id
stringlengths
11
14
content
stringlengths
424
1.17M
apps_data_2100
There are $n$ water tanks in a row, $i$-th of them contains $a_i$ liters of water. The tanks are numbered from $1$ to $n$ from left to right. You can perform the following operation: choose some subsegment $[l, r]$ ($1\le l \le r \le n$), and redistribute water in tanks $l, l+1, \dots, r$ evenly. In other words, repla...
apps_data_2101
Ujan has a lot of useless stuff in his drawers, a considerable part of which are his math notebooks: it is time to sort them out. This time he found an old dusty graph theory notebook with a description of a graph. It is an undirected weighted graph on $n$ vertices. It is a complete graph: each pair of vertices is con...
apps_data_2102
John Doe started thinking about graphs. After some thought he decided that he wants to paint an undirected graph, containing exactly k cycles of length 3. A cycle of length 3 is an unordered group of three distinct graph vertices a, b and c, such that each pair of them is connected by a graph edge. John has been pa...
apps_data_2103
Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water. The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: ...
apps_data_2104
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes. Strictly speaking, it makes a photo of all points with coordinates $(x, y)$, such that $x_1 \leq x \leq x_2$ and $y_1 \leq y \leq y_2$, where...
apps_data_2105
Sherlock has a new girlfriend (so unlike him!). Valentine's day is coming and he wants to gift her some jewelry. He bought n pieces of jewelry. The i-th piece has price equal to i + 1, that is, the prices of the jewelry are 2, 3, 4, ... n + 1. Watson gave Sherlock a challenge to color these jewelry pieces such that t...
apps_data_2106
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom o...
apps_data_2107
As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down will know and relocate him. [Image] Thus, he came up with a puz...
apps_data_2108
Our beloved detective, Sherlock is currently trying to catch a serial killer who kills a person each day. Using his powers of deduction, he came to know that the killer has a strategy for selecting his next victim. The killer starts with two potential victims on his first day, selects one of these two, kills selected ...
apps_data_2109
10^{10^{10}} participants, including Takahashi, competed in two programming contests. In each contest, all participants had distinct ranks from first through 10^{10^{10}}-th. The score of a participant is the product of his/her ranks in the two contests. Process the following Q queries: - In the i-th query, you are gi...
apps_data_2110
Recently, Duff has been practicing weight lifting. As a hard practice, Malek gave her a task. He gave her a sequence of weights. Weight of i-th of them is 2^{w}_{i} pounds. In each step, Duff can lift some of the remaining weights and throw them away. She does this until there's no more weight left. Malek asked her to ...
apps_data_2111
Lesha plays the recently published new version of the legendary game hacknet. In this version character skill mechanism was introduced. Now, each player character has exactly n skills. Each skill is represented by a non-negative integer a_{i} — the current skill level. All skills have the same maximum level A. Along w...
apps_data_2112
You are given an array $a$ consisting of $n$ non-negative integers. You have to choose a non-negative integer $x$ and form a new array $b$ of size $n$ according to the following rule: for all $i$ from $1$ to $n$, $b_i = a_i \oplus x$ ($\oplus$ denotes the operation bitwise XOR). An inversion in the $b$ array is a pair...
apps_data_2113
Jeff has become friends with Furik. Now these two are going to play one quite amusing game. At the beginning of the game Jeff takes a piece of paper and writes down a permutation consisting of n numbers: p_1, p_2, ..., p_{n}. Then the guys take turns to make moves, Jeff moves first. During his move, Jeff chooses two a...
apps_data_2114
DZY loves Physics, and he enjoys calculating density. Almost everything has density, even a graph. We define the density of a non-directed graph (nodes and edges of the graph have some values) as follows: $\left\{\begin{array}{ll}{\frac{v}{e}} & {(e > 0)} \\{0} & {(e = 0)} \end{array} \right.$ where v is the sum of th...
apps_data_2115
Little Petya likes points a lot. Recently his mom has presented him n points lying on the line OX. Now Petya is wondering in how many ways he can choose three distinct points so that the distance between the two farthest of them doesn't exceed d. Note that the order of the points inside the group of three chosen point...
