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apps_data_3900
Recently a serious bug has been found in the FOS code. The head of the F company wants to find the culprit and punish him. For that, he set up an organizational meeting, the issue is: who's bugged the code? Each of the n coders on the meeting said: 'I know for sure that either x or y did it!' The head of the company d...
apps_data_3901
You have an array a with length n, you can perform operations. Each operation is like this: choose two adjacent elements from a, say x and y, and replace one of them with gcd(x, y), where gcd denotes the greatest common divisor. What is the minimum number of operations you need to make all of the elements equal to 1? ...
apps_data_3902
First-rate specialists graduate from Berland State Institute of Peace and Friendship. You are one of the most talented students in this university. The education is not easy because you need to have fundamental knowledge in different areas, which sometimes are not related to each other. For example, you should know l...
apps_data_3903
The famous global economic crisis is approaching rapidly, so the states of Berman, Berance and Bertaly formed an alliance and allowed the residents of all member states to freely pass through the territory of any of them. In addition, it was decided that a road between the states should be built to guarantee so that on...
apps_data_3904
A bracketed sequence is called correct (regular) if by inserting "+" and "1" you can get a well-formed mathematical expression from it. For example, sequences "(())()", "()" and "(()(()))" are correct, while ")(", "(()" and "(()))(" are not. The teacher gave Dmitry's class a very strange task — she asked every student...
apps_data_3905
BigData Inc. is a corporation that has n data centers indexed from 1 to n that are located all over the world. These data centers provide storage for client data (you can figure out that client data is really big!). Main feature of services offered by BigData Inc. is the access availability guarantee even under the ci...
apps_data_3906
Recently Ivan the Fool decided to become smarter and study the probability theory. He thinks that he understands the subject fairly well, and so he began to behave like he already got PhD in that area. To prove his skills, Ivan decided to demonstrate his friends a concept of random picture. A picture is a field of $n$...
apps_data_3907
Let's call an array consisting of n integer numbers a_1, a_2, ..., a_{n}, beautiful if it has the following property: consider all pairs of numbers x, y (x ≠ y), such that number x occurs in the array a and number y occurs in the array a; for each pair x, y must exist some position j (1 ≤ j < n), such that at least...
apps_data_3908
Bessie the cow has just intercepted a text that Farmer John sent to Burger Queen! However, Bessie is sure that there is a secret message hidden inside. The text is a string $s$ of lowercase Latin letters. She considers a string $t$ as hidden in string $s$ if $t$ exists as a subsequence of $s$ whose indices form an ari...
apps_data_3909
Gerald has been selling state secrets at leisure. All the secrets cost the same: n marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of oth...
apps_data_3910
Note that girls in Arpa’s land are really attractive. Arpa loves overnight parties. In the middle of one of these parties Mehrdad suddenly appeared. He saw n pairs of friends sitting around a table. i-th pair consisted of a boy, sitting on the a_{i}-th chair, and his girlfriend, sitting on the b_{i}-th chair. The chai...
apps_data_3911
Your friend recently gave you some slimes for your birthday. You have n slimes all initially with value 1. You are going to play a game with these slimes. Initially, you put a single slime by itself in a row. Then, you will add the other n - 1 slimes one by one. When you add a slime, you place it at the right of all a...
apps_data_3912
Kolya has a string s of length n consisting of lowercase and uppercase Latin letters and digits. He wants to rearrange the symbols in s and cut it into the minimum number of parts so that each part is a palindrome and all parts have the same lengths. A palindrome is a string which reads the same backward as forward, s...
apps_data_3913
Polycarpus takes part in the "Field of Wonders" TV show. The participants of the show have to guess a hidden word as fast as possible. Initially all the letters of the word are hidden. The game consists of several turns. At each turn the participant tells a letter and the TV show host responds if there is such letter ...
apps_data_3914
Instructors of Some Informatics School make students go to bed. The house contains n rooms, in each room exactly b students were supposed to sleep. However, at the time of curfew it happened that many students are not located in their assigned rooms. The rooms are arranged in a row and numbered from 1 to n. Initially,...
