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


Ayoub had an array $$$a$$$ of integers of size $$$n$$$ and this array had two interesting properties:   All the integers in the array were between $$$l$$$ and $$$r$$$ (inclusive).  The sum of all the elements was divisible by $$$3$$$. Unfortunately, Ayoub has lost his array, but he remembers the size of the array $$$n$$$ and the numbers $$$l$$$ and $$$r$$$, so he asked you to find the number of ways to restore the array. Since the answer could be very large, print it modulo $$$10^9 + 7$$$ (i.e. the remainder when dividing by $$$10^9 + 7$$$). In case there are no satisfying arrays (Ayoub has a wrong memory), print $$$0$$$.

The first and only line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$1 \le n \le 2 \cdot 10^5 , 1 \le l \le r \le 10^9$$$) — the size of the lost array and the range of numbers in the array.

Print the remainder when dividing by $$$10^9 + 7$$$ the number of ways to restore the array.

NoteIn the first example, the possible arrays are : $$$[1,2], [2,1], [3, 3]$$$.In the second example, the only possible array is $$$[2, 2, 2]$$$.


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.


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 special properties, he wants to know how rare (or not rare) they are — in fact, he needs to calculate the quantity of really big numbers that are not greater than n.Ivan tried to do the calculations himself, but soon realized that it's too difficult for him. So he asked you to help him in calculations.

The first (and the only) line contains two integers n and s (1 ≤ n, s ≤ 1018).

Print one integer — the quantity of really big numbers that are not greater than n.

NoteIn the first example numbers 10, 11 and 12 are really big.In the second example there are no really big numbers that are not greater than 25 (in fact, the first really big number is 30: 30 - 3 ≥ 20).In the third example 10 is the only really big number (10 - 1 ≥ 9).


You have two integers $$$l$$$ and $$$r$$$. Find an integer $$$x$$$ which satisfies the conditions below:  $$$l \le x \le r$$$.  All digits of $$$x$$$ are different. If there are multiple answers, print any of them.

The first line contains two integers $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le 10^{5}$$$).

If an answer exists, print any of them. Otherwise, print $$$-1$$$.

NoteIn the first example, $$$123$$$ is one of the possible answers. However, $$$121$$$ can't be the answer, because there are multiple $$$1$$$s on different digits.In the second example, there is no valid answer.


Mr. Bender has a digital table of size n × n, each cell can be switched on or off. He wants the field to have at least c switched on squares. When this condition is fulfilled, Mr Bender will be happy.We'll consider the table rows numbered from top to bottom from 1 to n, and the columns — numbered from left to right from 1 to n. Initially there is exactly one switched on cell with coordinates (x, y) (x is the row number, y is the column number), and all other cells are switched off. Then each second we switch on the cells that are off but have the side-adjacent cells that are on.For a cell with coordinates (x, y) the side-adjacent cells are cells with coordinates (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1).In how many seconds will Mr. Bender get happy?

The first line contains four space-separated integers n, x, y, c (1 ≤ n, c ≤ 109; 1 ≤ x, y ≤ n; c ≤ n2).

In a single line print a single integer — the answer to the problem.

NoteInitially the first test has one painted cell, so the answer is 0. In the second test all events will go as is shown on the figure. .


A and B are preparing themselves for programming contests.To train their logical thinking and solve problems better, A and B decided to play chess. During the game A wondered whose position is now stronger.For each chess piece we know its weight:   the queen's weight is 9,  the rook's weight is 5,  the bishop's weight is 3,  the knight's weight is 3,  the pawn's weight is 1,  the king's weight isn't considered in evaluating position. The player's weight equals to the sum of weights of all his pieces on the board.As A doesn't like counting, he asked you to help him determine which player has the larger position weight.

The input contains eight lines, eight characters each — the board's description. The white pieces on the board are marked with uppercase letters, the black pieces are marked with lowercase letters. The white pieces are denoted as follows: the queen is represented is 'Q', the rook — as 'R', the bishop — as'B', the knight — as 'N', the pawn — as 'P', the king — as 'K'. The black pieces are denoted as 'q', 'r', 'b', 'n', 'p', 'k', respectively. An empty square of the board is marked as '.' (a dot).  It is not guaranteed that the given chess position can be achieved in a real game. Specifically, there can be an arbitrary (possibly zero) number pieces of each type, the king may be under attack and so on.