apps_data_2116
You are given a string s, consisting of lowercase English letters, and the integer m. One should choose some symbols from the given string so that any contiguous subsegment of length m has at least one selected symbol. Note that here we choose positions of symbols, not the symbols themselves. Then one uses the chosen...
apps_data_2117
Mike is the president of country What-The-Fatherland. There are n bears living in this country besides Mike. All of them are standing in a line and they are numbered from 1 to n from left to right. i-th bear is exactly a_{i} feet high. [Image] A group of bears is a non-empty contiguous segment of the line. The siz...
apps_data_2118
Sam has been teaching Jon the Game of Stones to sharpen his mind and help him devise a strategy to fight the white walkers. The rules of this game are quite simple: The game starts with n piles of stones indexed from 1 to n. The i-th pile contains s_{i} stones. The players make their moves alternatively. A move is con...
apps_data_2119
You are given an array consisting of n non-negative integers a_1, a_2, ..., a_{n}. You are going to destroy integers in the array one by one. Thus, you are given the permutation of integers from 1 to n defining the order elements of the array are destroyed. After each element is destroyed you have to find out the seg...
apps_data_2120
Bessie and the cows are playing with sequences and need your help. They start with a sequence, initially containing just the number 0, and perform n operations. Each operation is one of the following: Add the integer x_{i} to the first a_{i} elements of the sequence. Append an integer k_{i} to the end of the sequence...
apps_data_2121
There are n kangaroos with pockets. Each kangaroo has a size (integer number). A kangaroo can go into another kangaroo's pocket if and only if the size of kangaroo who hold the kangaroo is at least twice as large as the size of kangaroo who is held. Each kangaroo can hold at most one kangaroo, and the kangaroo who is ...
apps_data_2122
Polycarp starts his own business. Tomorrow will be the first working day of his car repair shop. For now the car repair shop is very small and only one car can be repaired at a given time. Polycarp is good at marketing, so he has already collected n requests from clients. The requests are numbered from 1 to n in order...
apps_data_2123
Oleg the bank client and Igor the analyst are arguing again. This time, they want to pick a gift as a present for their friend, ZS the coder. After a long thought, they decided that their friend loves to eat carrots the most and thus they want to pick the best carrot as their present. There are n carrots arranged in a...
apps_data_2124
Niwel is a little golden bear. As everyone knows, bears live in forests, but Niwel got tired of seeing all the trees so he decided to move to the city. In the city, Niwel took on a job managing bears to deliver goods. The city that he lives in can be represented as a directed graph with n nodes and m edges. Each edge ...
apps_data_2125
Wherever the destination is, whoever we meet, let's render this song together. On a Cartesian coordinate plane lies a rectangular stage of size w × h, represented by a rectangle with corners (0, 0), (w, 0), (w, h) and (0, h). It can be seen that no collisions will happen before one enters the stage. On the sides of t...
apps_data_2126
For the multiset of positive integers $s=\{s_1,s_2,\dots,s_k\}$, define the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of $s$ as follow: $\gcd(s)$ is the maximum positive integer $x$, such that all integers in $s$ are divisible on $x$. $\textrm{lcm}(s)$ is the minimum positive integer $x$, that divis...
apps_data_2127
There are many anime that are about "love triangles": Alice loves Bob, and Charlie loves Bob as well, but Alice hates Charlie. You are thinking about an anime which has n characters. The characters are labeled from 1 to n. Every pair of two characters can either mutually love each other or mutually hate each other (the...
apps_data_2128
Iahub helps his grandfather at the farm. Today he must milk the cows. There are n cows sitting in a row, numbered from 1 to n from left to right. Each cow is either facing to the left or facing to the right. When Iahub milks a cow, all the cows that see the current cow get scared and lose one unit of the quantity of mi...
apps_data_2129
Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of $n$ stations, enumerated from $1$ through $n$. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate station that the train will visi...
apps_data_2130
Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i...
apps_data_2131
There are $n$ startups. Startups can be active or acquired. If a startup is acquired, then that means it has exactly one active startup that it is following. An active startup can have arbitrarily many acquired startups that are following it. An active startup cannot follow any other startup. The following steps happe...