apps_data_3915
Rikhail Mubinchik believes that the current definition of prime numbers is obsolete as they are too complex and unpredictable. A palindromic number is another matter. It is aesthetically pleasing, and it has a number of remarkable properties. Help Rikhail to convince the scientific community in this! Let us remind you...
apps_data_3916
Æsir - CHAOS Æsir - V. "Everything has been planned out. No more hidden concerns. The condition of Cytus is also perfect. The time right now...... 00:01:12...... It's time." The emotion samples are now sufficient. After almost 3 years, it's time for Ivy to awake her bonded sister, Vanessa. The system inside A.R.C....
apps_data_3917
Iahub and Sorin are the best competitive programmers in their town. However, they can't both qualify to an important contest. The selection will be made with the help of a single problem. Blatnatalag, a friend of Iahub, managed to get hold of the problem before the contest. Because he wants to make sure Iahub will be t...
apps_data_3918
You are given two arrays A and B, each of size n. The error, E, between these two arrays is defined $E = \sum_{i = 1}^{n}(a_{i} - b_{i})^{2}$. You have to perform exactly k_1 operations on array A and exactly k_2 operations on array B. In one operation, you have to choose one element of the array and increase or decrea...
apps_data_3919
There is a string S of length N consisting of characters 0 and 1. You will perform the following operation for each i = 1, 2, ..., m: - Arbitrarily permute the characters within the substring of S starting at the l_i-th character from the left and extending through the r_i-th character. Here, the sequence l_i is non-d...
apps_data_3920
Gerald got a very curious hexagon for his birthday. The boy found out that all the angles of the hexagon are equal to $120^{\circ}$. Then he measured the length of its sides, and found that each of them is equal to an integer number of centimeters. There the properties of the hexagon ended and Gerald decided to draw on...
apps_data_3921
Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a_1, a_2, ..., a_{n} are good. Now she is interested in good sequences. A sequence x_1, x_2, ..., x_{k} is called good if it satisfies the following three conditions: The sequence is strictly increasing, i.e. x_{i} <...
apps_data_3922
You are an intergalactic surgeon and you have an alien patient. For the purposes of this problem, we can and we will model this patient's body using a $2 \times (2k + 1)$ rectangular grid. The alien has $4k + 1$ distinct organs, numbered $1$ to $4k + 1$. In healthy such aliens, the organs are arranged in a particular ...
apps_data_3923
For a permutation P[1... N] of integers from 1 to N, function f is defined as follows: $f(i, j) = \left\{\begin{array}{ll}{P [ i ]} & {\text{if} j = 1} \\{f(P [ i ], j - 1)} & {\text{otherwise}} \end{array} \right.$ Let g(i) be the minimum positive integer j such that f(i, j) = i. We can show such j always exists. ...
apps_data_3924
Enough is enough. Too many times it happened that Vasya forgot to dispose of garbage and his apartment stank afterwards. Now he wants to create a garbage disposal plan and stick to it. For each of next $n$ days Vasya knows $a_i$ — number of units of garbage he will produce on the $i$-th day. Each unit of garbage must ...
apps_data_3925
Is there anything better than going to the zoo after a tiresome week at work? No wonder Grisha feels the same while spending the entire weekend accompanied by pretty striped zebras. Inspired by this adventure and an accidentally found plasticine pack (represented as a sequence of black and white stripes), Grisha now ...
apps_data_3926
You are playing some computer game. One of its levels puts you in a maze consisting of n lines, each of which contains m cells. Each cell either is free or is occupied by an obstacle. The starting cell is in the row r and column c. In one step you can move one square up, left, down or right, if the target cell is not o...
apps_data_3927
You have a set of $n$ weights. You know that their masses are $a_1$, $a_2$, ..., $a_n$ grams, but you don't know which of them has which mass. You can't distinguish the weights. However, your friend does know the mass of each weight. You can ask your friend to give you exactly $k$ weights with the total mass $m$ (both...
apps_data_3928
Suppose you are given a string $s$ of length $n$ consisting of lowercase English letters. You need to compress it using the smallest possible number of coins. To compress the string, you have to represent $s$ as a concatenation of several non-empty strings: $s = t_{1} t_{2} \ldots t_{k}$. The $i$-th of these strings s...
