There is a legend in the IT City college. A student that failed to answer all questions on the game theory exam is given one more chance by his professor. The student has to play a game with the professor.The game is played on a square field consisting of n × n cells. Initially all cells are empty. On each turn a player chooses and paint an empty cell that has no common sides with previously painted cells. Adjacent corner of painted cells is allowed. On the next turn another player does the same, then the first one and so on. The player with no cells to paint on his turn loses.The professor have chosen the field size n and allowed the student to choose to be the first or the second player in the game. What should the student choose to win the game? Both players play optimally.

The only line of the input contains one integer n (1 ≤ n ≤ 1018) — the size of the field.

Output number 1, if the player making the first turn wins when both players play optimally, otherwise print number 2.


A tennis tournament with n participants is running. The participants are playing by an olympic system, so the winners move on and the losers drop out.The tournament takes place in the following way (below, m is the number of the participants of the current round):  let k be the maximal power of the number 2 such that k ≤ m,  k participants compete in the current round and a half of them passes to the next round, the other m - k participants pass to the next round directly,  when only one participant remains, the tournament finishes. Each match requires b bottles of water for each participant and one bottle for the judge. Besides p towels are given to each participant for the whole tournament.Find the number of bottles and towels needed for the tournament.Note that it's a tennis tournament so in each match two participants compete (one of them will win and the other will lose).

The only line contains three integers n, b, p (1 ≤ n, b, p ≤ 500) — the number of participants and the parameters described in the problem statement.

Print two integers x and y — the number of bottles and towels need for the tournament.

NoteIn the first example will be three rounds:  in the first round will be two matches and for each match 5 bottles of water are needed (two for each of the participants and one for the judge),  in the second round will be only one match, so we need another 5 bottles of water,  in the third round will also be only one match, so we need another 5 bottles of water. So in total we need 20 bottles of water.In the second example no participant will move on to some round directly.


Kolya has a turtle and a field of size $$$2 \times n$$$. The field rows are numbered from $$$1$$$ to $$$2$$$ from top to bottom, while the columns are numbered from $$$1$$$ to $$$n$$$ from left to right.Suppose in each cell of the field there is a lettuce leaf. The energy value of lettuce leaf in row $$$i$$$ and column $$$j$$$ is equal to $$$a_{i,j}$$$. The turtle is initially in the top left cell and wants to reach the bottom right cell. The turtle can only move right and down and among all possible ways it will choose a way, maximizing the total energy value of lettuce leaves (in case there are several such paths, it will choose any of them).Kolya is afraid, that if turtle will eat too much lettuce, it can be bad for its health. So he wants to reorder lettuce leaves in the field, so that the energetic cost of leaves eaten by turtle will be minimized.

The first line contains an integer $$$n$$$ ($$$2 \le n \le 25$$$) — the length of the field. The second line contains $$$n$$$ integers $$$a_{1, i}$$$ ($$$0 \le a_{1, i} \le 50\,000$$$), the energetic cost of lettuce leaves in the first row of the field. The third line contains $$$n$$$ integers $$$a_{2, i}$$$ ($$$0 \le a_{2, i} \le 50\,000$$$), the energetic cost of lettuce leaves in the second row of the field.

Print two lines with $$$n$$$ integers in each — the optimal reordering of lettuce from the input data. In case there are several optimal ways to reorder lettuce, print any of them.

NoteIn the first example, after reordering, the turtle will eat lettuce with total energetic cost $$$1+4+2 = 7$$$.In the second example, the turtle will eat lettuce with energetic cost equal $$$0$$$.In the third example, after reordering, the turtle will eat lettuce with total energetic cost equal $$$1$$$.


At regular competition Vladik and Valera won a and b candies respectively. Vladik offered 1 his candy to Valera. After that Valera gave Vladik 2 his candies, so that no one thought that he was less generous. Vladik for same reason gave 3 candies to Valera in next turn.More formally, the guys take turns giving each other one candy more than they received in the previous turn.This continued until the moment when one of them couldn’t give the right amount of candy. Candies, which guys got from each other, they don’t consider as their own. You need to know, who is the first who can’t give the right amount of candy.

Single line of input data contains two space-separated integers a, b (1 ≤ a, b ≤ 109) — number of Vladik and Valera candies respectively.

Pring a single line "Vladik’’ in case, if Vladik first who can’t give right amount of candy, or "Valera’’ otherwise.

NoteIllustration for first test case:Illustration for second test case:


You have r red, g green and b blue balloons. To decorate a single table for the banquet you need exactly three balloons. Three balloons attached to some table shouldn't have the same color. What maximum number t of tables can be decorated if we know number of balloons of each color?Your task is to write a program that for given values r, g and b will find the maximum number t of tables, that can be decorated in the required manner.

The single line contains three integers r, g and b (0 ≤ r, g, b ≤ 2·109) — the number of red, green and blue baloons respectively. The numbers are separated by exactly one space.

Print a single integer t — the maximum number of tables that can be decorated in the required manner.

NoteIn the first sample you can decorate the tables with the following balloon sets: "rgg", "gbb", "brr", "rrg", where "r", "g" and "b" represent the red, green and blue balls, respectively.


The only difference between easy and hard versions is on constraints. In this version constraints are lower. You can make hacks only if all versions of the problem are solved.Koa the Koala is at the beach!The beach consists (from left to right) of a shore, $$$n+1$$$ meters of sea and an island at $$$n+1$$$ meters from the shore.She measured the depth of the sea at $$$1, 2, \dots, n$$$ meters from the shore and saved them in array $$$d$$$. $$$d_i$$$ denotes the depth of the sea at $$$i$$$ meters from the shore for $$$1 \le i \le n$$$.Like any beach this one has tide, the intensity of the tide is measured by parameter $$$k$$$ and affects all depths from the beginning at time $$$t=0$$$ in the following way:  For a total of $$$k$$$ seconds, each second, tide increases all depths by $$$1$$$.  Then, for a total of $$$k$$$ seconds, each second, tide decreases all depths by $$$1$$$.  This process repeats again and again (ie. depths increase for $$$k$$$ seconds then decrease for $$$k$$$ seconds and so on ...).Formally, let's define $$$0$$$-indexed array $$$p = [0, 1, 2, \ldots, k - 2, k - 1, k, k - 1, k - 2, \ldots, 2, 1]$$$ of length $$$2k$$$. At time $$$t$$$ ($$$0 \le t$$$) depth at $$$i$$$ meters from the shore equals $$$d_i + p[t \bmod 2k]$$$ ($$$t \bmod 2k$$$ denotes the remainder of the division of $$$t$$$ by $$$2k$$$). Note that the changes occur instantaneously after each second, see the notes for better understanding. At time $$$t=0$$$ Koa is standing at the shore and wants to get to the island. Suppose that at some time $$$t$$$ ($$$0 \le t$$$) she is at $$$x$$$ ($$$0 \le x \le n$$$) meters from the shore:  In one second Koa can swim $$$1$$$ meter further from the shore ($$$x$$$ changes to $$$x+1$$$) or not swim at all ($$$x$$$ stays the same), in both cases $$$t$$$ changes to $$$t+1$$$.  As Koa is a bad swimmer, the depth of the sea at the point where she is can't exceed $$$l$$$ at integer points of time (or she will drown). More formally, if Koa is at $$$x$$$ ($$$1 \le x \le n$$$) meters from the shore at the moment $$$t$$$ (for some integer $$$t\ge 0$$$), the depth of the sea at this point  — $$$d_x + p[t \bmod 2k]$$$  — can't exceed $$$l$$$. In other words, $$$d_x + p[t \bmod 2k] \le l$$$ must hold always.  Once Koa reaches the island at $$$n+1$$$ meters from the shore, she stops and can rest.Note that while Koa swims tide doesn't have effect on her (ie. she can't drown while swimming). Note that Koa can choose to stay on the shore for as long as she needs and neither the shore or the island are affected by the tide (they are solid ground and she won't drown there). Koa wants to know whether she can go from the shore to the island. Help her!