apps_data_2132
Nauuo is a girl who loves drawing circles. One day she has drawn a circle and wanted to draw a tree on it. The tree is a connected undirected graph consisting of $n$ nodes and $n-1$ edges. The nodes are numbered from $1$ to $n$. Nauuo wants to draw a tree on the circle, the nodes of the tree should be in $n$ distinc...
apps_data_2133
There are n student groups at the university. During the study day, each group can take no more than 7 classes. Seven time slots numbered from 1 to 7 are allocated for the classes. The schedule on Monday is known for each group, i. e. time slots when group will have classes are known. Your task is to determine the mi...
apps_data_2134
Mitya has a rooted tree with $n$ vertices indexed from $1$ to $n$, where the root has index $1$. Each vertex $v$ initially had an integer number $a_v \ge 0$ written on it. For every vertex $v$ Mitya has computed $s_v$: the sum of all values written on the vertices on the path from vertex $v$ to the root, as well as $h_...
apps_data_2135
In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side. One example of a grid path is (0, 0) → (0, 1) → (0, 2) → (1, 2...
apps_data_2136
You are given a Young diagram. Given diagram is a histogram with $n$ columns of lengths $a_1, a_2, \ldots, a_n$ ($a_1 \geq a_2 \geq \ldots \geq a_n \geq 1$). [Image] Young diagram for $a=[3,2,2,2,1]$. Your goal is to find the largest number of non-overlapping dominos that you can draw inside of this histogram, a do...
apps_data_2137
Vasya's got a birthday coming up and his mom decided to give him an array of positive integers a of length n. Vasya thinks that an array's beauty is the greatest common divisor of all its elements. His mom, of course, wants to give him as beautiful an array as possible (with largest possible beauty). Unfortunately, th...
apps_data_2138
You are fishing with polar bears Alice and Bob. While waiting for the fish to bite, the polar bears get bored. They come up with a game. First Alice and Bob each writes a 01-string (strings that only contain character "0" and "1") a and b. Then you try to turn a into b using two types of operations: Write parity(a) to...
apps_data_2139
You are given an array $a$ of length $2n$. Consider a partition of array $a$ into two subsequences $p$ and $q$ of length $n$ each (each element of array $a$ should be in exactly one subsequence: either in $p$ or in $q$). Let's sort $p$ in non-decreasing order, and $q$ in non-increasing order, we can denote the sorted ...
apps_data_2140
While discussing a proper problem A for a Codeforces Round, Kostya created a cyclic array of positive integers $a_1, a_2, \ldots, a_n$. Since the talk was long and not promising, Kostya created a new cyclic array $b_1, b_2, \ldots, b_{n}$ so that $b_i = (a_i \mod a_{i + 1})$, where we take $a_{n+1} = a_1$. Here $mod$ i...
apps_data_2141
Evlampiy was gifted a rooted tree. The vertices of the tree are numbered from $1$ to $n$. Each of its vertices also has an integer $a_i$ written on it. For each vertex $i$, Evlampiy calculated $c_i$ — the number of vertices $j$ in the subtree of vertex $i$, such that $a_j < a_i$. [Image]Illustration for the second exam...
apps_data_2142
Recently Polycarpus has learned the "bitwise AND" operation (which is also called "AND") of non-negative integers. Now he wants to demonstrate the school IT teacher his superb manipulation with the learned operation. For that Polycarpus came to school a little earlier and wrote on the board a sequence of non-negative ...
apps_data_2143
Arkady plays Gardenscapes a lot. Arkady wants to build two new fountains. There are n available fountains, for each fountain its beauty and cost are known. There are two types of money in the game: coins and diamonds, so each fountain cost can be either in coins or diamonds. No money changes between the types are allow...
apps_data_2144
Ujan has a lot of numbers in his boxes. He likes order and balance, so he decided to reorder the numbers. There are $k$ boxes numbered from $1$ to $k$. The $i$-th box contains $n_i$ integer numbers. The integers can be negative. All of the integers are distinct. Ujan is lazy, so he will do the following reordering o...
