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apps_data_200
The 9-th grade student Gabriel noticed a caterpillar on a tree when walking around in a forest after the classes. The caterpillar was on the height h_1 cm from the ground. On the height h_2 cm (h_2 > h_1) on the same tree hung an apple and the caterpillar was crawling to the apple. Gabriel is interested when the cater...
apps_data_201
A sweet little monster Om Nom loves candies very much. One day he found himself in a rather tricky situation that required him to think a bit in order to enjoy candies the most. Would you succeed with the same task if you were on his place? [Image] One day, when he came to his friend Evan, Om Nom didn't find him at h...
apps_data_202
Professor GukiZ makes a new robot. The robot are in the point with coordinates (x_1, y_1) and should go to the point (x_2, y_2). In a single step the robot can change any of its coordinates (maybe both of them) by one (decrease or increase). So the robot can move in one of the 8 directions. Find the minimal number of s...
apps_data_203
There are n employees in Alternative Cake Manufacturing (ACM). They are now voting on some very important question and the leading world media are trying to predict the outcome of the vote. Each of the employees belongs to one of two fractions: depublicans or remocrats, and these two fractions have opposite opinions o...
apps_data_204
Monocarp has decided to buy a new TV set and hang it on the wall in his flat. The wall has enough free space so Monocarp can buy a TV set with screen width not greater than $a$ and screen height not greater than $b$. Monocarp is also used to TV sets with a certain aspect ratio: formally, if the width of the screen is $...
apps_data_205
The number "zero" is called "love" (or "l'oeuf" to be precise, literally means "egg" in French), for example when denoting the zero score in a game of tennis. Aki is fond of numbers, especially those with trailing zeros. For example, the number $9200$ has two trailing zeros. Aki thinks the more trailing zero digits a...
apps_data_206
A frog is initially at position $0$ on the number line. The frog has two positive integers $a$ and $b$. From a position $k$, it can either jump to position $k+a$ or $k-b$. Let $f(x)$ be the number of distinct integers the frog can reach if it never jumps on an integer outside the interval $[0, x]$. The frog doesn't ne...
apps_data_207
Where do odds begin, and where do they end? Where does hope emerge, and will they ever break? Given an integer sequence a_1, a_2, ..., a_{n} of length n. Decide whether it is possible to divide it into an odd number of non-empty subsegments, the each of which has an odd length and begins and ends with odd numbers. A ...
apps_data_208
Pashmak has fallen in love with an attractive girl called Parmida since one year ago... Today, Pashmak set up a meeting with his partner in a romantic garden. Unfortunately, Pashmak has forgotten where the garden is. But he remembers that the garden looks like a square with sides parallel to the coordinate axes. He al...
apps_data_209
Jzzhu has invented a kind of sequences, they meet the following property:$f_{1} = x ; f_{2} = y ; \forall i(i \geq 2), f_{i} = f_{i - 1} + f_{i + 1}$ You are given x and y, please calculate f_{n} modulo 1000000007 (10^9 + 7). -----Input----- The first line contains two integers x and y (|x|, |y| ≤ 10^9). The second...
apps_data_210
One spring day on his way to university Lesha found an array A. Lesha likes to split arrays into several parts. This time Lesha decided to split the array A into several, possibly one, new arrays so that the sum of elements in each of the new arrays is not zero. One more condition is that if we place the new arrays one...
apps_data_211
Manao is taking part in a quiz. The quiz consists of n consecutive questions. A correct answer gives one point to the player. The game also has a counter of consecutive correct answers. When the player answers a question correctly, the number on this counter increases by 1. If the player answers a question incorrectly,...
apps_data_212
You are given a non-negative integer n, its decimal representation consists of at most 100 digits and doesn't contain leading zeroes. Your task is to determine if it is possible in this case to remove some of the digits (possibly not remove any digit at all) so that the result contains at least one digit, forms a non-...
apps_data_213
In a building where Polycarp lives there are equal number of flats on each floor. Unfortunately, Polycarp don't remember how many flats are on each floor, but he remembers that the flats are numbered from 1 from lower to upper floors. That is, the first several flats are on the first floor, the next several flats are o...
apps_data_214
Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states: XX XX .X X. X. .X XX XX Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't oc...
apps_data_215
Polycarp loves lowercase letters and dislikes uppercase ones. Once he got a string s consisting only of lowercase and uppercase Latin letters. Let A be a set of positions in the string. Let's call it pretty if following conditions are met: letters on positions from A in the string are all distinct and lowercase; the...