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 100$$$)  — the number of test cases. Description of the test cases follows. The first line of each test case contains three integers $$$n$$$, $$$k$$$ and $$$l$$$ ($$$1 \le n \le 100; 1 \le k \le 100; 1 \le l \le 100$$$) — the number of meters of sea Koa measured and parameters $$$k$$$ and $$$l$$$. The second line of each test case contains $$$n$$$ integers $$$d_1, d_2, \ldots, d_n$$$ ($$$0 \le d_i \le 100$$$)  — the depths of each meter of sea Koa measured. It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$100$$$.

For each test case: Print Yes if Koa can get from the shore to the island, and No otherwise. You may print each letter in any case (upper or lower).

NoteIn the following $$$s$$$ denotes the shore, $$$i$$$ denotes the island, $$$x$$$ denotes distance from Koa to the shore, the underline denotes the position of Koa, and values in the array below denote current depths, affected by tide, at $$$1, 2, \dots, n$$$ meters from the shore.In test case $$$1$$$ we have $$$n = 2, k = 1, l = 1, p = [ 0, 1 ]$$$.Koa wants to go from shore (at $$$x = 0$$$) to the island (at $$$x = 3$$$). Let's describe a possible solution:  Initially at $$$t = 0$$$ the beach looks like this: $$$[\underline{s}, 1, 0, i]$$$.  At $$$t = 0$$$ if Koa would decide to swim to $$$x = 1$$$, beach would look like: $$$[s, \underline{2}, 1, i]$$$ at $$$t = 1$$$, since $$$2 > 1$$$ she would drown. So Koa waits $$$1$$$ second instead and beach looks like $$$[\underline{s}, 2, 1, i]$$$ at $$$t = 1$$$.  At $$$t = 1$$$ Koa swims to $$$x = 1$$$, beach looks like $$$[s, \underline{1}, 0, i]$$$ at $$$t = 2$$$. Koa doesn't drown because $$$1 \le 1$$$.  At $$$t = 2$$$ Koa swims to $$$x = 2$$$, beach looks like $$$[s, 2, \underline{1}, i]$$$ at $$$t = 3$$$. Koa doesn't drown because $$$1 \le 1$$$.  At $$$t = 3$$$ Koa swims to $$$x = 3$$$, beach looks like $$$[s, 1, 0, \underline{i}]$$$ at $$$t = 4$$$.  At $$$t = 4$$$ Koa is at $$$x = 3$$$ and she made it! We can show that in test case $$$2$$$ Koa can't get to the island.


Two bored soldiers are playing card war. Their card deck consists of exactly n cards, numbered from 1 to n, all values are different. They divide cards between them in some manner, it's possible that they have different number of cards. Then they play a "war"-like card game. The rules are following. On each turn a fight happens. Each of them picks card from the top of his stack and puts on the table. The one whose card value is bigger wins this fight and takes both cards from the table to the bottom of his stack. More precisely, he first takes his opponent's card and puts to the bottom of his stack, and then he puts his card to the bottom of his stack. If after some turn one of the player's stack becomes empty, he loses and the other one wins. You have to calculate how many fights will happen and who will win the game, or state that game won't end.

First line contains a single integer n (2 ≤ n ≤ 10), the number of cards. Second line contains integer k1 (1 ≤ k1 ≤ n - 1), the number of the first soldier's cards. Then follow k1 integers that are the values on the first soldier's cards, from top to bottom of his stack. Third line contains integer k2 (k1 + k2 = n), the number of the second soldier's cards. Then follow k2 integers that are the values on the second soldier's cards, from top to bottom of his stack. All card values are different.

If somebody wins in this game, print 2 integers where the first one stands for the number of fights before end of game and the second one is 1 or 2 showing which player has won. If the game won't end and will continue forever output  - 1.


Capitalization is writing a word with its first letter as a capital letter. Your task is to capitalize the given word.Note, that during capitalization all the letters except the first one remains unchanged.

A single line contains a non-empty word. This word consists of lowercase and uppercase English letters. The length of the word will not exceed 103.

Output the given word after capitalization.


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 Vasya round it.

The first line contains single integer n (0 ≤ n ≤ 109) — number that Vasya has.

Print result of rounding n. Pay attention that in some cases answer isn't unique. In that case print any correct answer.

NoteIn the first example n = 5. Nearest integers, that ends up with zero are 0 and 10. Any of these answers is correct, so you can print 0 or 10.


Little Petya loves training spiders. Petya has a board n × m in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idle or to move from current cell to some of the four side-neighboring cells (that is, one command for each of the four possible directions). Petya gives the commands so that no spider leaves the field. It is allowed for spiders to pass through each other when they crawl towards each other in opposite directions. All spiders crawl simultaneously and several spiders may end up in one cell. Petya wants to know the maximum possible number of spider-free cells after one second.

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 40, n·m ≤ 40) — the board sizes.

In the first line print the maximum number of cells without spiders.

NoteIn the first sample the only possible answer is:sIn the second sample one of the possible solutions is: rdlruls denotes command "stay idle", l, r, d, u denote commands "crawl left", "crawl right", "crawl down", "crawl up", correspondingly.


Welcome to Codeforces Stock Exchange! We're pretty limited now as we currently allow trading on one stock, Codeforces Ltd. We hope you'll still be able to make profit from the market!In the morning, there are $$$n$$$ opportunities to buy shares. The $$$i$$$-th of them allows to buy as many shares as you want, each at the price of $$$s_i$$$ bourles.In the evening, there are $$$m$$$ opportunities to sell shares. The $$$i$$$-th of them allows to sell as many shares as you want, each at the price of $$$b_i$$$ bourles. You can't sell more shares than you have.It's morning now and you possess $$$r$$$ bourles and no shares.What is the maximum number of bourles you can hold after the evening?

The first line of the input contains three integers $$$n, m, r$$$ ($$$1 \leq n \leq 30$$$, $$$1 \leq m \leq 30$$$, $$$1 \leq r \leq 1000$$$) — the number of ways to buy the shares on the market, the number of ways to sell the shares on the market, and the number of bourles you hold now. The next line contains $$$n$$$ integers $$$s_1, s_2, \dots, s_n$$$ ($$$1 \leq s_i \leq 1000$$$); $$$s_i$$$ indicates the opportunity to buy shares at the price of $$$s_i$$$ bourles. The following line contains $$$m$$$ integers $$$b_1, b_2, \dots, b_m$$$ ($$$1 \leq b_i \leq 1000$$$); $$$b_i$$$ indicates the opportunity to sell shares at the price of $$$b_i$$$ bourles.

Output a single integer — the maximum number of bourles you can hold after the evening.

NoteIn the first example test, you have $$$11$$$ bourles in the morning. It's optimal to buy $$$5$$$ shares of a stock at the price of $$$2$$$ bourles in the morning, and then to sell all of them at the price of $$$5$$$ bourles in the evening. It's easy to verify that you'll have $$$26$$$ bourles after the evening.In the second example test, it's optimal not to take any action.


Cucumber boy is fan of Kyubeat, a famous music game.Kyubeat has 16 panels for playing arranged in 4 × 4 table. When a panel lights up, he has to press that panel.Each panel has a timing to press (the preffered time when a player should press it), and Cucumber boy is able to press at most k panels in a time with his one hand. Cucumber boy is trying to press all panels in perfect timing, that is he wants to press each panel exactly in its preffered time. If he cannot press the panels with his two hands in perfect timing, his challenge to press all the panels in perfect timing will fail.You are given one scene of Kyubeat's panel from the music Cucumber boy is trying. Tell him is he able to press all the panels in perfect timing.

The first line contains a single integer k (1 ≤ k ≤ 5) — the number of panels Cucumber boy can press with his one hand. Next 4 lines contain 4 characters each (digits from 1 to 9, or period) — table of panels. If a digit i was written on the panel, it means the boy has to press that panel in time i. If period was written on the panel, he doesn't have to press that panel.