apps_data_2145
Hamed has recently found a string t and suddenly became quite fond of it. He spent several days trying to find all occurrences of t in other strings he had. Finally he became tired and started thinking about the following problem. Given a string s how many ways are there to extract k ≥ 1 non-overlapping substrings from...
apps_data_2146
Have you ever used the chat application QQ? Well, in a chat group of QQ, administrators can muzzle a user for days. In Boboniu's chat group, there's a person called Du Yi who likes to make fun of Boboniu every day. Du will chat in the group for $n$ days. On the $i$-th day: If Du can speak, he'll make fun of Boboniu ...
apps_data_2147
Ziota found a video game called "Monster Invaders". Similar to every other shooting RPG game, "Monster Invaders" involves killing monsters and bosses with guns. For the sake of simplicity, we only consider two different types of monsters and three different types of guns. Namely, the two types of monsters are: a n...
apps_data_2148
You are given several queries. Each query consists of three integers $p$, $q$ and $b$. You need to answer whether the result of $p/q$ in notation with base $b$ is a finite fraction. A fraction in notation with base $b$ is finite if it contains finite number of numerals after the decimal point. It is also possible that...
apps_data_2149
You are given a set of size $m$ with integer elements between $0$ and $2^{n}-1$ inclusive. Let's build an undirected graph on these integers in the following way: connect two integers $x$ and $y$ with an edge if and only if $x \& y = 0$. Here $\&$ is the bitwise AND operation. Count the number of connected components i...
apps_data_2150
In this problem, we will deal with binary strings. Each character of a binary string is either a 0 or a 1. We will also deal with substrings; recall that a substring is a contiguous subsequence of a string. We denote the substring of string $s$ starting from the $l$-th character and ending with the $r$-th character as ...
apps_data_2151
You are given an array $a$ of $n$ integers and an integer $s$. It is guaranteed that $n$ is odd. In one operation you can either increase or decrease any single element by one. Calculate the minimum number of operations required to make the median of the array being equal to $s$. The median of the array with odd leng...
apps_data_2152
This is the easier version of the problem. In this version, $1 \le n \le 10^5$ and $0 \le a_i \le 1$. You can hack this problem only if you solve and lock both problems. Christmas is coming, and our protagonist, Bob, is preparing a spectacular present for his long-time best friend Alice. This year, he decides to prepa...
apps_data_2153
In order to fly to the Moon Mister B just needs to solve the following problem. There is a complete indirected graph with n vertices. You need to cover it with several simple cycles of length 3 and 4 so that each edge is in exactly 2 cycles. We are sure that Mister B will solve the problem soon and will fly to the Mo...
apps_data_2154
Jon Snow is on the lookout for some orbs required to defeat the white walkers. There are k different types of orbs and he needs at least one of each. One orb spawns daily at the base of a Weirwood tree north of the wall. The probability of this orb being of any kind is equal. As the north of wall is full of dangers, he...
apps_data_2155
Summer is coming! It's time for Iahub and Iahubina to work out, as they both want to look hot at the beach. The gym where they go is a matrix a with n lines and m columns. Let number a[i][j] represents the calories burned by performing workout at the cell of gym in the i-th line and the j-th column. Iahub starts with ...
apps_data_2156
One of Timofey's birthday presents is a colourbook in a shape of an infinite plane. On the plane n rectangles with sides parallel to coordinate axes are situated. All sides of the rectangles have odd length. Rectangles cannot intersect, but they can touch each other. Help Timofey to color his rectangles in 4 different...
apps_data_2157
You are given a set Y of n distinct positive integers y_1, y_2, ..., y_{n}. Set X of n distinct positive integers x_1, x_2, ..., x_{n} is said to generate set Y if one can transform X to Y by applying some number of the following two operation to integers in X: Take any integer x_{i} and multiply it by two, i.e. repl...
apps_data_2158
Consider a sequence [a_1, a_2, ... , a_{n}]. Define its prefix product sequence $[ a_{1} \operatorname{mod} n,(a_{1} a_{2}) \operatorname{mod} n, \cdots,(a_{1} a_{2} \cdots a_{n}) \operatorname{mod} n ]$. Now given n, find a permutation of [1, 2, ..., n], such that its prefix product sequence is a permutation of [0, 1...