apps_data_216
You are given a sequence a consisting of n integers. You may partition this sequence into two sequences b and c in such a way that every element belongs exactly to one of these sequences. Let B be the sum of elements belonging to b, and C be the sum of elements belonging to c (if some of these sequences is empty, the...
apps_data_217
A bus moves along the coordinate line Ox from the point x = 0 to the point x = a. After starting from the point x = 0, it reaches the point x = a, immediately turns back and then moves to the point x = 0. After returning to the point x = 0 it immediately goes back to the point x = a and so on. Thus, the bus moves from ...
apps_data_218
You are given the string s of length n and the numbers p, q. Split the string s to pieces of length p and q. For example, the string "Hello" for p = 2, q = 3 can be split to the two strings "Hel" and "lo" or to the two strings "He" and "llo". Note it is allowed to split the string s to the strings only of length p or...
apps_data_219
A sportsman starts from point x_{start} = 0 and runs to point with coordinate x_{finish} = m (on a straight line). Also, the sportsman can jump — to jump, he should first take a run of length of not less than s meters (in this case for these s meters his path should have no obstacles), and after that he can jump over a...
apps_data_220
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)? -----Input----- The first line of the input contains two integers s and x (2 ≤ s ≤ 10^12, 0 ≤ x ≤ 10^12), the sum and bitwise xor of the pair of positive integers, respectively. ---...
apps_data_221
Long story short, shashlik is Miroslav's favorite food. Shashlik is prepared on several skewers simultaneously. There are two states for each skewer: initial and turned over. This time Miroslav laid out $n$ skewers parallel to each other, and enumerated them with consecutive integers from $1$ to $n$ in order from left...
apps_data_222
You are given a positive integer $n$, written without leading zeroes (for example, the number 04 is incorrect). In one operation you can delete any digit of the given integer so that the result remains a positive integer without leading zeros. Determine the minimum number of operations that you need to consistently ...
apps_data_223
Let's define a function $f(p)$ on a permutation $p$ as follows. Let $g_i$ be the greatest common divisor (GCD) of elements $p_1$, $p_2$, ..., $p_i$ (in other words, it is the GCD of the prefix of length $i$). Then $f(p)$ is the number of distinct elements among $g_1$, $g_2$, ..., $g_n$. Let $f_{max}(n)$ be the maximum...
apps_data_224
One day, the Grasshopper was jumping on the lawn and found a piece of paper with a string. Grasshopper became interested what is the minimum jump ability he should have in order to be able to reach the far end of the string, jumping only on vowels of the English alphabet. Jump ability is the maximum possible length of ...
apps_data_225
Dawid has four bags of candies. The $i$-th of them contains $a_i$ candies. Also, Dawid has two friends. He wants to give each bag to one of his two friends. Is it possible to distribute the bags in such a way that each friend receives the same amount of candies in total? Note, that you can't keep bags for yourself or ...
apps_data_226
You may have heard of the pie rule before. It states that if two people wish to fairly share a slice of pie, one person should cut the slice in half, and the other person should choose who gets which slice. Alice and Bob have many slices of pie, and rather than cutting the slices in half, each individual slice will be ...
apps_data_227
You've got a positive integer sequence a_1, a_2, ..., a_{n}. All numbers in the sequence are distinct. Let's fix the set of variables b_1, b_2, ..., b_{m}. Initially each variable b_{i} (1 ≤ i ≤ m) contains the value of zero. Consider the following sequence, consisting of n operations. The first operation is assigning...
apps_data_228
Alice and Bob are playing a game with $n$ piles of stones. It is guaranteed that $n$ is an even number. The $i$-th pile has $a_i$ stones. Alice and Bob will play a game alternating turns with Alice going first. On a player's turn, they must choose exactly $\frac{n}{2}$ nonempty piles and independently remove a positi...
apps_data_229
Today, hedgehog Filya went to school for the very first time! Teacher gave him a homework which Filya was unable to complete without your help. Filya is given an array of non-negative integers a_1, a_2, ..., a_{n}. First, he pick an integer x and then he adds x to some elements of the array (no more than once), subtra...
apps_data_230
Given is a string S of length N. Find the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping. More formally, find the maximum positive integer len such that there exist integers l_1 and l_2 ( 1 \leq l_1, l_2 \leq N - len + 1 ) that satisfy the following: - ...