apps_data_3929
Snuke has decided to play with N cards and a deque (that is, a double-ended queue). Each card shows an integer from 1 through N, and the deque is initially empty. Snuke will insert the cards at the beginning or the end of the deque one at a time, in order from 1 to N. Then, he will perform the following action N times:...
apps_data_3930
Molly Hooper has n different kinds of chemicals arranged in a line. Each of the chemicals has an affection value, The i-th of them has affection value a_{i}. Molly wants Sherlock to fall in love with her. She intends to do this by mixing a contiguous segment of chemicals together to make a love potion with total affec...
apps_data_3931
In the evening Polycarp decided to analyze his today's travel expenses on public transport. The bus system in the capital of Berland is arranged in such a way that each bus runs along the route between two stops. Each bus has no intermediate stops. So each of the buses continuously runs along the route from one stop t...
apps_data_3932
Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. Iahub asks Iahubina: can you build a rooted tree, such that each in...
apps_data_3933
Vasya came up with his own weather forecasting method. He knows the information about the average air temperature for each of the last n days. Assume that the average air temperature for each day is integral. Vasya believes that if the average temperatures over the last n days form an arithmetic progression, where the...
apps_data_3934
Note that this is the first problem of the two similar problems. You can hack this problem only if you solve both problems. You are given a tree with $n$ nodes. In the beginning, $0$ is written on all edges. In one operation, you can choose any $2$ distinct leaves $u$, $v$ and any real number $x$ and add $x$ to values...
apps_data_3935
Boy Dima gave Julian a birthday present — set $B$ consisting of positive integers. However, he didn't know, that Julian hates sets, but enjoys bipartite graphs more than anything else! Julian was almost upset, but her friend Alex said, that he can build an undirected graph using this set in such a way: let all integer...
apps_data_3936
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square. Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors....
apps_data_3937
Consider a table G of size n × m such that G(i, j) = GCD(i, j) for all 1 ≤ i ≤ n, 1 ≤ j ≤ m. GCD(a, b) is the greatest common divisor of numbers a and b. You have a sequence of positive integer numbers a_1, a_2, ..., a_{k}. We say that this sequence occurs in table G if it coincides with consecutive elements in some r...
apps_data_3938
There is a square grid of size $n \times n$. Some cells are colored in black, all others are colored in white. In one operation you can select some rectangle and color all its cells in white. It costs $\min(h, w)$ to color a rectangle of size $h \times w$. You are to make all cells white for minimum total cost. The sq...
apps_data_3939
Slime has a sequence of positive integers $a_1, a_2, \ldots, a_n$. In one operation Orac can choose an arbitrary subsegment $[l \ldots r]$ of this sequence and replace all values $a_l, a_{l + 1}, \ldots, a_r$ to the value of median of $\{a_l, a_{l + 1}, \ldots, a_r\}$. In this problem, for the integer multiset $s$, t...
apps_data_3940
Alyona's mother wants to present an array of n non-negative integers to Alyona. The array should be special. Alyona is a capricious girl so after she gets the array, she inspects m of its subarrays. Subarray is a set of some subsequent elements of the array. The i-th subarray is described with two integers l_{i} and ...
apps_data_3941
Moriarty has trapped n people in n distinct rooms in a hotel. Some rooms are locked, others are unlocked. But, there is a condition that the people in the hotel can only escape when all the doors are unlocked at the same time. There are m switches. Each switch control doors of some rooms, but each door is controlled by...
apps_data_3942
Malek has recently found a treasure map. While he was looking for a treasure he found a locked door. There was a string s written on the door consisting of characters '(', ')' and '#'. Below there was a manual on how to open the door. After spending a long time Malek managed to decode the manual and found out that the ...
apps_data_3943
User ainta loves to play with cards. He has a cards containing letter "o" and b cards containing letter "x". He arranges the cards in a row, and calculates the score of the deck by the formula below. At first, the score is 0. For each block of contiguous "o"s with length x the score increases by x^2. For each block ...