apps_data_2159
Polycarp is making a quest for his friends. He has already made n tasks, for each task the boy evaluated how interesting it is as an integer q_{i}, and the time t_{i} in minutes needed to complete the task. An interesting feature of his quest is: each participant should get the task that is best suited for him, depen...
apps_data_2160
Polycarp took $n$ videos, the duration of the $i$-th video is $a_i$ seconds. The videos are listed in the chronological order, i.e. the $1$-st video is the earliest, the $2$-nd video is the next, ..., the $n$-th video is the last. Now Polycarp wants to publish exactly $k$ ($1 \le k \le n$) posts in Instabram. Each vid...
apps_data_2161
Just to remind, girls in Arpa's land are really nice. Mehrdad wants to invite some Hoses to the palace for a dancing party. Each Hos has some weight w_{i} and some beauty b_{i}. Also each Hos may have some friends. Hoses are divided in some friendship groups. Two Hoses x and y are in the same friendship group if and o...
apps_data_2162
Consider a tree $T$ (that is, a connected graph without cycles) with $n$ vertices labelled $1$ through $n$. We start the following process with $T$: while $T$ has more than one vertex, do the following: choose a random edge of $T$ equiprobably; shrink the chosen edge: if the edge was connecting vertices $v$ and $...
apps_data_2163
Koa the Koala has a binary string $s$ of length $n$. Koa can perform no more than $n-1$ (possibly zero) operations of the following form: In one operation Koa selects positions $i$ and $i+1$ for some $i$ with $1 \le i < |s|$ and sets $s_i$ to $max(s_i, s_{i+1})$. Then Koa deletes position $i+1$ from $s$ (after the rem...
apps_data_2164
Everybody seems to think that the Martians are green, but it turns out they are metallic pink and fat. Ajs has two bags of distinct nonnegative integers. The bags are disjoint, and the union of the sets of numbers in the bags is $\{0,1,…,M-1\}$, for some positive integer $M$. Ajs draws a number from the first bag and a...
apps_data_2165
Giant chess is quite common in Geraldion. We will not delve into the rules of the game, we'll just say that the game takes place on an h × w field, and it is painted in two colors, but not like in chess. Almost all cells of the field are white and only some of them are black. Currently Gerald is finishing a game of gia...
apps_data_2166
Rick and Morty are playing their own version of Berzerk (which has nothing in common with the famous Berzerk game). This game needs a huge space, so they play it with a computer. In this game there are n objects numbered from 1 to n arranged in a circle (in clockwise order). Object number 1 is a black hole and the oth...
apps_data_2167
A function $f : R \rightarrow R$ is called Lipschitz continuous if there is a real constant K such that the inequality |f(x) - f(y)| ≤ K·|x - y| holds for all $x, y \in R$. We'll deal with a more... discrete version of this term. For an array $h [ 1 . . n ]$, we define it's Lipschitz constant $L(h)$ as follows: if n ...
apps_data_2168
Greg has a weighed directed graph, consisting of n vertices. In this graph any pair of distinct vertices has an edge between them in both directions. Greg loves playing with the graph and now he has invented a new game: The game consists of n steps. On the i-th step Greg removes vertex number x_{i} from the graph. As...
apps_data_2169
You are given a prime number $p$, $n$ integers $a_1, a_2, \ldots, a_n$, and an integer $k$. Find the number of pairs of indexes $(i, j)$ ($1 \le i < j \le n$) for which $(a_i + a_j)(a_i^2 + a_j^2) \equiv k \bmod p$. -----Input----- The first line contains integers $n, p, k$ ($2 \le n \le 3 \cdot 10^5$, $2 \le p \l...
apps_data_2170
There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought $n$ carrots with lengths $a_1, a_2, a_3, \ldots, a_n$. However, rabbits are very fertile and multiply very quickly. Zookeeper now has $k$ rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut ...