Print "White" (without quotes) if the weight of the position of the white pieces is more than the weight of the position of the black pieces, print "Black" if the weight of the black pieces is more than the weight of the white pieces and print "Draw" if the weights of the white and black pieces are equal.

rnbqkbnr
pppppppp
........
........
........
........
PPPPPPPP
RNBQKBNR

NoteIn the first test sample the weight of the position of the white pieces equals to 9, the weight of the position of the black pieces equals 5.In the second test sample the weights of the positions of the black and the white pieces are equal to 39.In the third test sample the weight of the position of the white pieces equals to 9, the weight of the position of the black pieces equals to 16.


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?

The only line of input contains an integer m (1 ≤ m ≤ 100 000) — the required number of trailing zeroes in factorial.

First print k — the number of values of n such that the factorial of n ends with m zeroes. Then print these k integers in increasing order.

NoteThe factorial of n is equal to the product of all integers from 1 to n inclusive, that is n! = 1·2·3·...·n.In the first sample, 5! = 120, 6! = 720, 7! = 5040, 8! = 40320 and 9! = 362880.


A burglar got into a matches warehouse and wants to steal as many matches as possible. In the warehouse there are m containers, in the i-th container there are ai matchboxes, and each matchbox contains bi matches. All the matchboxes are of the same size. The burglar's rucksack can hold n matchboxes exactly. Your task is to find out the maximum amount of matches that a burglar can carry away. He has no time to rearrange matches in the matchboxes, that's why he just chooses not more than n matchboxes so that the total amount of matches in them is maximal.

The first line of the input contains integer n (1 ≤ n ≤ 2·108) and integer m (1 ≤ m ≤ 20). The i + 1-th line contains a pair of numbers ai and bi (1 ≤ ai ≤ 108, 1 ≤ bi ≤ 10). All the input numbers are integer.

Output the only number — answer to the problem.


Bob and Alice are often participating in various programming competitions. Like many competitive programmers, Alice and Bob have good and bad days. They noticed, that their lucky and unlucky days are repeating with some period. For example, for Alice days $$$[l_a; r_a]$$$ are lucky, then there are some unlucky days: $$$[r_a + 1; l_a + t_a - 1]$$$, and then there are lucky days again: $$$[l_a + t_a; r_a + t_a]$$$ and so on. In other words, the day is lucky for Alice if it lies in the segment $$$[l_a + k t_a; r_a + k t_a]$$$ for some non-negative integer $$$k$$$.The Bob's lucky day have similar structure, however the parameters of his sequence are different: $$$l_b$$$, $$$r_b$$$, $$$t_b$$$. So a day is a lucky for Bob if it lies in a segment $$$[l_b + k t_b; r_b + k t_b]$$$, for some non-negative integer $$$k$$$.Alice and Bob want to participate in team competitions together and so they want to find out what is the largest possible number of consecutive days, which are lucky for both Alice and Bob.

The first line contains three integers $$$l_a$$$, $$$r_a$$$, $$$t_a$$$ ($$$0 \le l_a \le r_a \le t_a - 1, 2 \le t_a \le 10^9$$$) and describes Alice's lucky days. The second line contains three integers $$$l_b$$$, $$$r_b$$$, $$$t_b$$$ ($$$0 \le l_b \le r_b \le t_b - 1, 2 \le t_b \le 10^9$$$) and describes Bob's lucky days. It is guaranteed that both Alice and Bob have some unlucky days.

Print one integer: the maximum number of days in the row that are lucky for both Alice and Bob.

NoteThe graphs below correspond to the two sample tests and show the lucky and unlucky days of Alice and Bob as well as the possible solutions for these tests.


Petr has just bought a new car. He's just arrived at the most known Petersburg's petrol station to refuel it when he suddenly discovered that the petrol tank is secured with a combination lock! The lock has a scale of $$$360$$$ degrees and a pointer which initially points at zero:  Petr called his car dealer, who instructed him to rotate the lock's wheel exactly $$$n$$$ times. The $$$i$$$-th rotation should be $$$a_i$$$ degrees, either clockwise or counterclockwise, and after all $$$n$$$ rotations the pointer should again point at zero.This confused Petr a little bit as he isn't sure which rotations should be done clockwise and which should be done counterclockwise. As there are many possible ways of rotating the lock, help him and find out whether there exists at least one, such that after all $$$n$$$ rotations the pointer will point at zero again.