apps_data_3944
Alice, Bob and Charlie are playing Card Game for Three, as below: - At first, each of the three players has a deck consisting of some number of cards. Alice's deck has N cards, Bob's deck has M cards, and Charlie's deck has K cards. Each card has a letter a, b or c written on it. The orders of the cards in the decks c...
apps_data_3945
Dora loves adventures quite a lot. During some journey she encountered an amazing city, which is formed by $n$ streets along the Eastern direction and $m$ streets across the Southern direction. Naturally, this city has $nm$ intersections. At any intersection of $i$-th Eastern street and $j$-th Southern street there is ...
apps_data_3946
The only difference between easy and hard versions is constraints. Nauuo is a girl who loves random picture websites. One day she made a random picture website by herself which includes $n$ pictures. When Nauuo visits the website, she sees exactly one picture. The website does not display each picture with equal pro...
apps_data_3947
Artem has an array of n positive integers. Artem decided to play with it. The game consists of n moves. Each move goes like this. Artem chooses some element of the array and removes it. For that, he gets min(a, b) points, where a and b are numbers that were adjacent with the removed number. If the number doesn't have a...
apps_data_3948
Someone give a strange birthday present to Ivan. It is hedgehog — connected undirected graph in which one vertex has degree at least $3$ (we will call it center) and all other vertices has degree 1. Ivan thought that hedgehog is too boring and decided to make himself $k$-multihedgehog. Let us define $k$-multihedgehog ...
apps_data_3949
A monopole magnet is a magnet that only has one pole, either north or south. They don't actually exist since real magnets have two poles, but this is a programming contest problem, so we don't care. There is an $n\times m$ grid. Initially, you may place some north magnets and some south magnets into the cells. You are...
apps_data_3950
Initially there was an array $a$ consisting of $n$ integers. Positions in it are numbered from $1$ to $n$. Exactly $q$ queries were performed on the array. During the $i$-th query some segment $(l_i, r_i)$ $(1 \le l_i \le r_i \le n)$ was selected and values of elements on positions from $l_i$ to $r_i$ inclusive got ch...
apps_data_3951
The GCD table G of size n × n for an array of positive integers a of length n is defined by formula $g_{ij} = \operatorname{gcd}(a_{i}, a_{j})$ Let us remind you that the greatest common divisor (GCD) of two positive integers x and y is the greatest integer that is divisor of both x and y, it is denoted as $\operato...
apps_data_3952
There are $n$ points on the plane, the $i$-th of which is at $(x_i, y_i)$. Tokitsukaze wants to draw a strange rectangular area and pick all the points in the area. The strange area is enclosed by three lines, $x = l$, $y = a$ and $x = r$, as its left side, its bottom side and its right side respectively, where $l$, $...
apps_data_3953
You are an adventurer currently journeying inside an evil temple. After defeating a couple of weak zombies, you arrived at a square room consisting of tiles forming an n × n grid. The rows are numbered 1 through n from top to bottom, and the columns are numbered 1 through n from left to right. At the far side of the ro...
apps_data_3954
As usual, Sereja has array a, its elements are integers: a[1], a[2], ..., a[n]. Let's introduce notation: $f(a, l, r) = \sum_{i = l}^{r} a [ i ] ; m(a) = \operatorname{max}_{1 \leq l \leq r \leq n} f(a, l, r)$ A swap operation is the following sequence of actions: choose two indexes i, j (i ≠ j); perform assignme...
apps_data_3955
You are given n numbers a_1, a_2, ..., a_{n}. You can perform at most k operations. For each operation you can multiply one of the numbers by x. We want to make [Image] as large as possible, where $1$ denotes the bitwise OR. Find the maximum possible value of [Image] after performing at most k operations optimally. ...
apps_data_3956
Takahashi throws N dice, each having K sides with all integers from 1 to K. The dice are NOT pairwise distinguishable. For each i=2,3,...,2K, find the following value modulo 998244353: - The number of combinations of N sides shown by the dice such that the sum of no two different sides is i. Note that the dice are NOT...
