alphabet. For example, string "abaca" contains ugly pairs at positions $(1, 2)$ — "... |
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On a chessboard with a width of $10^9$ and a height of $10^9$, the rows are numbered from bottom to top from $1$ to $10^9$, and the columns are numbered from left to right from $1$ to $10^9$. Therefore, for each cell of the chessboard you can assign the... |
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One day Polycarp published a funny picture in a social network making a poll about the color of his handle. Many of his friends started reposting Polycarp's joke to their news feed. Some of them reposted the reposts and so on.
These events are given as... |
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Vasya's house is situated in a forest, and there is a mushroom glade near it. The glade consists of two rows, each of which can be divided into n consecutive cells. For each cell Vasya knows how fast the mushrooms grow in this cell (more formally, how m... |
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The main road in Bytecity is a straight line from south to north. Conveniently, there are coordinates measured in meters from the southernmost building in north direction.
At some points on the road there are n friends, and i-th of them is standing at ... |
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ZS the Coder and Chris the Baboon has explored Udayland for quite some time. They realize that it consists of n towns numbered from 1 to n.
There are n directed roads in the Udayland. i-th of them goes from town i to some other town a_{i} (a_{i} ≠ i).... |
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Jack decides to invite Emma out for a dinner. Jack is a modest student, he doesn't want to go to an expensive restaurant. Emma is a girl with high taste, she prefers elite places.
Munhattan consists of n streets and m avenues. There is exactly one rest... |
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As Famil Door’s birthday is coming, some of his friends (like Gabi) decided to buy a present for him. His friends are going to buy a string consisted of round brackets since Famil Door loves string of brackets of length n more than any other strings!
T... |
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Alice is playing with some stones.
Now there are three numbered heaps of stones. The first of them contains $a$ stones, the second of them contains $b$ stones and the third of them contains $c$ stones.
Each time she can do one of two operations: take... |
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Today Johnny wants to increase his contribution. His plan assumes writing $n$ blogs. One blog covers one topic, but one topic can be covered by many blogs. Moreover, some blogs have references to each other. Each pair of blogs that are connected by a re... |
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There is a square of size $10^6 \times 10^6$ on the coordinate plane with four points $(0, 0)$, $(0, 10^6)$, $(10^6, 0)$, and $(10^6, 10^6)$ as its vertices.
You are going to draw segments on the plane. All segments are either horizontal or vertical an... |
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In the Bus of Characters there are $n$ rows of seat, each having $2$ seats. The width of both seats in the $i$-th row is $w_i$ centimeters. All integers $w_i$ are distinct.
Initially the bus is empty. On each of $2n$ stops one passenger enters the bus.... |
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You are given an array a consisting of n elements. The imbalance value of some subsegment of this array is the difference between the maximum and minimum element from this segment. The imbalance value of the array is the sum of imbalance values of all s... |
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Of course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains a_{i} animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so ... |
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In this problem you will have to deal with a real algorithm that is used in the VK social network.
As in any other company that creates high-loaded websites, the VK developers have to deal with request statistics regularly. An important indicator refle... |
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The marmots have prepared a very easy problem for this year's HC^2 – this one. It involves numbers n, k and a sequence of n positive integers a_1, a_2, ..., a_{n}. They also came up with a beautiful and riveting story for the problem statement. It expla... |
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Ridhiman challenged Ashish to find the maximum valued subsequence of an array $a$ of size $n$ consisting of positive integers.
The value of a non-empty subsequence of $k$ elements of $a$ is defined as $\sum 2^i$ over all integers $i \ge 0$ such that a... |
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In distant future on Earth day lasts for n hours and that's why there are n timezones. Local times in adjacent timezones differ by one hour. For describing local time, hours numbers from 1 to n are used, i.e. there is no time "0 hours", instead of it "n... |
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There is one apple tree in Arkady's garden. It can be represented as a set of junctions connected with branches so that there is only one way to reach any junctions from any other one using branches. The junctions are enumerated from $1$ to $n$, the jun... |
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Little town Nsk consists of n junctions connected by m bidirectional roads. Each road connects two distinct junctions and no two roads connect the same pair of junctions. It is possible to get from any junction to any other junction by these roads. The ... |
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You have a playlist consisting of $n$ songs. The $i$-th song is characterized by two numbers $t_i$ and $b_i$ — its length and beauty respectively. The pleasure of listening to set of songs is equal to the total length of the songs in the set multiplied ... |
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This is the hard version of the problem. The difference is the constraint on the sum of lengths of strings and the number of test cases. You can make hacks only if you solve all versions of this task.