The first line contains one integer $$$n$$$ ($$$1 \leq n \leq 15$$$) — the number of rotations. Each of the following $$$n$$$ lines contains one integer $$$a_i$$$ ($$$1 \leq a_i \leq 180$$$) — the angle of the $$$i$$$-th rotation in degrees.

If it is possible to do all the rotations so that the pointer will point at zero after all of them are performed, print a single word "YES". Otherwise, print "NO". Petr will probably buy a new car in this case. You can print each letter in any case (upper or lower).

NoteIn the first example, we can achieve our goal by applying the first and the second rotation clockwise, and performing the third rotation counterclockwise.In the second example, it's impossible to perform the rotations in order to make the pointer point at zero in the end.In the third example, Petr can do all three rotations clockwise. In this case, the whole wheel will be rotated by $$$360$$$ degrees clockwise and the pointer will point at zero again.


During the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second. Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from 1 to n, at that the person in the position number 1 is served first. Then, if at time x a boy stands on the i-th position and a girl stands on the (i + 1)-th position, then at time x + 1 the i-th position will have a girl and the (i + 1)-th position will have a boy. The time is given in seconds.You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after t seconds.

The first line contains two integers n and t (1 ≤ n, t ≤ 50), which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find.  The next line contains string s, which represents the schoolchildren's initial arrangement. If the i-th position in the queue contains a boy, then the i-th character of string s equals "B", otherwise the i-th character equals "G".

Print string a, which describes the arrangement after t seconds. If the i-th position has a boy after the needed time, then the i-th character a must equal "B", otherwise it must equal "G".


Polycarpus is an amateur businessman. Recently he was surprised to find out that the market for paper scissors is completely free! Without further ado, Polycarpus decided to start producing and selling such scissors.Polycaprus calculated that the optimal celling price for such scissors would be p bourles. However, he read somewhere that customers are attracted by prices that say something like "Special Offer! Super price 999 bourles!". So Polycarpus decided to lower the price a little if it leads to the desired effect.Polycarpus agrees to lower the price by no more than d bourles so that the number of nines at the end of the resulting price is maximum. If there are several ways to do it, he chooses the maximum possible price.Note, Polycarpus counts only the trailing nines in a price.

The first line contains two integers p and d (1 ≤ p ≤ 1018; 0 ≤ d < p) — the initial price of scissors and the maximum possible price reduction. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Print the required price — the maximum price that ends with the largest number of nines and that is less than p by no more than d. The required number shouldn't have leading zeroes.


The only difference between this problem and D2 is that you don't have to provide the way to construct the answer in this problem, but you have to do it in D2.There's a table of $$$n \times m$$$ cells ($$$n$$$ rows and $$$m$$$ columns). The value of $$$n \cdot m$$$ is even.A domino is a figure that consists of two cells having a common side. It may be horizontal (one of the cells is to the right of the other) or vertical (one of the cells is above the other).You need to find out whether it is possible to place $$$\frac{nm}{2}$$$ dominoes on the table so that exactly $$$k$$$ of them are horizontal and all the other dominoes are vertical. The dominoes cannot overlap and must fill the whole table.

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10$$$) — the number of test cases. Then $$$t$$$ test cases follow. Each test case consists of a single line. The line contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1 \le n,m \le 100$$$, $$$0 \le k \le \frac{nm}{2}$$$, $$$n \cdot m$$$ is even) — the number of rows, columns and horizontal dominoes, respectively.

For each test case output "YES", if it is possible to place dominoes in the desired way, or "NO" otherwise. You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).


In some game by Playrix it takes t minutes for an oven to bake k carrot cakes, all cakes are ready at the same moment t minutes after they started baking. Arkady needs at least n cakes to complete a task, but he currently don't have any. However, he has infinitely many ingredients and one oven. Moreover, Arkady can build one more similar oven to make the process faster, it would take d minutes to build the oven. While the new oven is being built, only old one can bake cakes, after the new oven is built, both ovens bake simultaneously. Arkady can't build more than one oven.Determine if it is reasonable to build the second oven, i.e. will it decrease the minimum time needed to get n cakes or not. If the time needed with the second oven is the same as with one oven, then it is unreasonable.