apps_data_3957
Treeland is a country in which there are n towns connected by n - 1 two-way road such that it's possible to get from any town to any other town. In Treeland there are 2k universities which are located in different towns. Recently, the president signed the decree to connect universities by high-speed network.The Min...
apps_data_3958
Oleg writes down the history of the days he lived. For each day he decides if it was good or bad. Oleg calls a non-empty sequence of days a zebra, if it starts with a bad day, ends with a bad day, and good and bad days are alternating in it. Let us denote bad days as 0 and good days as 1. Then, for example, sequences o...
apps_data_3959
It's that time of the year, Felicity is around the corner and you can see people celebrating all around the Himalayan region. The Himalayan region has n gyms. The i-th gym has g_{i} Pokemon in it. There are m distinct Pokemon types in the Himalayan region numbered from 1 to m. There is a special evolution camp set up i...
apps_data_3960
Something happened in Uzhlyandia again... There are riots on the streets... Famous Uzhlyandian superheroes Shean the Sheep and Stas the Giraffe were called in order to save the situation. Upon the arriving, they found that citizens are worried about maximum values of the Main Uzhlyandian Function f, which is defined as...
apps_data_3961
One day, little Vasya found himself in a maze consisting of (n + 1) rooms, numbered from 1 to (n + 1). Initially, Vasya is at the first room and to get out of the maze, he needs to get to the (n + 1)-th one. The maze is organized as follows. Each room of the maze has two one-way portals. Let's consider room number i (...
apps_data_3962
You invited $n$ guests to dinner! You plan to arrange one or more circles of chairs. Each chair is going to be either occupied by one guest, or be empty. You can make any number of circles. Your guests happen to be a little bit shy, so the $i$-th guest wants to have a least $l_i$ free chairs to the left of his chair,...
apps_data_3963
There are n types of coins in Byteland. Conveniently, the denomination of the coin type k divides the denomination of the coin type k + 1, the denomination of the coin type 1 equals 1 tugrick. The ratio of the denominations of coin types k + 1 and k equals a_{k}. It is known that for each x there are at most 20 coin ty...
apps_data_3964
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly a_{i} bugs in every line of code that he writes. Let's call a sequence of non-negative integers v_1, v_2, ..., v_{n} a plan, if v_1 + v_2 + .....
apps_data_3965
You are given a text consisting of n lines. Each line contains some space-separated words, consisting of lowercase English letters. We define a syllable as a string that contains exactly one vowel and any arbitrary number (possibly none) of consonants. In English alphabet following letters are considered to be vowels:...
apps_data_3966
Appleman and Toastman play a game. Initially Appleman gives one group of n numbers to the Toastman, then they start to complete the following tasks: Each time Toastman gets a group of numbers, he sums up all the numbers and adds this sum to the score. Then he gives the group to the Appleman. Each time Appleman gets a...
apps_data_3967
Vladimir wants to modernize partitions in his office. To make the office more comfortable he decided to remove a partition and plant several bamboos in a row. He thinks it would be nice if there are n bamboos in a row, and the i-th from the left is a_{i} meters high. Vladimir has just planted n bamboos in a row, each...
apps_data_3968
A deadly virus is sweeping across the globe! You are part of an elite group of programmers tasked with tracking the spread of the virus. You have been given the timestamps of people entering and exiting a room. Now your job is to determine how the virus will spread. Hurry up, time is of the essence! There are $N$ peop...
apps_data_3969
Emuskald is an avid horticulturist and owns the world's longest greenhouse — it is effectively infinite in length. Over the years Emuskald has cultivated n plants in his greenhouse, of m different plant species numbered from 1 to m. His greenhouse is very narrow and can be viewed as an infinite line, with each plant o...
apps_data_3970
A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k. You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-mu...
apps_data_3971
Alex doesn't like boredom. That's why whenever he gets bored, he comes up with games. One long winter evening he came up with a game and decided to play it. Given a sequence a consisting of n integers. The player can make several steps. In a single step he can choose an element of the sequence (let's denote it a_{k}) ...
apps_data_3972
How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions? - The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j. - For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_...