Output "YES" (without quotes), if he is able to press all the panels in perfect timing. If not, output "NO" (without quotes).

NoteIn the third sample boy cannot press all panels in perfect timing. He can press all the panels in timing in time 1, but he cannot press the panels in time 2 in timing with his two hands.


The cows have just learned what a primitive root is! Given a prime p, a primitive root  is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime p, help the cows find the number of primitive roots .

The input contains a single line containing an integer p (2 ≤ p < 2000). It is guaranteed that p is a prime.

Output on a single line the number of primitive roots .

NoteThe only primitive root  is 2.The primitive roots  are 2 and 3.


The math faculty of Berland State University has suffered the sudden drop in the math skills of enrolling students. This year the highest grade on the entrance math test was 8. Out of 100! Thus, the decision was made to make the test easier.Future students will be asked just a single question. They are given a sequence of integer numbers $$$a_1, a_2, \dots, a_n$$$, each number is from $$$1$$$ to $$$3$$$ and $$$a_i \ne a_{i + 1}$$$ for each valid $$$i$$$. The $$$i$$$-th number represents a type of the $$$i$$$-th figure:  circle;  isosceles triangle with the length of height equal to the length of base;  square. The figures of the given sequence are placed somewhere on a Cartesian plane in such a way that:  $$$(i + 1)$$$-th figure is inscribed into the $$$i$$$-th one;  each triangle base is parallel to OX;  the triangle is oriented in such a way that the vertex opposite to its base is at the top;  each square sides are parallel to the axes;  for each $$$i$$$ from $$$2$$$ to $$$n$$$ figure $$$i$$$ has the maximum possible length of side for triangle and square and maximum radius for circle. Note that the construction is unique for some fixed position and size of just the first figure.The task is to calculate the number of distinct points (not necessarily with integer coordinates) where figures touch. The trick is, however, that the number is sometimes infinite. But that won't make the task difficult for you, will it?So can you pass the math test and enroll into Berland State University?

The first line contains a single integer $$$n$$$ ($$$2 \le n \le 100$$$) — the number of figures. The second line contains $$$n$$$ integer numbers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 3$$$, $$$a_i \ne a_{i + 1}$$$) — types of the figures.

The first line should contain either the word "Infinite" if the number of distinct points where figures touch is infinite or "Finite" otherwise. If the number is finite than print it in the second line. It's guaranteed that the number fits into 32-bit integer type.

NoteHere are the glorious pictures for the examples. Note that the triangle is not equilateral but just isosceles with the length of height equal to the length of base. Thus it fits into a square in a unique way.The distinct points where figures touch are marked red.In the second example the triangle and the square touch each other for the whole segment, it contains infinite number of points.


In a small but very proud high school it was decided to win ACM ICPC. This goal requires to compose as many teams of three as possible, but since there were only 6 students who wished to participate, the decision was to build exactly two teams.After practice competition, participant number i got a score of ai. Team score is defined as sum of scores of its participants. High school management is interested if it's possible to build two teams with equal scores. Your task is to answer that question.

The single line contains six integers a1, ..., a6 (0 ≤ ai ≤ 1000) — scores of the participants

Print "YES" (quotes for clarity), if it is possible to build teams with equal score, and "NO" otherwise. You can print each character either upper- or lowercase ("YeS" and "yes" are valid when the answer is "YES").

NoteIn the first sample, first team can be composed of 1st, 2nd and 6th participant, second — of 3rd, 4th and 5th: team scores are 1 + 3 + 1 = 2 + 1 + 2 = 5.In the second sample, score of participant number 6 is too high: his team score will be definitely greater.


Find the minimum number with the given sum of digits $$$s$$$ such that all digits in it are distinct (i.e. all digits are unique).For example, if $$$s=20$$$, then the answer is $$$389$$$. This is the minimum number in which all digits are different and the sum of the digits is $$$20$$$ ($$$3+8+9=20$$$).For the given $$$s$$$ print the required number.

The first line contains an integer $$$t$$$ ($$$1 \le t \le 45$$$) — the number of test cases. Each test case is specified by a line that contains the only integer $$$s$$$ ($$$1 \le s \le 45$$$).

Print $$$t$$$ integers — the answers to the given test cases.


Vasily the Programmer loves romance, so this year he decided to illuminate his room with candles.Vasily has a candles.When Vasily lights up a new candle, it first burns for an hour and then it goes out. Vasily is smart, so he can make b went out candles into a new candle. As a result, this new candle can be used like any other new candle.Now Vasily wonders: for how many hours can his candles light up the room if he acts optimally well? Help him find this number.

The single line contains two integers, a and b (1 ≤ a ≤ 1000; 2 ≤ b ≤ 1000).

Print a single integer — the number of hours Vasily can light up the room for.

NoteConsider the first sample. For the first four hours Vasily lights up new candles, then he uses four burned out candles to make two new ones and lights them up. When these candles go out (stop burning), Vasily can make another candle. Overall, Vasily can light up the room for 7 hours.


One quite ordinary day Valera went to school (there's nowhere else he should go on a week day). In a maths lesson his favorite teacher Ms. Evans told students about divisors. Despite the fact that Valera loved math, he didn't find this particular topic interesting. Even more, it seemed so boring that he fell asleep in the middle of a lesson. And only a loud ringing of a school bell could interrupt his sweet dream. Of course, the valuable material and the teacher's explanations were lost. However, Valera will one way or another have to do the homework. As he does not know the new material absolutely, he cannot do the job himself. That's why he asked you to help. You're his best friend after all, you just cannot refuse to help. Valera's home task has only one problem, which, though formulated in a very simple way, has not a trivial solution. Its statement looks as follows: if we consider all positive integers in the interval [a;b] then it is required to count the amount of such numbers in this interval that their smallest divisor will be a certain integer k (you do not have to consider divisor equal to one). In other words, you should count the amount of such numbers from the interval [a;b], that are not divisible by any number between 2 and k - 1 and yet are divisible by k.

The first and only line contains three positive integers a, b, k (1 ≤ a ≤ b ≤ 2·109, 2 ≤ k ≤ 2·109).

Print on a single line the answer to the given problem.

NoteComments to the samples from the statement: In the first sample the answer is numbers 2, 4, 6, 8, 10.In the second one — 15, 21In the third one there are no such numbers.


InputThe only line of the input contains a string of digits. The length of the string is between 1 and 10, inclusive.OutputOutput "Yes" or "No".ExamplesInput373OutputYesInput121OutputNoInput436OutputYes


Calendars in widespread use today include the Gregorian calendar, which is the de facto international standard, and is used almost everywhere in the world for civil purposes. The Gregorian reform modified the Julian calendar's scheme of leap years as follows: Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year.   In this problem, you have been given two dates and your task is to calculate how many days are between them. Note, that leap years have unusual number of days in February.Look at the sample to understand what borders are included in the aswer.

The first two lines contain two dates, each date is in the format yyyy:mm:dd (1900 ≤ yyyy ≤ 2038 and yyyy:mm:dd is a legal date).

Print a single integer — the answer to the problem.


You found a mysterious function f. The function takes two strings s1 and s2. These strings must consist only of lowercase English letters, and must be the same length.The output of the function f is another string of the same length. The i-th character of the output is equal to the minimum of the i-th character of s1 and the i-th character of s2.For example, f("ab", "ba") = "aa", and f("nzwzl", "zizez") = "niwel".You found two strings x and y of the same length and consisting of only lowercase English letters. Find any string z such that f(x, z) = y, or print -1 if no such string z exists.

The first line of input contains the string x. The second line of input contains the string y. Both x and y consist only of lowercase English letters, x and y have same length and this length is between 1 and 100.