apps_data_231
The main street of Berland is a straight line with n houses built along it (n is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to n - 1 in the order from the beginning of the street to the end (in the picture: from ...
apps_data_232
There is unrest in the Galactic Senate. Several thousand solar systems have declared their intentions to leave the Republic. Master Heidi needs to select the Jedi Knights who will go on peacekeeping missions throughout the galaxy. It is well-known that the success of any peacekeeping mission depends on the colors of th...
apps_data_233
Mishka is a little polar bear. As known, little bears loves spending their free time playing dice for chocolates. Once in a wonderful sunny morning, walking around blocks of ice, Mishka met her friend Chris, and they started playing the game. Rules of the game are very simple: at first number of rounds n is defined. I...
apps_data_234
One day Alex decided to remember childhood when computers were not too powerful and lots of people played only default games. Alex enjoyed playing Minesweeper that time. He imagined that he saved world from bombs planted by terrorists, but he rarely won. Alex has grown up since then, so he easily wins the most difficu...
apps_data_235
After passing a test, Vasya got himself a box of $n$ candies. He decided to eat an equal amount of candies each morning until there are no more candies. However, Petya also noticed the box and decided to get some candies for himself. This means the process of eating candies is the following: in the beginning Vasya cho...
apps_data_236
A necklace can be described as a string of links ('-') and pearls ('o'), with the last link or pearl connected to the first one. $0$ You can remove a link or a pearl and insert it between two other existing links or pearls (or between a link and a pearl) on the necklace. This process can be repeated as many times as ...
apps_data_237
n hobbits are planning to spend the night at Frodo's house. Frodo has n beds standing in a row and m pillows (n ≤ m). Each hobbit needs a bed and at least one pillow to sleep, however, everyone wants as many pillows as possible. Of course, it's not always possible to share pillows equally, but any hobbit gets hurt if h...
apps_data_238
You are given an array $a_1, a_2, \dots , a_n$ and two integers $m$ and $k$. You can choose some subarray $a_l, a_{l+1}, \dots, a_{r-1}, a_r$. The cost of subarray $a_l, a_{l+1}, \dots, a_{r-1}, a_r$ is equal to $\sum\limits_{i=l}^{r} a_i - k \lceil \frac{r - l + 1}{m} \rceil$, where $\lceil x \rceil$ is the least i...
apps_data_239
You are given a rectangular grid of lattice points from (0, 0) to (n, m) inclusive. You have to choose exactly 4 different points to build a polyline possibly with self-intersections and self-touching. This polyline should be as long as possible. A polyline defined by points p_1, p_2, p_3, p_4 consists of the line seg...
apps_data_240
Vasya decided to pass a very large integer n to Kate. First, he wrote that number as a string, then he appended to the right integer k — the number of digits in n. Magically, all the numbers were shuffled in arbitrary order while this note was passed to Kate. The only thing that Vasya remembers, is a non-empty substr...
apps_data_241
Not so long ago company R2 bought company R1 and consequently, all its developments in the field of multicore processors. Now the R2 laboratory is testing one of the R1 processors. The testing goes in n steps, at each step the processor gets some instructions, and then its temperature is measured. The head engineer in...
apps_data_242
Mr. Santa asks all the great programmers of the world to solve a trivial problem. He gives them an integer m and asks for the number of positive integers n, such that the factorial of n ends with exactly m zeroes. Are you among those great programmers who can solve this problem? -----Input----- The only line of inpu...
apps_data_243
Chouti was tired of the tedious homework, so he opened up an old programming problem he created years ago. You are given a connected undirected graph with $n$ vertices and $m$ weighted edges. There are $k$ special vertices: $x_1, x_2, \ldots, x_k$. Let's define the cost of the path as the maximum weight of the edges ...
apps_data_244
Bomboslav likes to look out of the window in his room and watch lads outside playing famous shell game. The game is played by two persons: operator and player. Operator takes three similar opaque shells and places a ball beneath one of them. Then he shuffles the shells by swapping some pairs and the player has to guess...
apps_data_245
You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle). Your task is to determine if the rectan...
apps_data_246
Ivan likes to learn different things about numbers, but he is especially interested in really big numbers. Ivan thinks that a positive integer number x is really big if the difference between x and the sum of its digits (in decimal representation) is not less than s. To prove that these numbers may have different speci...
apps_data_247
You are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct. You may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines? -----Input----...