apps_data_2171
Iahub is very proud of his recent discovery, propagating trees. Right now, he invented a new tree, called xor-tree. After this new revolutionary discovery, he invented a game for kids which uses xor-trees. The game is played on a tree having n nodes, numbered from 1 to n. Each node i has an initial value init_{i}, whi...
apps_data_2172
Let's assume that v(n) is the largest prime number, that does not exceed n; u(n) is the smallest prime number strictly greater than n. Find $\sum_{i = 2}^{n} \frac{1}{v(i) u(i)}$. -----Input----- The first line contains integer t (1 ≤ t ≤ 500) — the number of testscases. Each of the following t lines of the ...
apps_data_2173
Appleman has a very big sheet of paper. This sheet has a form of rectangle with dimensions 1 × n. Your task is help Appleman with folding of such a sheet. Actually, you need to perform q queries. Each query will have one of the following types: Fold the sheet of paper at position p_{i}. After this query the leftmost p...
apps_data_2174
Polycarpus has a sequence, consisting of n non-negative integers: a_1, a_2, ..., a_{n}. Let's define function f(l, r) (l, r are integer, 1 ≤ l ≤ r ≤ n) for sequence a as an operation of bitwise OR of all the sequence elements with indexes from l to r. Formally: f(l, r) = a_{l} | a_{l} + 1 | ...  | a_{r}. Polycarpus ...
apps_data_2175
After Misha's birthday he had many large numbers left, scattered across the room. Now it's time to clean up and Misha needs to put them in a basket. He ordered this task to his pet robot that agreed to complete the task at certain conditions. Before the robot puts a number x to the basket, Misha should answer the quest...
apps_data_2176
Let's consider a simplified version of order book of some stock. The order book is a list of orders (offers) from people that want to buy or sell one unit of the stock, each order is described by direction (BUY or SELL) and price. At every moment of time, every SELL offer has higher price than every BUY offer. In th...
apps_data_2177
Vasily has a deck of cards consisting of n cards. There is an integer on each of the cards, this integer is between 1 and 100 000, inclusive. It is possible that some cards have the same integers on them. Vasily decided to sort the cards. To do this, he repeatedly takes the top card from the deck, and if the number on...
apps_data_2178
The Little Elephant loves permutations of integers from 1 to n very much. But most of all he loves sorting them. To sort a permutation, the Little Elephant repeatedly swaps some elements. As a result, he must receive a permutation 1, 2, 3, ..., n. This time the Little Elephant has permutation p_1, p_2, ..., p_{n}. Its...
apps_data_2179
A robber has attempted to rob a bank but failed to complete his task. However, he had managed to open all the safes. Oleg the bank client loves money (who doesn't), and decides to take advantage of this failed robbery and steal some money from the safes. There are many safes arranged in a line, where the i-th safe fro...
apps_data_2180
There is an automatic door at the entrance of a factory. The door works in the following way: when one or several people come to the door and it is closed, the door immediately opens automatically and all people immediately come inside, when one or several people come to the door and it is open, all people immediatel...
apps_data_2181
Polycarp plans to conduct a load testing of its new project Fakebook. He already agreed with his friends that at certain points in time they will send requests to Fakebook. The load testing will last n minutes and in the i-th minute friends will send a_{i} requests. Polycarp plans to test Fakebook under a special kind...
apps_data_2182
Oleg the client and Igor the analyst are good friends. However, sometimes they argue over little things. Recently, they started a new company, but they are having trouble finding a name for the company. To settle this problem, they've decided to play a game. The company name will consist of n letters. Oleg and Igor ea...
apps_data_2183
We start with a string $s$ consisting only of the digits $1$, $2$, or $3$. The length of $s$ is denoted by $|s|$. For each $i$ from $1$ to $|s|$, the $i$-th character of $s$ is denoted by $s_i$. There is one cursor. The cursor's location $\ell$ is denoted by an integer in $\{0, \ldots, |s|\}$, with the following mean...
apps_data_2184
This is an easier version of the next problem. In this version, $q = 0$. A sequence of integers is called nice if its elements are arranged in blocks like in $[3, 3, 3, 4, 1, 1]$. Formally, if two elements are equal, everything in between must also be equal. Let's define difficulty of a sequence as a minimum possible...