If there is no string z such that f(x, z) = y, print -1. Otherwise, print a string z such that f(x, z) = y. If there are multiple possible answers, print any of them. The string z should be the same length as x and y and consist only of lowercase English letters.

NoteThe first case is from the statement.Another solution for the second case is "zizez"There is no solution for the third case. That is, there is no z such that f("ab", z) =  "ba".


InputThe only line of the input is a string of 7 characters. The first character is letter A, followed by 6 digits. The input is guaranteed to be valid (for certain definition of "valid").OutputOutput a single integer.ExamplesInputA221033Output21InputA223635Output22InputA232726Output23


As a tradition, every year before IOI all the members of Natalia Fan Club are invited to Malek Dance Club to have a fun night together. Malek Dance Club has 2n members and coincidentally Natalia Fan Club also has 2n members. Each member of MDC is assigned a unique id i from 0 to 2n - 1. The same holds for each member of NFC.One of the parts of this tradition is one by one dance, where each member of MDC dances with a member of NFC. A dance pair is a pair of numbers (a, b) such that member a from MDC dances with member b from NFC.The complexity of a pairs' assignment is the number of pairs of dancing pairs (a, b) and (c, d) such that a < c and b > d.You are given a binary number of length n named x. We know that member i from MDC dances with member  from NFC. Your task is to calculate the complexity of this assignment modulo 1000000007 (109 + 7).Expression  denotes applying «XOR» to numbers x and y. This operation exists in all modern programming languages, for example, in C++ and Java it denotes as «^», in Pascal — «xor».

The first line of input contains a binary number x of lenght n, (1 ≤ n ≤ 100). This number may contain leading zeros.

Print the complexity of the given dance assignent modulo 1000000007 (109 + 7).


Tarly has two different type of items, food boxes and wine barrels. There are f food boxes and w wine barrels. Tarly stores them in various stacks and each stack can consist of either food boxes or wine barrels but not both. The stacks are placed in a line such that no two stacks of food boxes are together and no two stacks of wine barrels are together.The height of a stack is defined as the number of items in the stack. Two stacks are considered different if either their heights are different or one of them contains food and other contains wine.Jon Snow doesn't like an arrangement if any stack of wine barrels has height less than or equal to h. What is the probability that Jon Snow will like the arrangement if all arrangement are equiprobably?Two arrangement of stacks are considered different if exists such i, that i-th stack of one arrangement is different from the i-th stack of the other arrangement.

The first line of input contains three integers f, w, h (0 ≤ f, w, h ≤ 105) — number of food boxes, number of wine barrels and h is as described above. It is guaranteed that he has at least one food box or at least one wine barrel.

Output the probability that Jon Snow will like the arrangement. The probability is of the form , then you need to output a single integer p·q - 1 mod (109 + 7).

NoteIn the first example f  =  1, w = 1 and h = 1, there are only two possible arrangement of stacks and Jon Snow doesn't like any of them.In the second example f = 1, w = 2 and h = 1, there are three arrangements. Jon Snow likes the (1) and (3) arrangement. So the probabilty is .


The hero of our story, Valera, and his best friend Arcady are still in school, and therefore they spend all the free time playing turn-based strategy "GAGA: Go And Go Again". The gameplay is as follows. There are two armies on the playing field each of which consists of n men (n is always even). The current player specifies for each of her soldiers an enemy's soldier he will shoot (a target) and then all the player's soldiers shot simultaneously. This is a game world, and so each soldier shoots perfectly, that is he absolutely always hits the specified target. If an enemy soldier is hit, he will surely die. It may happen that several soldiers had been indicated the same target. Killed soldiers do not participate in the game anymore. The game "GAGA" consists of three steps: first Valera makes a move, then Arcady, then Valera again and the game ends. You are asked to calculate the maximum total number of soldiers that may be killed during the game.

The input data consist of a single integer n (2 ≤ n ≤ 108, n is even). Please note that before the game starts there are 2n soldiers on the fields.

Print a single number — a maximum total number of soldiers that could be killed in the course of the game in three turns.

NoteThe first sample test:1) Valera's soldiers 1 and 2 shoot at Arcady's soldier 1.2) Arcady's soldier 2 shoots at Valera's soldier 1.3) Valera's soldier 1 shoots at Arcady's soldier 2.There are 3 soldiers killed in total: Valera's soldier 1 and Arcady's soldiers 1 and 2.


Gerald is setting the New Year table. The table has the form of a circle; its radius equals R. Gerald invited many guests and is concerned whether the table has enough space for plates for all those guests. Consider all plates to be round and have the same radii that equal r. Each plate must be completely inside the table and must touch the edge of the table. Of course, the plates must not intersect, but they can touch each other. Help Gerald determine whether the table is large enough for n plates.

The first line contains three integers n, R and r (1 ≤ n ≤ 100, 1 ≤ r, R ≤ 1000) — the number of plates, the radius of the table and the plates' radius.

Print "YES" (without the quotes) if it is possible to place n plates on the table by the rules given above. If it is impossible, print "NO". Remember, that each plate must touch the edge of the table.

NoteThe possible arrangement of the plates for the first sample is:


Recently Luba learned about a special kind of numbers that she calls beautiful numbers. The number is called beautiful iff its binary representation consists of k + 1 consecutive ones, and then k consecutive zeroes.Some examples of beautiful numbers:   12 (110);  1102 (610);  11110002 (12010);  1111100002 (49610). More formally, the number is beautiful iff there exists some positive integer k such that the number is equal to (2k - 1) * (2k - 1).Luba has got an integer number n, and she wants to find its greatest beautiful divisor. Help her to find it!

The only line of input contains one number n (1 ≤ n ≤ 105) — the number Luba has got.

Output one number — the greatest beautiful divisor of Luba's number. It is obvious that the answer always exists.


Iahub got bored, so he invented a game to be played on paper. He writes n integers a1, a2, ..., an. Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices i and j (1 ≤ i ≤ j ≤ n) and flips all values ak for which their positions are in range [i, j] (that is i ≤ k ≤ j). Flip the value of x means to apply operation x = 1 - x.The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.

The first line of the input contains an integer n (1 ≤ n ≤ 100). In the second line of the input there are n integers: a1, a2, ..., an. It is guaranteed that each of those n values is either 0 or 1.

Print an integer — the maximal number of 1s that can be obtained after exactly one move.

NoteIn the first case, flip the segment from 2 to 5 (i = 2, j = 5). That flip changes the sequence, it becomes: [1 1 1 0 1]. So, it contains four ones. There is no way to make the whole sequence equal to [1 1 1 1 1].In the second case, flipping only the second and the third element (i = 2, j = 3) will turn all numbers into 1.


This task will exclusively concentrate only on the arrays where all elements equal 1 and/or 2.Array a is k-period if its length is divisible by k and there is such array b of length k, that a is represented by array b written exactly  times consecutively. In other words, array a is k-periodic, if it has period of length k.For example, any array is n-periodic, where n is the array length. Array [2, 1, 2, 1, 2, 1] is at the same time 2-periodic and 6-periodic and array [1, 2, 1, 1, 2, 1, 1, 2, 1] is at the same time 3-periodic and 9-periodic.For the given array a, consisting only of numbers one and two, find the minimum number of elements to change to make the array k-periodic. If the array already is k-periodic, then the required value equals 0.

The first line of the input contains a pair of integers n, k (1 ≤ k ≤ n ≤ 100), where n is the length of the array and the value n is divisible by k. The second line contains the sequence of elements of the given array a1, a2, ..., an (1 ≤ ai ≤ 2), ai is the i-th element of the array.

Print the minimum number of array elements we need to change to make the array k-periodic. If the array already is k-periodic, then print 0.

NoteIn the first sample it is enough to change the fourth element from 2 to 1, then the array changes to [2, 1, 2, 1, 2, 1].In the second sample, the given array already is 4-periodic.In the third sample it is enough to replace each occurrence of number two by number one. In this case the array will look as [1, 1, 1, 1, 1, 1, 1, 1, 1] — this array is simultaneously 1-, 3- and 9-periodic.