apps_data_248
Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among - k, - k + 1, - k + 2, ..., - 2, - 1, 0, 1, 2, ..., k - 1, k) and...
apps_data_249
Valery is a PE teacher at a school in Berland. Soon the students are going to take a test in long jumps, and Valery has lost his favorite ruler! However, there is no reason for disappointment, as Valery has found another ruler, its length is l centimeters. The ruler already has n marks, with which he can make measure...
apps_data_250
As you know, every birthday party has a cake! This time, Babaei is going to prepare the very special birthday party's cake. Simple cake is a cylinder of some radius and height. The volume of the simple cake is equal to the volume of corresponding cylinder. Babaei has n simple cakes and he is going to make a special ca...
apps_data_251
There is a toy building consisting of $n$ towers. Each tower consists of several cubes standing on each other. The $i$-th tower consists of $h_i$ cubes, so it has height $h_i$. Let's define operation slice on some height $H$ as following: for each tower $i$, if its height is greater than $H$, then remove some top cube...
apps_data_252
Alice and Bob are playing yet another card game. This time the rules are the following. There are $n$ cards lying in a row in front of them. The $i$-th card has value $a_i$. First, Alice chooses a non-empty consecutive segment of cards $[l; r]$ ($l \le r$). After that Bob removes a single card $j$ from that segment $...
apps_data_253
Mishka is decorating the Christmas tree. He has got three garlands, and all of them will be put on the tree. After that Mishka will switch these garlands on. When a garland is switched on, it periodically changes its state — sometimes it is lit, sometimes not. Formally, if i-th garland is switched on during x-th secon...
apps_data_254
You are given a string $s$ of length $n$ consisting of lowercase Latin letters. You may apply some operations to this string: in one operation you can delete some contiguous substring of this string, if all letters in the substring you delete are equal. For example, after deleting substring bbbb from string abbbbaccdd ...
apps_data_255
The Berland State University is hosting a ballroom dance in celebration of its 100500-th anniversary! n boys and m girls are already busy rehearsing waltz, minuet, polonaise and quadrille moves. We know that several boy&girl pairs are going to be invited to the ball. However, the partners' dancing skill in each pair m...
apps_data_256
Kicker (table football) is a board game based on football, in which players control the footballers' figures mounted on rods by using bars to get the ball into the opponent's goal. When playing two on two, one player of each team controls the goalkeeper and the full-backs (plays defence), the other player controls the ...
apps_data_257
Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i. Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where...
apps_data_258
Monocarp and Bicarp live in Berland, where every bus ticket consists of $n$ digits ($n$ is an even number). During the evening walk Monocarp and Bicarp found a ticket where some of the digits have been erased. The number of digits that have been erased is even. Monocarp and Bicarp have decided to play a game with this...
apps_data_259
It is raining heavily. But this is the first day for Serval, who just became 3 years old, to go to the kindergarten. Unfortunately, he lives far from kindergarten, and his father is too busy to drive him there. The only choice for this poor little boy is to wait for a bus on this rainy day. Under such circumstances, th...
apps_data_260
One day, after a difficult lecture a diligent student Sasha saw a graffitied desk in the classroom. She came closer and read: "Find such positive integer n, that among numbers n + 1, n + 2, ..., 2·n there are exactly m numbers which binary representation contains exactly k digits one". The girl got interested in the t...
apps_data_261
In this problem you will meet the simplified model of game King of Thieves. In a new ZeptoLab game called "King of Thieves" your aim is to reach a chest with gold by controlling your character, avoiding traps and obstacles on your way. [Image] An interesting feature of the game is that you can design your own levels...
apps_data_262
ZS the Coder and Chris the Baboon arrived at the entrance of Udayland. There is a n × n magic grid on the entrance which is filled with integers. Chris noticed that exactly one of the cells in the grid is empty, and to enter Udayland, they need to fill a positive integer into the empty cell. Chris tried filling in ran...
apps_data_263
There are $n$ benches in the Berland Central park. It is known that $a_i$ people are currently sitting on the $i$-th bench. Another $m$ people are coming to the park and each of them is going to have a seat on some bench out of $n$ available. Let $k$ be the maximum number of people sitting on one bench after additiona...
apps_data_264
There is an airplane which has n rows from front to back. There will be m people boarding this airplane. This airplane has an entrance at the very front and very back of the plane. Each person has some assigned seat. It is possible for multiple people to have the same assigned seat. The people will then board the pla...