apps_data_3973
Snuke is buying a lamp. The light of the lamp can be adjusted to m levels of brightness, represented by integers from 1 through m, by the two buttons on the remote control. The first button is a "forward" button. When this button is pressed, the brightness level is increased by 1, except when the brightness level is m,...
apps_data_3974
Polycarpus just has been out of luck lately! As soon as he found a job in the "Binary Cat" cafe, the club got burgled. All ice-cream was stolen. On the burglary night Polycarpus kept a careful record of all club visitors. Each time a visitor entered the club, Polycarpus put down character "+" in his notes. Similarly, ...
apps_data_3975
Natasha travels around Mars in the Mars rover. But suddenly it broke down, namely — the logical scheme inside it. The scheme is an undirected tree (connected acyclic graph) with a root in the vertex $1$, in which every leaf (excluding root) is an input, and all other vertices are logical elements, including the root, w...
apps_data_3976
Sereja has two sequences a and b and number p. Sequence a consists of n integers a_1, a_2, ..., a_{n}. Similarly, sequence b consists of m integers b_1, b_2, ..., b_{m}. As usual, Sereja studies the sequences he has. Today he wants to find the number of positions q (q + (m - 1)·p ≤ n; q ≥ 1), such that sequence b can b...
apps_data_3977
Hongcow is ruler of the world. As ruler of the world, he wants to make it easier for people to travel by road within their own countries. The world can be modeled as an undirected graph with n nodes and m edges. k of the nodes are home to the governments of the k countries that make up the world. There is at most one...
apps_data_3978
You are given a sequence of integers $a_1, a_2, \dots, a_n$. You need to paint elements in colors, so that: If we consider any color, all elements of this color must be divisible by the minimal element of this color. The number of used colors must be minimized. For example, it's fine to paint elements $[40, 10, 60...
apps_data_3979
You all know that the Library of Bookland is the largest library in the world. There are dozens of thousands of books in the library. Some long and uninteresting story was removed... The alphabet of Bookland is so large that its letters are denoted by positive integers. Each letter can be small or large, the large ve...
apps_data_3980
Little penguin Polo likes permutations. But most of all he likes permutations of integers from 0 to n, inclusive. For permutation p = p_0, p_1, ..., p_{n}, Polo has defined its beauty — number $(0 \oplus p_{0}) +(1 \oplus p_{1}) + \cdots +(n \oplus p_{n})$. Expression $x \oplus y$ means applying the operation of bitw...
apps_data_3981
After the war, the supersonic rocket became the most common public transportation. Each supersonic rocket consists of two "engines". Each engine is a set of "power sources". The first engine has $n$ power sources, and the second one has $m$ power sources. A power source can be described as a point $(x_i, y_i)$ on a 2-...
apps_data_3982
In Morse code, an letter of English alphabet is represented as a string of some length from $1$ to $4$. Moreover, each Morse code representation of an English letter contains only dots and dashes. In this task, we will represent a dot with a "0" and a dash with a "1". Because there are $2^1+2^2+2^3+2^4 = 30$ strings w...
apps_data_3983
Given is an undirected graph G consisting of N vertices numbered 1 through N and M edges numbered 1 through M. Edge i connects Vertex a_i and Vertex b_i bidirectionally. G is said to be a good graph when both of the conditions below are satisfied. It is guaranteed that G is initially a good graph. - Vertex 1 and Verte...
apps_data_3984
Mike and Ann are sitting in the classroom. The lesson is boring, so they decided to play an interesting game. Fortunately, all they need to play this game is a string $s$ and a number $k$ ($0 \le k < |s|$). At the beginning of the game, players are given a substring of $s$ with left border $l$ and right border $r$, bo...
apps_data_3985
You have written on a piece of paper an array of n positive integers a[1], a[2], ..., a[n] and m good pairs of integers (i_1, j_1), (i_2, j_2), ..., (i_{m}, j_{m}). Each good pair (i_{k}, j_{k}) meets the following conditions: i_{k} + j_{k} is an odd number and 1 ≤ i_{k} < j_{k} ≤ n. In one operation you can perform a...