Do you remember how Kai constructed the word "eternity" using pieces of ice as components?Little Sheldon plays with pieces of ice, each piece has exactly one digit between 0 and 9. He wants to construct his favourite number t. He realized that digits 6 and 9 are very similar, so he can rotate piece of ice with 6 to use as 9 (and vice versa). Similary, 2 and 5 work the same. There is no other pair of digits with similar effect. He called this effect "Digital Mimicry".Sheldon favourite number is t. He wants to have as many instances of t as possible. How many instances he can construct using the given sequence of ice pieces. He can use any piece at most once.

The first line contains integer t (1 ≤ t ≤ 10000). The second line contains the sequence of digits on the pieces. The length of line is equal to the number of pieces and between 1 and 200, inclusive. It contains digits between 0 and 9.

NoteThis problem contains very weak pretests.


A word or a sentence in some language is called a pangram if all the characters of the alphabet of this language appear in it at least once. Pangrams are often used to demonstrate fonts in printing or test the output devices.You are given a string consisting of lowercase and uppercase Latin letters. Check whether this string is a pangram. We say that the string contains a letter of the Latin alphabet if this letter occurs in the string in uppercase or lowercase.

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of characters in the string. The second line contains the string. The string consists only of uppercase and lowercase Latin letters.

Output "YES", if the string is a pangram and "NO" otherwise.


The numbers of all offices in the new building of the Tax Office of IT City will have lucky numbers.Lucky number is a number that consists of digits 7 and 8 only. Find the maximum number of offices in the new building of the Tax Office given that a door-plate can hold a number not longer than n digits.

The only line of input contains one integer n (1 ≤ n ≤ 55) — the maximum length of a number that a door-plate can hold.

Output one integer — the maximum number of offices, than can have unique lucky numbers not longer than n digits.


You are given a mysterious language (codenamed "Secret") available in "Custom Test" tab. Find out what this language is and write a program which outputs its name. Note that the program must be written in this language.

This program has only one test, and it's empty (it doesn't give your program anything to read).

Output the name of the mysterious language.


You are given a rectangular cake, represented as an r × c grid. Each cell either has an evil strawberry, or is empty. For example, a 3 × 4 cake may look as follows:  The cakeminator is going to eat the cake! Each time he eats, he chooses a row or a column that does not contain any evil strawberries and contains at least one cake cell that has not been eaten before, and eats all the cake cells there. He may decide to eat any number of times.Please output the maximum number of cake cells that the cakeminator can eat.

The first line contains two integers r and c (2 ≤ r, c ≤ 10), denoting the number of rows and the number of columns of the cake. The next r lines each contains c characters — the j-th character of the i-th line denotes the content of the cell at row i and column j, and is either one of these:    '.' character denotes a cake cell with no evil strawberry;  'S' character denotes a cake cell with an evil strawberry.

Output the maximum number of cake cells that the cakeminator can eat.

NoteFor the first example, one possible way to eat the maximum number of cake cells is as follows (perform 3 eats).


There are three doors in front of you, numbered from $$$1$$$ to $$$3$$$ from left to right. Each door has a lock on it, which can only be opened with a key with the same number on it as the number on the door.There are three keys — one for each door. Two of them are hidden behind the doors, so that there is no more than one key behind each door. So two doors have one key behind them, one door doesn't have a key behind it. To obtain a key hidden behind a door, you should first unlock that door. The remaining key is in your hands.Can you open all the doors?

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 18$$$) — the number of testcases. The first line of each testcase contains a single integer $$$x$$$ ($$$1 \le x \le 3$$$) — the number on the key in your hands. The second line contains three integers $$$a, b$$$ and $$$c$$$ ($$$0 \le a, b, c \le 3$$$) — the number on the key behind each of the doors. If there is no key behind the door, the number is equal to $$$0$$$. Values $$$1, 2$$$ and $$$3$$$ appear exactly once among $$$x, a, b$$$ and $$$c$$$.

For each testcase, print "YES" if you can open all the doors. Otherwise, print "NO".


In mathematics, the Pythagorean theorem — is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states: In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:a2 + b2 = c2where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.  Given n, your task is to count how many right-angled triangles with side-lengths a, b and c that satisfied an inequality 1 ≤ a ≤ b ≤ c ≤ n.

The only line contains one integer n (1 ≤ n ≤ 104) as we mentioned above.


Roman is a young mathematician, very famous in Uzhland. Unfortunately, Sereja doesn't think so. To make Sereja change his mind, Roman is ready to solve any mathematical problem. After some thought, Sereja asked Roma to find, how many numbers are close to number n, modulo m.Number x is considered close to number n modulo m, if:  it can be obtained by rearranging the digits of number n,  it doesn't have any leading zeroes,  the remainder after dividing number x by m equals 0. Roman is a good mathematician, but the number of such numbers is too huge for him. So he asks you to help him.

The first line contains two integers: n (1 ≤ n < 1018) and m (1 ≤ m ≤ 100).

In a single line print a single integer — the number of numbers close to number n modulo m.

NoteIn the first sample the required numbers are: 104, 140, 410.In the second sample the required number is 232.


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 $$$w$$$, and the height of the screen is $$$h$$$, then the following condition should be met: $$$\frac{w}{h} = \frac{x}{y}$$$.There are many different TV sets in the shop. Monocarp is sure that for any pair of positive integers $$$w$$$ and $$$h$$$ there is a TV set with screen width $$$w$$$ and height $$$h$$$ in the shop.Monocarp isn't ready to choose the exact TV set he is going to buy. Firstly he wants to determine the optimal screen resolution. He has decided to try all possible variants of screen size. But he must count the number of pairs of positive integers $$$w$$$ and $$$h$$$, beforehand, such that $$$(w \le a)$$$, $$$(h \le b)$$$ and $$$(\frac{w}{h} = \frac{x}{y})$$$.In other words, Monocarp wants to determine the number of TV sets having aspect ratio $$$\frac{x}{y}$$$, screen width not exceeding $$$a$$$, and screen height not exceeding $$$b$$$. Two TV sets are considered different if they have different screen width or different screen height.

The first line contains four integers $$$a$$$, $$$b$$$, $$$x$$$, $$$y$$$ ($$$1 \le a, b, x, y \le 10^{18}$$$) — the constraints on the screen width and height, and on the aspect ratio.

Print one integer — the number of different variants to choose TV screen width and screen height so that they meet the aforementioned constraints.

NoteIn the first example, there are $$$3$$$ possible variants: $$$(5, 3)$$$, $$$(10, 6)$$$, $$$(15, 9)$$$.In the second example, there is no TV set meeting the constraints.In the third example, there is only one variant: $$$(3, 2)$$$.


A famous Berland's painter Kalevitch likes to shock the public. One of his last obsessions is chess. For more than a thousand years people have been playing this old game on uninteresting, monotonous boards. Kalevitch decided to put an end to this tradition and to introduce a new attitude to chessboards.As before, the chessboard is a square-checkered board with the squares arranged in a 8 × 8 grid, each square is painted black or white. Kalevitch suggests that chessboards should be painted in the following manner: there should be chosen a horizontal or a vertical line of 8 squares (i.e. a row or a column), and painted black. Initially the whole chessboard is white, and it can be painted in the above described way one or more times. It is allowed to paint a square many times, but after the first time it does not change its colour any more and remains black. Kalevitch paints chessboards neatly, and it is impossible to judge by an individual square if it was painted with a vertical or a horizontal stroke.Kalevitch hopes that such chessboards will gain popularity, and he will be commissioned to paint chessboards, which will help him ensure a comfortable old age. The clients will inform him what chessboard they want to have, and the painter will paint a white chessboard meeting the client's requirements.It goes without saying that in such business one should economize on everything — for each commission he wants to know the minimum amount of strokes that he has to paint to fulfill the client's needs. You are asked to help Kalevitch with this task.