You are given a string $s$, consisting of lowercase... |
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You are playing a computer game, where you lead a party of $m$ soldiers. Each soldier is characterised by his agility $a_i$.
The level you are trying to get through can be represented as a straight line segment from point $0$ (where you and your squad ... |
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Your program fails again. This time it gets "Wrong answer on test 233".
This is the harder version of the problem. In this version, $1 \le n \le 2\cdot10^5$. You can hack this problem if you locked it. But you can hack the previous problem only if you ... |
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Little Susie, thanks to her older brother, likes to play with cars. Today she decided to set up a tournament between them. The process of a tournament is described in the next paragraph.
There are n toy cars. Each pair collides. The result of a collisi... |
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Guy-Manuel and Thomas have an array $a$ of $n$ integers [$a_1, a_2, \dots, a_n$]. In one step they can add $1$ to any element of the array. Formally, in one step they can choose any integer index $i$ ($1 \le i \le n$) and do $a_i := a_i + 1$.
If either... |
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Monocarp has drawn a tree (an undirected connected acyclic graph) and then has given each vertex an index. All indices are distinct numbers from $1$ to $n$. For every edge $e$ of this tree, Monocarp has written two numbers: the maximum indices of the ve... |
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Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For... |
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One foggy Stockholm morning, Karlsson decided to snack on some jam in his friend Lillebror Svantenson's house. Fortunately for Karlsson, there wasn't anybody in his friend's house. Karlsson was not going to be hungry any longer, so he decided to get som... |
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You are given three multisets of pairs of colored sticks: $R$ pairs of red sticks, the first pair has length $r_1$, the second pair has length $r_2$, $\dots$, the $R$-th pair has length $r_R$; $G$ pairs of green sticks, the first pair has length $g_1... |
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After battling Shikamaru, Tayuya decided that her flute is too predictable, and replaced it with a guitar. The guitar has $6$ strings and an infinite number of frets numbered from $1$. Fretting the fret number $j$ on the $i$-th string produces the note ... |
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Given an array $a$ of length $n$, find another array, $b$, of length $n$ such that:
for each $i$ $(1 \le i \le n)$ $MEX(\{b_1$, $b_2$, $\ldots$, $b_i\})=a_i$.
The $MEX$ of a set of integers is the smallest non-negative integer that doesn't belong t... |
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Happy new year! The year 2020 is also known as Year Gyeongja (경자년, gyeongja-nyeon) in Korea. Where did the name come from? Let's briefly look at the Gapja system, which is traditionally used in Korea to name the years.
There are two sequences of $n$ st... |
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There are n cities in the country where the Old Peykan lives. These cities are located on a straight line, we'll denote them from left to right as c_1, c_2, ..., c_{n}. The Old Peykan wants to travel from city c_1 to c_{n} using roads. There are (n - 1)... |
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Dima loves Inna very much. He decided to write a song for her. Dima has a magic guitar with n strings and m frets. Dima makes the guitar produce sounds like that: to play a note, he needs to hold one of the strings on one of the frets and then pull the ... |
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You are given an undirected graph without self-loops or multiple edges which consists of $n$ vertices and $m$ edges. Also you are given three integers $n_1$, $n_2$ and $n_3$.
Can you label each vertex with one of three numbers 1, 2 or 3 in such way, th... |
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Vitaly has an array of n distinct integers. Vitaly wants to divide this array into three non-empty sets so as the following conditions hold:
The product of all numbers in the first set is less than zero ( < 0). The product of all numbers in the sec... |
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There are many freight trains departing from Kirnes planet every day. One day on that planet consists of $h$ hours, and each hour consists of $m$ minutes, where $m$ is an even number. Currently, there are $n$ freight trains, and they depart every day at... |
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Andrewid the Android is a galaxy-known detective. Now he does not investigate any case and is eating chocolate out of boredom.
A bar of chocolate can be presented as an n × n table, where each cell represents one piece of chocolate. The columns of the ... |
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There are $n$ warriors in a row. The power of the $i$-th warrior is $a_i$. All powers are pairwise distinct.
You have two types of spells which you may cast: Fireball: you spend $x$ mana and destroy exactly $k$ consecutive warriors; Berserk: you spe... |
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Mahmoud and Ehab continue their adventures! As everybody in the evil land knows, Dr. Evil likes bipartite graphs, especially trees.