apps_data_265
A company of $n$ friends wants to order exactly two pizzas. It is known that in total there are $9$ pizza ingredients in nature, which are denoted by integers from $1$ to $9$. Each of the $n$ friends has one or more favorite ingredients: the $i$-th of friends has the number of favorite ingredients equal to $f_i$ ($1 \...
apps_data_266
You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes. -----Input----- The single line of the input co...
apps_data_267
You are given two integers $l$ and $r$ ($l \le r$). Your task is to calculate the sum of numbers from $l$ to $r$ (including $l$ and $r$) such that each number contains at most $k$ different digits, and print this sum modulo $998244353$. For example, if $k = 1$ then you have to calculate all numbers from $l$ to $r$ suc...
apps_data_268
Mishka received a gift of multicolored pencils for his birthday! Unfortunately he lives in a monochrome world, where everything is of the same color and only saturation differs. This pack can be represented as a sequence a_1, a_2, ..., a_{n} of n integer numbers — saturation of the color of each pencil. Now Mishka want...
apps_data_269
Nothing is eternal in the world, Kostya understood it on the 7-th of January when he saw partially dead four-color garland. Now he has a goal to replace dead light bulbs, however he doesn't know how many light bulbs for each color are required. It is guaranteed that for each of four colors at least one light is workin...
apps_data_270
There is a cave consisting of N rooms and M one-directional passages. The rooms are numbered 1 through N. Takahashi is now in Room 1, and Room N has the exit. The i-th passage connects Room s_i and Room t_i (s_i < t_i) and can only be traversed in the direction from Room s_i to Room t_i. It is known that, for each room...
apps_data_271
Vasya has a non-negative integer n. He wants to round it to nearest integer, which ends up with 0. If n already ends up with 0, Vasya considers it already rounded. For example, if n = 4722 answer is 4720. If n = 5 Vasya can round it to 0 or to 10. Both ways are correct. For given n find out to which integer will Vasy...
apps_data_272
Santa Claus decided to disassemble his keyboard to clean it. After he returned all the keys back, he suddenly realized that some pairs of keys took each other's place! That is, Santa suspects that each key is either on its place, or on the place of another key, which is located exactly where the first key should be. ...
apps_data_273
The preferred way to generate user login in Polygon is to concatenate a prefix of the user's first name and a prefix of their last name, in that order. Each prefix must be non-empty, and any of the prefixes can be the full name. Typically there are multiple possible logins for each person. You are given the first and ...
apps_data_274
A sequence of square brackets is regular if by inserting symbols "+" and "1" into it, you can get a regular mathematical expression from it. For example, sequences "[[]][]", "[]" and "[[][[]]]" — are regular, at the same time "][", "[[]" and "[[]]][" — are irregular. Draw the given sequence using a minimalistic pseud...
apps_data_275
Piegirl got bored with binary, decimal and other integer based counting systems. Recently she discovered some interesting properties about number $q = \frac{\sqrt{5} + 1}{2}$, in particular that q^2 = q + 1, and she thinks it would make a good base for her new unique system. She called it "golden system". In golden sys...
apps_data_276
You took a peek on Thanos wearing Infinity Gauntlet. In the Gauntlet there is a place for six Infinity Gems: the Power Gem of purple color, the Time Gem of green color, the Space Gem of blue color, the Soul Gem of orange color, the Reality Gem of red color, the Mind Gem of yellow color. Using colors of Gems you...
apps_data_277
The last stage of Football World Cup is played using the play-off system. There are n teams left in this stage, they are enumerated from 1 to n. Several rounds are held, in each round the remaining teams are sorted in the order of their ids, then the first in this order plays with the second, the third — with the four...
apps_data_278
Pavel cooks barbecue. There are n skewers, they lay on a brazier in a row, each on one of n positions. Pavel wants each skewer to be cooked some time in every of n positions in two directions: in the one it was directed originally and in the reversed direction. Pavel has a plan: a permutation p and a sequence b_1, b_2...
apps_data_279
The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals v_1 meters per second, and in the end it is v_2 meters per second. We know that this section of the route took exactly t seconds to pass. Assuming that at each of the seconds the speed is constant, a...
apps_data_280
There are N camels numbered 1 through N. The weight of Camel i is w_i. You will arrange the camels in a line and make them cross a bridge consisting of M parts. Before they cross the bridge, you can choose their order in the line - it does not have to be Camel 1, 2, \ldots, N from front to back - and specify the distan...