The input file contains 8 lines, each of the lines contains 8 characters. The given matrix describes the client's requirements, W character stands for a white square, and B character — for a square painted black. It is guaranteed that client's requirments can be fulfilled with a sequence of allowed strokes (vertical/column or horizontal/row).

Output the only number — the minimum amount of rows and columns that Kalevitch has to paint on the white chessboard to meet the client's requirements.

WWWBWWBW
BBBBBBBB
WWWBWWBW
WWWBWWBW
WWWBWWBW
WWWBWWBW
WWWBWWBW
WWWBWWBW

WWWWWWWW
BBBBBBBB
WWWWWWWW
WWWWWWWW
WWWWWWWW
WWWWWWWW
WWWWWWWW
WWWWWWWW


Bizon the Champion isn't just a bison. He also is a favorite of the "Bizons" team.At a competition the "Bizons" got the following problem: "You are given two distinct words (strings of English letters), s and t. You need to transform word s into word t". The task looked simple to the guys because they know the suffix data structures well. Bizon Senior loves suffix automaton. By applying it once to a string, he can remove from this string any single character. Bizon Middle knows suffix array well. By applying it once to a string, he can swap any two characters of this string. The guys do not know anything about the suffix tree, but it can help them do much more. Bizon the Champion wonders whether the "Bizons" can solve the problem. Perhaps, the solution do not require both data structures. Find out whether the guys can solve the problem and if they can, how do they do it? Can they solve it either only with use of suffix automaton or only with use of suffix array or they need both structures? Note that any structure may be used an unlimited number of times, the structures may be used in any order.

The first line contains a non-empty word s. The second line contains a non-empty word t. Words s and t are different. Each word consists only of lowercase English letters. Each word contains at most 100 letters.

In the single line print the answer to the problem. Print "need tree" (without the quotes) if word s cannot be transformed into word t even with use of both suffix array and suffix automaton. Print "automaton" (without the quotes) if you need only the suffix automaton to solve the problem. Print "array" (without the quotes) if you need only the suffix array to solve the problem. Print "both" (without the quotes), if you need both data structures to solve the problem. It's guaranteed that if you can solve the problem only with use of suffix array, then it is impossible to solve it only with use of suffix automaton. This is also true for suffix automaton.

NoteIn the third sample you can act like that: first transform "both" into "oth" by removing the first character using the suffix automaton and then make two swaps of the string using the suffix array and get "hot".


Programmers' kids solve this riddle in 5-10 minutes. How fast can you do it?

The input contains a single integer n (0 ≤ n ≤ 2000000000).


A stowaway and a controller play the following game. The train is represented by n wagons which are numbered with positive integers from 1 to n from the head to the tail. The stowaway and the controller are initially in some two different wagons. Every minute the train can be in one of two conditions — moving or idle. Every minute the players move.The controller's move is as follows. The controller has the movement direction — to the train's head or to its tail. During a move the controller moves to the neighbouring wagon correspondingly to its movement direction. If at the end of his move the controller enters the 1-st or the n-th wagon, that he changes the direction of his movement into the other one. In other words, the controller cyclically goes from the train's head to its tail and back again during all the time of a game, shifting during each move by one wagon. Note, that the controller always have exactly one possible move.The stowaway's move depends from the state of the train. If the train is moving, then the stowaway can shift to one of neighbouring wagons or he can stay where he is without moving. If the train is at a station and is idle, then the stowaway leaves the train (i.e. he is now not present in any train wagon) and then, if it is not the terminal train station, he enters the train again into any of n wagons (not necessarily into the one he's just left and not necessarily into the neighbouring one). If the train is idle for several minutes then each such minute the stowaway leaves the train and enters it back.Let's determine the order of the players' moves. If at the given minute the train is moving, then first the stowaway moves and then the controller does. If at this minute the train is idle, then first the stowaway leaves the train, then the controller moves and then the stowaway enters the train.If at some point in time the stowaway and the controller happen to be in one wagon, then the controller wins: he makes the stowaway pay fine. If after a while the stowaway reaches the terminal train station, then the stowaway wins: he simply leaves the station during his move and never returns there again.At any moment of time the players know each other's positions. The players play in the optimal way. Specifically, if the controller wins, then the stowaway plays so as to lose as late as possible. As all the possible moves for the controller are determined uniquely, then he is considered to play optimally always. Determine the winner.

The first line contains three integers n, m and k. They represent the number of wagons in the train, the stowaway's and the controller's initial positions correspondingly (2 ≤ n ≤ 50, 1 ≤ m, k ≤ n, m ≠ k). The second line contains the direction in which a controller moves. "to head" means that the controller moves to the train's head and "to tail" means that the controller moves to its tail. It is guaranteed that in the direction in which the controller is moving, there is at least one wagon. Wagon 1 is the head, and wagon n is the tail. The third line has the length from 1 to 200 and consists of symbols "0" and "1". The i-th symbol contains information about the train's state at the i-th minute of time. "0" means that in this very minute the train moves and "1" means that the train in this very minute stands idle. The last symbol of the third line is always "1" — that's the terminal train station.

If the stowaway wins, print "Stowaway" without quotes. Otherwise, print "Controller" again without quotes, then, separated by a space, print the number of a minute, at which the stowaway will be caught.


Alice is the leader of the State Refactoring Party, and she is about to become the prime minister. The elections have just taken place. There are $$$n$$$ parties, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th party has received $$$a_i$$$ seats in the parliament.Alice's party has number $$$1$$$. In order to become the prime minister, she needs to build a coalition, consisting of her party and possibly some other parties. There are two conditions she needs to fulfil:   The total number of seats of all parties in the coalition must be a strict majority of all the seats, i.e. it must have strictly more than half of the seats. For example, if the parliament has $$$200$$$ (or $$$201$$$) seats, then the majority is $$$101$$$ or more seats.  Alice's party must have at least $$$2$$$ times more seats than any other party in the coalition. For example, to invite a party with $$$50$$$ seats, Alice's party must have at least $$$100$$$ seats. For example, if $$$n=4$$$ and $$$a=[51, 25, 99, 25]$$$ (note that Alice'a party has $$$51$$$ seats), then the following set $$$[a_1=51, a_2=25, a_4=25]$$$ can create a coalition since both conditions will be satisfied. However, the following sets will not create a coalition:  $$$[a_2=25, a_3=99, a_4=25]$$$ since Alice's party is not there;  $$$[a_1=51, a_2=25]$$$ since coalition should have a strict majority;  $$$[a_1=51, a_2=25, a_3=99]$$$ since Alice's party should have at least $$$2$$$ times more seats than any other party in the coalition. Alice does not have to minimise the number of parties in a coalition. If she wants, she can invite as many parties as she wants (as long as the conditions are satisfied). If Alice's party has enough people to create a coalition on her own, she can invite no parties.Note that Alice can either invite a party as a whole or not at all. It is not possible to invite only some of the deputies (seats) from another party. In other words, if Alice invites a party, she invites all its deputies.Find and print any suitable coalition.

The first line contains a single integer $$$n$$$ ($$$2 \leq n \leq 100$$$) — the number of parties. The second line contains $$$n$$$ space separated integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 100$$$) — the number of seats the $$$i$$$-th party has.

If no coalition satisfying both conditions is possible, output a single line with an integer $$$0$$$. Otherwise, suppose there are $$$k$$$ ($$$1 \leq k \leq n$$$) parties in the coalition (Alice does not have to minimise the number of parties in a coalition), and their indices are $$$c_1, c_2, \dots, c_k$$$ ($$$1 \leq c_i \leq n$$$). Output two lines, first containing the integer $$$k$$$, and the second the space-separated indices $$$c_1, c_2, \dots, c_k$$$.  You may print the parties in any order. Alice's party (number $$$1$$$) must be on that list. If there are multiple solutions, you may print any of them.