A tree is a connected acyclic graph. A bipartite graph is a graph, whose vertices can be partitioned into 2 sets in such... |
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Egor wants to achieve a rating of 1600 points on the well-known chess portal ChessForces and he needs your help!
Before you start solving the problem, Egor wants to remind you how the chess pieces move. Chess rook moves along straight lines up and down... |
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You are given a sequence of positive integers a_1, a_2, ..., a_{n}.
While possible, you perform the following operation: find a pair of equal consecutive elements. If there are more than one such pair, find the leftmost (with the smallest indices of e... |
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Ayush is a cashier at the shopping center. Recently his department has started a ''click and collect" service which allows users to shop online.
The store contains k items. n customers have already used the above service. Each user paid for m items. L... |
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The Resistance is trying to take control over as many planets of a particular solar system as possible. Princess Heidi is in charge of the fleet, and she must send ships to some planets in order to maximize the number of controlled planets.
The Galaxy ... |
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Merge sort is a well-known sorting algorithm. The main function that sorts the elements of array a with indices from [l, r) can be implemented as follows: If the segment [l, r) is already sorted in non-descending order (that is, for any i such that l ≤... |
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Vasya owns three big integers — $a, l, r$. Let's define a partition of $x$ such a sequence of strings $s_1, s_2, \dots, s_k$ that $s_1 + s_2 + \dots + s_k = x$, where $+$ is a concatanation of strings. $s_i$ is the $i$-th element of the partition. For e... |
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Whereas humans nowadays read fewer and fewer books on paper, book readership among marmots has surged. Heidi has expanded the library and is now serving longer request sequences.
-----Input-----
Same as the easy version, but the limits have changed: ... |
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Caisa solved the problem with the sugar and now he is on the way back to home.
Caisa is playing a mobile game during his path. There are (n + 1) pylons numbered from 0 to n in this game. The pylon with number 0 has zero height, the pylon with number i... |
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Innokenty works at a flea market and sells some random stuff rare items. Recently he found an old rectangular blanket. It turned out that the blanket is split in $n \cdot m$ colored pieces that form a rectangle with $n$ rows and $m$ columns.
The color... |
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Luckily, Serval got onto the right bus, and he came to the kindergarten on time. After coming to kindergarten, he found the toy bricks very funny.
He has a special interest to create difficult problems for others to solve. This time, with many $1 \time... |
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Polycarp has recently got himself a new job. He now earns so much that his old wallet can't even store all the money he has.
Berland bills somehow come in lots of different sizes. However, all of them are shaped as rectangles (possibly squares). All wa... |
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Creatnx has $n$ mirrors, numbered from $1$ to $n$. Every day, Creatnx asks exactly one mirror "Am I beautiful?". The $i$-th mirror will tell Creatnx that he is beautiful with probability $\frac{p_i}{100}$ for all $1 \le i \le n$.
Creatnx asks the mirro... |
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There are n cities and m two-way roads in Berland, each road connects two cities. It is known that there is no more than one road connecting each pair of cities, and there is no road which connects the city with itself. It is possible that there is no w... |
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Vitya has learned that the answer for The Ultimate Question of Life, the Universe, and Everything is not the integer 54 42, but an increasing integer sequence $a_1, \ldots, a_n$. In order to not reveal the secret earlier than needed, Vitya encrypted the... |
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Ramesses knows a lot about problems involving trees (undirected connected graphs without cycles)!
He created a new useful tree decomposition, but he does not know how to construct it, so he asked you for help!
The decomposition is the splitting the ed... |
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Polycarp has just attempted to pass the driving test. He ran over the straight road with the signs of four types.
speed limit: this sign comes with a positive integer number — maximal speed of the car after the sign (cancel the action of the previous... |
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Anton is growing a tree in his garden. In case you forgot, the tree is a connected acyclic undirected graph.
There are n vertices in the tree, each of them is painted black or white. Anton doesn't like multicolored trees, so he wants to change the tree... |
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Marcin is a coach in his university. There are $n$ students who want to attend a training camp. Marcin is a smart coach, so he wants to send only the students that can work calmly with each other.
Let's focus on the students. They are indexed with inte... |
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They say "years are like dominoes, tumbling one after the other". But would a year fit into a grid? I don't think so.
Limak is a little polar bear who loves to play. He has recently got a rectangular grid with h rows and w columns. Each cell is a squar... |
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Pink Floyd are pulling a prank on Roger Waters. They know he doesn't like walls, he wants to be able to walk freely, so they are blocking him from exiting his room which can be seen as a grid.