apps_data_2185
Vova and Marina love offering puzzles to each other. Today Marina offered Vova to cope with the following task. Vova has a non-directed graph consisting of n vertices and m edges without loops and multiple edges. Let's define the operation of contraction two vertices a and b that are not connected by an edge. As a res...
apps_data_2186
Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are colored white. Consider a set consisting of k (0 ≤ k < n) edges of Appleman's tree. If Appleman deletes these edges from the tree, then it will split into (k + 1) parts. Note, that each part will be a tree...
apps_data_2187
Jzzhu has picked n apples from his big apple tree. All the apples are numbered from 1 to n. Now he wants to sell them to an apple store. Jzzhu will pack his apples into groups and then sell them. Each group must contain two apples, and the greatest common divisor of numbers of the apples in each group must be greater...
apps_data_2188
Today Sonya learned about long integers and invited all her friends to share the fun. Sonya has an initially empty multiset with integers. Friends give her t queries, each of one of the following type: + a_{i} — add non-negative integer a_{i} to the multiset. Note, that she has a multiset, thus there may be many occ...
apps_data_2189
T is playing a game with his friend, HL. There are $n$ piles of stones, the $i$-th pile initially has $a_i$ stones. T and HL will take alternating turns, with T going first. In each turn, a player chooses a non-empty pile and then removes a single stone from it. However, one cannot choose a pile that has been chosen...
apps_data_2190
There are n psychos standing in a line. Each psycho is assigned a unique integer from 1 to n. At each step every psycho who has an id greater than the psycho to his right (if exists) kills his right neighbor in the line. Note that a psycho might kill and get killed at the same step. You're given the initial arrangeme...
apps_data_2191
You are given a sequence a consisting of n integers. Find the maximum possible value of $a_{i} \operatorname{mod} a_{j}$ (integer remainder of a_{i} divided by a_{j}), where 1 ≤ i, j ≤ n and a_{i} ≥ a_{j}. -----Input----- The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·10^5). The second l...
apps_data_2192
There are n beacons located at distinct positions on a number line. The i-th beacon has position a_{i} and power level b_{i}. When the i-th beacon is activated, it destroys all beacons to its left (direction of decreasing coordinates) within distance b_{i} inclusive. The beacon itself is not destroyed however. Saitama ...
apps_data_2193
John Smith knows that his son, Thomas Smith, is among the best students in his class and even in his school. After the students of the school took the exams in English, German, Math, and History, a table of results was formed. There are $n$ students, each of them has a unique id (from $1$ to $n$). Thomas's id is $1$. ...
apps_data_2194
Barney lives in country USC (United States of Charzeh). USC has n cities numbered from 1 through n and n - 1 roads between them. Cities and roads of USC form a rooted tree (Barney's not sure why it is rooted). Root of the tree is the city number 1. Thus if one will start his journey from city 1, he can visit any city h...
apps_data_2195
You are given an array of integers. Vasya can permute (change order) its integers. He wants to do it so that as many as possible integers will become on a place where a smaller integer used to stand. Help Vasya find the maximal number of such integers. For instance, if we are given an array $[10, 20, 30, 40]$, we can ...
apps_data_2196
You are given a string S of length n with each character being one of the first m lowercase English letters. Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1. Recall that LCS ...
apps_data_2197
You are given a string A. Find a string B, where B is a palindrome and A is a subsequence of B. A subsequence of a string is a string that can be derived from it by deleting some (not necessarily consecutive) characters without changing the order of the remaining characters. For example, "cotst" is a subsequence of "c...
apps_data_2198
There are some ambiguities when one writes Berland names with the letters of the Latin alphabet. For example, the Berland sound u can be written in the Latin alphabet as "u", and can be written as "oo". For this reason, two words "ulyana" and "oolyana" denote the same name. The second ambiguity is about the Berland s...
apps_data_2199
Writing light novels is the most important thing in Linova's life. Last night, Linova dreamed about a fantastic kingdom. She began to write a light novel for the kingdom as soon as she woke up, and of course, she is the queen of it. [Image]  There are $n$ cities and $n-1$ two-way roads connecting pairs of cities in t...