NoteIn the first example, Alice picks the second party. Note that she can also pick the third party or both of them. However, she cannot become prime minister without any of them, because $$$100$$$ is not a strict majority out of $$$200$$$.In the second example, there is no way of building a majority, as both other parties are too large to become a coalition partner.In the third example, Alice already has the majority. The fourth example is described in the problem statement.


JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer $$$n$$$, you can perform the following operations zero or more times:  mul $$$x$$$: multiplies $$$n$$$ by $$$x$$$ (where $$$x$$$ is an arbitrary positive integer).  sqrt: replaces $$$n$$$ with $$$\sqrt{n}$$$ (to apply this operation, $$$\sqrt{n}$$$ must be an integer). You can perform these operations as many times as you like. What is the minimum value of $$$n$$$, that can be achieved and what is the minimum number of operations, to achieve that minimum value?Apparently, no one in the class knows the answer to this problem, maybe you can help them?

The only line of the input contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the initial number.

Print two integers: the minimum integer $$$n$$$ that can be achieved using the described operations and the minimum number of operations required.

NoteIn the first example, you can apply the operation mul $$$5$$$ to get $$$100$$$ and then sqrt to get $$$10$$$.In the second example, you can first apply sqrt to get $$$72$$$, then mul $$$18$$$ to get $$$1296$$$ and finally two more sqrt and you get $$$6$$$.Note, that even if the initial value of $$$n$$$ is less or equal $$$10^6$$$, it can still become greater than $$$10^6$$$ after applying one or more operations.


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 the last name of a user. Return the alphabetically earliest login they can get (regardless of other potential Polygon users).As a reminder, a prefix of a string s is its substring which occurs at the beginning of s: "a", "ab", "abc" etc. are prefixes of string "{abcdef}" but "b" and 'bc" are not. A string a is alphabetically earlier than a string b, if a is a prefix of b, or a and b coincide up to some position, and then a has a letter that is alphabetically earlier than the corresponding letter in b: "a" and "ab" are alphabetically earlier than "ac" but "b" and "ba" are alphabetically later than "ac".

The input consists of a single line containing two space-separated strings: the first and the last names. Each character of each string is a lowercase English letter. The length of each string is between 1 and 10, inclusive.

Output a single string — alphabetically earliest possible login formed from these names. The output should be given in lowercase as well.


Recently a Golden Circle of Beetlovers was found in Byteland. It is a circle route going through $$$n \cdot k$$$ cities. The cities are numerated from $$$1$$$ to $$$n \cdot k$$$, the distance between the neighboring cities is exactly $$$1$$$ km.Sergey does not like beetles, he loves burgers. Fortunately for him, there are $$$n$$$ fast food restaurants on the circle, they are located in the $$$1$$$-st, the $$$(k + 1)$$$-st, the $$$(2k + 1)$$$-st, and so on, the $$$((n-1)k + 1)$$$-st cities, i.e. the distance between the neighboring cities with fast food restaurants is $$$k$$$ km.Sergey began his journey at some city $$$s$$$ and traveled along the circle, making stops at cities each $$$l$$$ km ($$$l > 0$$$), until he stopped in $$$s$$$ once again. Sergey then forgot numbers $$$s$$$ and $$$l$$$, but he remembers that the distance from the city $$$s$$$ to the nearest fast food restaurant was $$$a$$$ km, and the distance from the city he stopped at after traveling the first $$$l$$$ km from $$$s$$$ to the nearest fast food restaurant was $$$b$$$ km. Sergey always traveled in the same direction along the circle, but when he calculated distances to the restaurants, he considered both directions.Now Sergey is interested in two integers. The first integer $$$x$$$ is the minimum number of stops (excluding the first) Sergey could have done before returning to $$$s$$$. The second integer $$$y$$$ is the maximum number of stops (excluding the first) Sergey could have done before returning to $$$s$$$.

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 100\,000$$$) — the number of fast food restaurants on the circle and the distance between the neighboring restaurants, respectively. The second line contains two integers $$$a$$$ and $$$b$$$ ($$$0 \le a, b \le \frac{k}{2}$$$) — the distances to the nearest fast food restaurants from the initial city and from the city Sergey made the first stop at, respectively.

Print the two integers $$$x$$$ and $$$y$$$.

NoteIn the first example the restaurants are located in the cities $$$1$$$ and $$$4$$$, the initial city $$$s$$$ could be $$$2$$$, $$$3$$$, $$$5$$$, or $$$6$$$. The next city Sergey stopped at could also be at cities $$$2, 3, 5, 6$$$. Let's loop through all possible combinations of these cities. If both $$$s$$$ and the city of the first stop are at the city $$$2$$$ (for example, $$$l = 6$$$), then Sergey is at $$$s$$$ after the first stop already, so $$$x = 1$$$. In other pairs Sergey needs $$$1, 2, 3$$$, or $$$6$$$ stops to return to $$$s$$$, so $$$y = 6$$$.In the second example Sergey was at cities with fast food restaurant both initially and after the first stop, so $$$l$$$ is $$$2$$$, $$$4$$$, or $$$6$$$. Thus $$$x = 1$$$, $$$y = 3$$$.In the third example there is only one restaurant, so the possible locations of $$$s$$$ and the first stop are: $$$(6, 8)$$$ and $$$(6, 4)$$$. For the first option $$$l = 2$$$, for the second $$$l = 8$$$. In both cases Sergey needs $$$x=y=5$$$ stops to go to $$$s$$$.


Furik and Rubik love playing computer games. Furik has recently found a new game that greatly interested Rubik. The game consists of n parts and to complete each part a player may probably need to complete some other ones. We know that the game can be fully completed, that is, its parts do not form cyclic dependencies. Rubik has 3 computers, on which he can play this game. All computers are located in different houses. Besides, it has turned out that each part of the game can be completed only on one of these computers. Let's number the computers with integers from 1 to 3. Rubik can perform the following actions:   Complete some part of the game on some computer. Rubik spends exactly 1 hour on completing any part on any computer.  Move from the 1-st computer to the 2-nd one. Rubik spends exactly 1 hour on that.  Move from the 1-st computer to the 3-rd one. Rubik spends exactly 2 hours on that.  Move from the 2-nd computer to the 1-st one. Rubik spends exactly 2 hours on that.  Move from the 2-nd computer to the 3-rd one. Rubik spends exactly 1 hour on that.  Move from the 3-rd computer to the 1-st one. Rubik spends exactly 1 hour on that.  Move from the 3-rd computer to the 2-nd one. Rubik spends exactly 2 hours on that. Help Rubik to find the minimum number of hours he will need to complete all parts of the game. Initially Rubik can be located at the computer he considers necessary.

The first line contains integer n (1 ≤ n ≤ 200) — the number of game parts. The next line contains n integers, the i-th integer — ci (1 ≤ ci ≤ 3) represents the number of the computer, on which you can complete the game part number i.  Next n lines contain descriptions of game parts. The i-th line first contains integer ki (0 ≤ ki ≤ n - 1), then ki distinct integers ai, j (1 ≤ ai, j ≤ n; ai, j ≠ i) — the numbers of parts to complete before part i. Numbers on all lines are separated by single spaces. You can assume that the parts of the game are numbered from 1 to n in some way. It is guaranteed that there are no cyclic dependencies between the parts of the game.

On a single line print the answer to the problem.

NoteNote to the second sample: before the beginning of the game the best strategy is to stand by the third computer. First we complete part 5. Then we go to the 1-st computer and complete parts 3 and 4. Then we go to the 2-nd computer and complete parts 1 and 2. In total we get 1+1+2+1+2, which equals 7 hours.


Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.

The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).

If it's impossible to find the representation of n as a product of k numbers, print -1. Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.