Roger Waters has a square grid of size $n\times n$ and he w... |
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Ghosts live in harmony and peace, they travel the space without any purpose other than scare whoever stands in their way.
There are $n$ ghosts in the universe, they move in the $OXY$ plane, each one of them has its own velocity that does not change in ... |
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Pasha got a very beautiful string s for his birthday, the string consists of lowercase Latin letters. The letters in the string are numbered from 1 to |s| from left to right, where |s| is the length of the given string.
Pasha didn't like his present ve... |
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You are given a chess board with $n$ rows and $n$ columns. Initially all cells of the board are empty, and you have to put a white or a black knight into each cell of the board.
A knight is a chess piece that can attack a piece in cell ($x_2$, $y_2$) f... |
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You are given two arrays of integers $a_1,\ldots,a_n$ and $b_1,\ldots,b_m$.
Your task is to find a non-empty array $c_1,\ldots,c_k$ that is a subsequence of $a_1,\ldots,a_n$, and also a subsequence of $b_1,\ldots,b_m$. If there are multiple answers, fi... |
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Mike decided to teach programming to children in an elementary school. He knows that it is not an easy task to interest children in that age to code. That is why he decided to give each child two sweets.
Mike has $n$ sweets with sizes $a_1, a_2, \ldots... |
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You are given two integers $a$ and $m$. Calculate the number of integers $x$ such that $0 \le x < m$ and $\gcd(a, m) = \gcd(a + x, m)$.
Note: $\gcd(a, b)$ is the greatest common divisor of $a$ and $b$.
-----Input-----
The first line contains the sin... |
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Recently Petya walked in the forest and found a magic stick.
Since Petya really likes numbers, the first thing he learned was spells for changing numbers. So far, he knows only two spells that can be applied to a positive integer: If the chosen numbe... |
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Recently, Mike was very busy with studying for exams and contests. Now he is going to chill a bit by doing some sight seeing in the city.
City consists of n intersections numbered from 1 to n. Mike starts walking from his house located at the intersect... |
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A Large Software Company develops its own social network. Analysts have found that during the holidays, major sporting events and other significant events users begin to enter the network more frequently, resulting in great load increase on the infrastr... |
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Carol is currently curling.
She has n disks each with radius r on the 2D plane.
Initially she has all these disks above the line y = 10^100.
She then will slide the disks towards the line y = 0 one by one in order from 1 to n.
When she slides the ... |
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Alicia has an array, $a_1, a_2, \ldots, a_n$, of non-negative integers. For each $1 \leq i \leq n$, she has found a non-negative integer $x_i = max(0, a_1, \ldots, a_{i-1})$. Note that for $i=1$, $x_i = 0$.
For example, if Alicia had the array $a = \{0... |
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You are given a sequence $s$ consisting of $n$ digits from $1$ to $9$.
You have to divide it into at least two segments (segment — is a consecutive sequence of elements) (in other words, you have to place separators between some digits of the sequence)... |
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There are $n$ beautiful skyscrapers in New York, the height of the $i$-th one is $h_i$. Today some villains have set on fire first $n - 1$ of them, and now the only safety building is $n$-th skyscraper.
Let's call a jump from $i$-th skyscraper to $j$-t... |
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You can perfectly predict the price of a certain stock for the next N days. You would like to profit on this knowledge, but only want to transact one share of stock per day. That is, each day you will either buy one share, sell one share, or do nothing.... |
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Since Sonya has just learned the basics of matrices, she decided to play with them a little bit.
Sonya imagined a new type of matrices that she called rhombic matrices. These matrices have exactly one zero, while all other cells have the Manhattan dist... |
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Consider a sequence of digits of length $2^k$ $[a_1, a_2, \ldots, a_{2^k}]$. We perform the following operation with it: replace pairs $(a_{2i+1}, a_{2i+2})$ with $(a_{2i+1} + a_{2i+2})\bmod 10$ for $0\le i<2^{k-1}$. For every $i$ where $a_{2i+1} + a_{2... |
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The little girl loves the problems on array queries very much.