apps_data_3986
Little penguin Polo adores strings. But most of all he adores strings of length n. One day he wanted to find a string that meets the following conditions: The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. No two neighbouring letters o...
apps_data_3987
A dragon symbolizes wisdom, power and wealth. On Lunar New Year's Day, people model a dragon with bamboo strips and clothes, raise them with rods, and hold the rods high and low to resemble a flying dragon. A performer holding the rod low is represented by a 1, while one holding it high is represented by a 2. Thus, th...
apps_data_3988
Vasya has a graph containing both directed (oriented) and undirected (non-oriented) edges. There can be multiple edges between a pair of vertices. Vasya has picked a vertex s from the graph. Now Vasya wants to create two separate plans: to orient each undirected edge in one of two possible directions to maximize nu...
apps_data_3989
You have number a, whose decimal representation quite luckily contains digits 1, 6, 8, 9. Rearrange the digits in its decimal representation so that the resulting number will be divisible by 7. Number a doesn't contain any leading zeroes and contains digits 1, 6, 8, 9 (it also can contain another digits). The resultin...
apps_data_3990
In Absurdistan, there are n towns (numbered 1 through n) and m bidirectional railways. There is also an absurdly simple road network — for each pair of different towns x and y, there is a bidirectional road between towns x and y if and only if there is no railway between them. Travelling to a different town using one r...
apps_data_3991
Leha decided to move to a quiet town Vičkopolis, because he was tired by living in Bankopolis. Upon arrival he immediately began to expand his network of hacked computers. During the week Leha managed to get access to n computers throughout the town. Incidentally all the computers, which were hacked by Leha, lie on the...
apps_data_3992
This is the harder version of the problem. In this version, $1 \le n \le 10^6$ and $0 \leq a_i \leq 10^6$. You can hack this problem if you locked it. But you can hack the previous problem only if you locked both problems Christmas is coming, and our protagonist, Bob, is preparing a spectacular present for his long-ti...
apps_data_3993
Recently, Tokitsukaze found an interesting game. Tokitsukaze had $n$ items at the beginning of this game. However, she thought there were too many items, so now she wants to discard $m$ ($1 \le m \le n$) special items of them. These $n$ items are marked with indices from $1$ to $n$. In the beginning, the item with ind...
apps_data_3994
It is a holiday season, and Koala is decorating his house with cool lights! He owns $n$ lights, all of which flash periodically. After taking a quick glance at them, Koala realizes that each of his lights can be described with two parameters $a_i$ and $b_i$. Light with parameters $a_i$ and $b_i$ will toggle (on to off...
apps_data_3995
Let $s$ be some string consisting of symbols "0" or "1". Let's call a string $t$ a substring of string $s$, if there exists such number $1 \leq l \leq |s| - |t| + 1$ that $t = s_l s_{l+1} \ldots s_{l + |t| - 1}$. Let's call a substring $t$ of string $s$ unique, if there exist only one such $l$. For example, let $s = ...
apps_data_3996
As we all know Barney's job is "PLEASE" and he has not much to do at work. That's why he started playing "cups and key". In this game there are three identical cups arranged in a line from left to right. Initially key to Barney's heart is under the middle cup. [Image] Then at one turn Barney swaps the cup in the midd...
apps_data_3997
Alyona has a tree with n vertices. The root of the tree is the vertex 1. In each vertex Alyona wrote an positive integer, in the vertex i she wrote a_{i}. Moreover, the girl wrote a positive integer to every edge of the tree (possibly, different integers on different edges). Let's define dist(v, u) as the sum of the i...
apps_data_3998
A group of n friends enjoys playing popular video game Toda 2. There is a rating system describing skill level of each player, initially the rating of the i-th friend is r_{i}. The friends decided to take part in the championship as a team. But they should have equal ratings to be allowed to compose a single team cons...
apps_data_3999
AtCoDeer the deer has N square tiles. The tiles are numbered 1 through N, and the number given to each tile is written on one side of the tile. Also, each corner of each tile is painted in one of the 1000 colors, which are represented by the integers 0 between 999. The top-left, top-right, bottom-right and bottom-left ...