Princess Twilight went to Celestia and Luna's old castle to research the chest from the Elements of Harmony.  A sequence of positive integers bi is harmony if and only if for every two elements of the sequence their greatest common divisor equals 1. According to an ancient book, the key of the chest is a harmony sequence bi which minimizes the following expression:You are given sequence ai, help Princess Twilight to find the key.

The first line contains an integer n (1 ≤ n ≤ 100) — the number of elements of the sequences a and b. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 30).

Output the key — sequence bi that minimizes the sum described above. If there are multiple optimal sequences, you can output any of them.


Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.

The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands. The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.

Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.

NoteIn the first case, the entire source code works, as well as the "RL" substring in the second and third characters.Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.


There are n walruses sitting in a circle. All of them are numbered in the clockwise order: the walrus number 2 sits to the left of the walrus number 1, the walrus number 3 sits to the left of the walrus number 2, ..., the walrus number 1 sits to the left of the walrus number n.The presenter has m chips. The presenter stands in the middle of the circle and starts giving the chips to the walruses starting from walrus number 1 and moving clockwise. The walrus number i gets i chips. If the presenter can't give the current walrus the required number of chips, then the presenter takes the remaining chips and the process ends. Determine by the given n and m how many chips the presenter will get in the end.

The first line contains two integers n and m (1 ≤ n ≤ 50, 1 ≤ m ≤ 104) — the number of walruses and the number of chips correspondingly.

Print the number of chips the presenter ended up with.

NoteIn the first sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, four chips to the walrus number 4, then again one chip to the walrus number 1. After that the presenter runs out of chips. He can't give anything to the walrus number 2 and the process finishes.In the third sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, then again one chip to the walrus number 1. The presenter has one chip left and he can't give two chips to the walrus number 2, that's why the presenter takes the last chip.


A number is called quasibinary if its decimal representation contains only digits 0 or 1. For example, numbers 0, 1, 101, 110011 — are quasibinary and numbers 2, 12, 900 are not.You are given a positive integer n. Represent it as a sum of minimum number of quasibinary numbers.

The first line contains a single integer n (1 ≤ n ≤ 106).

In the first line print a single integer k — the minimum number of numbers in the representation of number n as a sum of quasibinary numbers. In the second line print k numbers — the elements of the sum. All these numbers should be quasibinary according to the definition above, their sum should equal n. Do not have to print the leading zeroes in the numbers. The order of numbers doesn't matter. If there are multiple possible representations, you are allowed to print any of them.


Today an outstanding event is going to happen in the forest — hedgehog Filya will come to his old fried Sonya!Sonya is an owl and she sleeps during the day and stay awake from minute l1 to minute r1 inclusive. Also, during the minute k she prinks and is unavailable for Filya.Filya works a lot and he plans to visit Sonya from minute l2 to minute r2 inclusive.Calculate the number of minutes they will be able to spend together.

The only line of the input contains integers l1, r1, l2, r2 and k (1 ≤ l1, r1, l2, r2, k ≤ 1018, l1 ≤ r1, l2 ≤ r2), providing the segments of time for Sonya and Filya and the moment of time when Sonya prinks.

Print one integer — the number of minutes Sonya and Filya will be able to spend together.

NoteIn the first sample, they will be together during minutes 9 and 10.In the second sample, they will be together from minute 50 to minute 74 and from minute 76 to minute 100.


Fox Ciel has some flowers: r red flowers, g green flowers and b blue flowers. She wants to use these flowers to make several bouquets. There are 4 types of bouquets:  To make a "red bouquet", it needs 3 red flowers.  To make a "green bouquet", it needs 3 green flowers.  To make a "blue bouquet", it needs 3 blue flowers.  To make a "mixing bouquet", it needs 1 red, 1 green and 1 blue flower. Help Fox Ciel to find the maximal number of bouquets she can make.

The first line contains three integers r, g and b (0 ≤ r, g, b ≤ 109) — the number of red, green and blue flowers.

Print the maximal number of bouquets Fox Ciel can make.

NoteIn test case 1, we can make 1 red bouquet, 2 green bouquets and 3 blue bouquets.In test case 2, we can make 1 red, 1 green, 1 blue and 1 mixing bouquet.


You have a nuts and lots of boxes. The boxes have a wonderful feature: if you put x (x ≥ 0) divisors (the spacial bars that can divide a box) to it, you get a box, divided into x + 1 sections.You are minimalist. Therefore, on the one hand, you are against dividing some box into more than k sections. On the other hand, you are against putting more than v nuts into some section of the box. What is the minimum number of boxes you have to use if you want to put all the nuts in boxes, and you have b divisors?Please note that you need to minimize the number of used boxes, not sections. You do not have to minimize the number of used divisors.

The first line contains four space-separated integers k, a, b, v (2 ≤ k ≤ 1000; 1 ≤ a, b, v ≤ 1000) — the maximum number of sections in the box, the number of nuts, the number of divisors and the capacity of each section of the box.

Print a single integer — the answer to the problem.

NoteIn the first sample you can act like this:   Put two divisors to the first box. Now the first box has three sections and we can put three nuts into each section. Overall, the first box will have nine nuts.  Do not put any divisors into the second box. Thus, the second box has one section for the last nut. In the end we've put all the ten nuts into boxes.The second sample is different as we have exactly one divisor and we put it to the first box. The next two boxes will have one section each.


The Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an n × n size matrix, where n is odd. The Smart Beaver considers the following matrix elements good:    Elements of the main diagonal.   Elements of the secondary diagonal.   Elements of the "middle" row — the row which has exactly  rows above it and the same number of rows below it.   Elements of the "middle" column — the column that has exactly  columns to the left of it and the same number of columns to the right of it.    The figure shows a 5 × 5 matrix.   The good elements are marked with green.  Help the Smart Beaver count the sum of good elements of the given matrix.

The first line of input data contains a single odd integer n. Each of the next n lines contains n integers aij (0 ≤ aij ≤ 100) separated by single spaces — the elements of the given matrix. The input limitations for getting 30 points are:    1 ≤ n ≤ 5  The input limitations for getting 100 points are:   1 ≤ n ≤ 101

Print a single integer — the sum of good matrix elements.

NoteIn the first sample all matrix elements will be good. Good elements in the second sample are shown on the figure.


Petya has equal wooden bars of length n. He wants to make a frame for two equal doors. Each frame has two vertical (left and right) sides of length a and one top side of length b. A solid (i.e. continuous without breaks) piece of bar is needed for each side.Determine a minimal number of wooden bars which are needed to make the frames for two doors. Petya can cut the wooden bars into any parts, but each side of each door should be a solid piece of a wooden bar (or a whole wooden bar).

The first line contains a single integer n (1 ≤ n ≤ 1 000) — the length of each wooden bar. The second line contains a single integer a (1 ≤ a ≤ n) — the length of the vertical (left and right) sides of a door frame. The third line contains a single integer b (1 ≤ b ≤ n) — the length of the upper side of a door frame.

Print the minimal number of wooden bars with length n which are needed to make the frames for two doors.

NoteIn the first example one wooden bar is enough, since the total length of all six sides of the frames for two doors is 8.In the second example 6 wooden bars is enough, because for each side of the frames the new wooden bar is needed.


Several months later Alex finally got his brother Bob's creation by post. And now, in his turn, Alex wants to boast about something to his brother. He thought for a while, and came to the conclusion that he has no ready creations, and decided to write a program for rectangles detection. According to his plan, the program detects if the four given segments form a rectangle of a positive area and with sides parallel to coordinate axes. As Alex does badly at school and can't write this program by himself, he asks you to help him.

The input data contain four lines. Each of these lines contains four integers x1, y1, x2, y2 ( - 109 ≤ x1, y1, x2, y2 ≤ 109) — coordinates of segment's beginning and end positions. The given segments can degenerate into points.

Output the word «YES», if the given four segments form the required rectangle, otherwise output «NO».


Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.

The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.

Print a single number: the number of times x occurs in the table.

NoteA table for the second sample test is given below. The occurrences of number 12 are marked bold.