One day she came across a rather well-known problem: you've got an array of n elements (the elements of the array are indexed starting from 1); also, there are q queries, each one is define... |
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Heidi's friend Jenny is asking Heidi to deliver an important letter to one of their common friends. Since Jenny is Irish, Heidi thinks that this might be a prank. More precisely, she suspects that the message she is asked to deliver states: "Send the fo... |
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Alice and Bob are playing a game on a line with $n$ cells. There are $n$ cells labeled from $1$ through $n$. For each $i$ from $1$ to $n-1$, cells $i$ and $i+1$ are adjacent.
Alice initially has a token on some cell on the line, and Bob tries to guess ... |
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Vasya has several phone books, in which he recorded the telephone numbers of his friends. Each of his friends can have one or several phone numbers.
Vasya decided to organize information about the phone numbers of friends. You will be given n strings —... |
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A team of three programmers is going to play a contest. The contest consists of $n$ problems, numbered from $1$ to $n$. Each problem is printed on a separate sheet of paper. The participants have decided to divide the problem statements into three parts... |
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For a sequence a of n integers between 1 and m, inclusive, denote f(a) as the number of distinct subsequences of a (including the empty subsequence).
You are given two positive integers n and m. Let S be the set of all sequences of length n consisting ... |
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This is the easy version of the problem. The difference is the constraint on the sum of lengths of strings and the number of test cases. You can make hacks only if you solve all versions of this task.
You are given a string $s$, consisting of lowercase... |
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Consider a system of n water taps all pouring water into the same container. The i-th water tap can be set to deliver any amount of water from 0 to a_{i} ml per second (this amount may be a real number). The water delivered by i-th tap has temperature t... |
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Iahub is so happy about inventing bubble sort graphs that he's staying all day long at the office and writing permutations. Iahubina is angry that she is no more important for Iahub. When Iahub goes away, Iahubina comes to his office and sabotage his re... |
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Polycarpus has an array, consisting of n integers a_1, a_2, ..., a_{n}. Polycarpus likes it when numbers in an array match. That's why he wants the array to have as many equal numbers as possible. For that Polycarpus performs the following operation mul... |
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A conglomerate consists of $n$ companies. To make managing easier, their owners have decided to merge all companies into one. By law, it is only possible to merge two companies, so the owners plan to select two companies, merge them into one, and contin... |
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We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i,j).
The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_{i,j}.
You, a magical gir... |
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Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions:
- A_i \neq B_i, for every i such that 1\leq i\leq N.
- A_i \ne... |
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This morning Chef wants to jump a little. In a few minutes he will arrive at the point 0. Then he will perform a lot of jumps in such a sequence: 1-jump, 2-jump, 3-jump, 1-jump, 2-jump, 3-jump, 1-jump, and so on.
1-jump means that if Chef is at the poin... |
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You have a new professor of graph theory and he speaks very quickly. You come up with the following plan to keep up with his lecture and make notes.
You know two languages, and the professor is giving the lecture in the first one. The words in both lan... |
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One very well-known internet resource site (let's call it X) has come up with a New Year adventure. Specifically, they decided to give ratings to all visitors.
There are n users on the site, for each user we know the rating value he wants to get as a N... |
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Permutation p is an ordered set of integers p_1, p_2, ..., p_{n}, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as p_{i}. We'll call number n the size or the length of permut... |
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You are given a sequence of $n$ pairs of integers: $(a_1, b_1), (a_2, b_2), \dots , (a_n, b_n)$. This sequence is called bad if it is sorted in non-descending order by first elements or if it is sorted in non-descending order by second elements. Otherwi... |
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You are given two integers $A$ and $B$, calculate the number of pairs $(a, b)$ such that $1 \le a \le A$, $1 \le b \le B$, and the equation $a \cdot b + a + b = conc(a, b)$ is true; $conc(a, b)$ is the concatenation of $a$ and $b$ (for example, $conc(12... |
Solve the programming task below in a Python markdown code block.
Vasya has got $n$ books, numbered from $1$ to $n$, arranged in a stack. The topmost book has number $a_1$, the next one — $a_2$, and so on. The book at the bottom of the stack has number $a_n$. All numbers are distinct.
Vasya wants to move all the book... |
Solve the programming task below in a Python markdown code block.
Iahub likes chess very much. He even invented a new chess piece named Coder. A Coder can move (and attack) one square horizontally or vertically. More precisely, if the Coder is located at position (x, y), he can move to (or attack) positions (x + 1, y)... |
Solve the programming task below in a Python markdown code block.
Valera takes part in the Berland Marathon. The marathon race starts at the stadium that can be represented on the plane as a square whose lower left corner is located at point with coordinates (0, 0) and the length of the side equals a meters. The sides... |
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