apps_data_281
Even if the world is full of counterfeits, I still regard it as wonderful. Pile up herbs and incense, and arise again from the flames and ashes of its predecessor — as is known to many, the phoenix does it like this. The phoenix has a rather long lifespan, and reincarnates itself once every a! years. Here a! denotes ...
apps_data_282
A frog lives on the axis Ox and needs to reach home which is in the point n. She starts from the point 1. The frog can jump to the right at a distance not more than d. So, after she jumped from the point x she can reach the point x + a, where a is an integer from 1 to d. For each point from 1 to n is known if there is...
apps_data_283
PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: "There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number". Unfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Co...
apps_data_284
Kolya is developing an economy simulator game. His most favourite part of the development process is in-game testing. Once he was entertained by the testing so much, that he found out his game-coin score become equal to 0. Kolya remembers that at the beginning of the game his game-coin score was equal to n and that he...
apps_data_285
The teacher gave Anton a large geometry homework, but he didn't do it (as usual) as he participated in a regular round on Codeforces. In the task he was given a set of n lines defined by the equations y = k_{i}·x + b_{i}. It was necessary to determine whether there is at least one point of intersection of two of these ...
apps_data_286
Let's define a split of $n$ as a nonincreasing sequence of positive integers, the sum of which is $n$. For example, the following sequences are splits of $8$: $[4, 4]$, $[3, 3, 2]$, $[2, 2, 1, 1, 1, 1]$, $[5, 2, 1]$. The following sequences aren't splits of $8$: $[1, 7]$, $[5, 4]$, $[11, -3]$, $[1, 1, 4, 1, 1]$. Th...
apps_data_287
Maxim wants to buy an apartment in a new house at Line Avenue of Metropolis. The house has n apartments that are numbered from 1 to n and are arranged in a row. Two apartments are adjacent if their indices differ by 1. Some of the apartments can already be inhabited, others are available for sale. Maxim often visits h...
apps_data_288
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately. Organizers are stil...
apps_data_289
Tonio has a keyboard with only two letters, "V" and "K". One day, he has typed out a string s with only these two letters. He really likes it when the string "VK" appears, so he wishes to change at most one letter in the string (or do no changes) to maximize the number of occurrences of that string. Compute the maximu...
apps_data_290
Little Sofia is in fourth grade. Today in the geometry lesson she learned about segments and squares. On the way home, she decided to draw $n$ squares in the snow with a side length of $1$. For simplicity, we assume that Sofia lives on a plane and can draw only segments of length $1$, parallel to the coordinate axes, w...
apps_data_291
Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob. Right now, Limak and Bob weigh a and b respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight. Limak eats a lot and his weight is tripled after every year, while Bob's weight...
apps_data_292
Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to ...
apps_data_293
Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two a...
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Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December. ...
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You are given a positive integer $n$. Find a sequence of fractions $\frac{a_i}{b_i}$, $i = 1 \ldots k$ (where $a_i$ and $b_i$ are positive integers) for some $k$ such that: $$ \begin{cases} \text{$b_i$ divides $n$, $1 < b_i < n$ for $i = 1 \ldots k$} \\ \text{$1 \le a_i < b_i$ for $i = 1 \ldots k$} \\ \text{$\sum\lim...
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Vasya should paint a fence in front of his own cottage. The fence is a sequence of n wooden boards arranged in a single row. Each board is a 1 centimeter wide rectangle. Let's number the board fence using numbers 1, 2, ..., n from left to right. The height of the i-th board is h_{i} centimeters. Vasya has a 1 centimet...
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Vasya has got three integers $n$, $m$ and $k$. He'd like to find three integer points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$, such that $0 \le x_1, x_2, x_3 \le n$, $0 \le y_1, y_2, y_3 \le m$ and the area of the triangle formed by these points is equal to $\frac{nm}{k}$. Help Vasya! Find such points (if it's possib...
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It's one more school day now. Sasha doesn't like classes and is always bored at them. So, each day he invents some game and plays in it alone or with friends. Today he invented one simple game to play with Lena, with whom he shares a desk. The rules are simple. Sasha draws n sticks in a row. After that the players tak...
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Greg is a beginner bodybuilder. Today the gym coach gave him the training plan. All it had was n integers a_1, a_2, ..., a_{n}. These numbers mean that Greg needs to do exactly n exercises today. Besides, Greg should repeat the i-th in order exercise a_{i} times. Greg now only does three types of exercises: "chest" ex...