The only line contains four integers n, t, k, d (1 ≤ n, t, k, d ≤ 1 000) — the number of cakes needed, the time needed for one oven to bake k cakes, the number of cakes baked at the same time, the time needed to build the second oven.

If it is reasonable to build the second oven, print "YES". Otherwise print "NO".

NoteIn the first example it is possible to get 8 cakes in 12 minutes using one oven. The second oven can be built in 5 minutes, so after 6 minutes the first oven bakes 4 cakes, the second oven bakes 4 more ovens after 11 minutes. Thus, it is reasonable to build the second oven. In the second example it doesn't matter whether we build the second oven or not, thus it takes 12 minutes to bake 8 cakes in both cases. Thus, it is unreasonable to build the second oven.In the third example the first oven bakes 11 cakes in 3 minutes, that is more than needed 10. It is unreasonable to build the second oven, because its building takes more time that baking the needed number of cakes using the only oven.


Running with barriers on the circle track is very popular in the country where Dasha lives, so no wonder that on her way to classes she saw the following situation:The track is the circle with length L, in distinct points of which there are n barriers. Athlete always run the track in counterclockwise direction if you look on him from above. All barriers are located at integer distance from each other along the track. Her friends the parrot Kefa and the leopard Sasha participated in competitions and each of them ran one lap. Each of the friends started from some integral point on the track. Both friends wrote the distance from their start along the track to each of the n barriers. Thus, each of them wrote n integers in the ascending order, each of them was between 0 and L - 1, inclusively.    Consider an example. Let L = 8, blue points are barriers, and green points are Kefa's start (A) and Sasha's start (B). Then Kefa writes down the sequence [2, 4, 6], and Sasha writes down [1, 5, 7]. There are several tracks in the country, all of them have same length and same number of barriers, but the positions of the barriers can differ among different tracks. Now Dasha is interested if it is possible that Kefa and Sasha ran the same track or they participated on different tracks. Write the program which will check that Kefa's and Sasha's tracks coincide (it means that one can be obtained from the other by changing the start position). Note that they always run the track in one direction — counterclockwise, if you look on a track from above.

The first line contains two integers n and L (1 ≤ n ≤ 50, n ≤ L ≤ 100) — the number of barriers on a track and its length.  The second line contains n distinct integers in the ascending order — the distance from Kefa's start to each barrier in the order of its appearance. All integers are in the range from 0 to L - 1 inclusively. The second line contains n distinct integers in the ascending order — the distance from Sasha's start to each barrier in the order of its overcoming. All integers are in the range from 0 to L - 1 inclusively.

Print "YES" (without quotes), if Kefa and Sasha ran the coinciding tracks (it means that the position of all barriers coincides, if they start running from the same points on the track). Otherwise print "NO" (without quotes).

NoteThe first test is analyzed in the statement.


This winter is so cold in Nvodsk! A group of n friends decided to buy k bottles of a soft drink called "Take-It-Light" to warm up a bit. Each bottle has l milliliters of the drink. Also they bought c limes and cut each of them into d slices. After that they found p grams of salt.To make a toast, each friend needs nl milliliters of the drink, a slice of lime and np grams of salt. The friends want to make as many toasts as they can, provided they all drink the same amount. How many toasts can each friend make?

The first and only line contains positive integers n, k, l, c, d, p, nl, np, not exceeding 1000 and no less than 1. The numbers are separated by exactly one space.

Print a single integer — the number of toasts each friend can make.

NoteA comment to the first sample: Overall the friends have 4 * 5 = 20 milliliters of the drink, it is enough to make 20 / 3 = 6 toasts. The limes are enough for 10 * 8 = 80 toasts and the salt is enough for 100 / 1 = 100 toasts. However, there are 3 friends in the group, so the answer is min(6, 80, 100) / 3 = 2.


The recent All-Berland Olympiad in Informatics featured n participants with each scoring a certain amount of points.As the head of the programming committee, you are to determine the set of participants to be awarded with diplomas with respect to the following criteria:   At least one participant should get a diploma.  None of those with score equal to zero should get awarded.  When someone is awarded, all participants with score not less than his score should also be awarded. Determine the number of ways to choose a subset of participants that will receive the diplomas.

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of participants. The next line contains a sequence of n integers a1, a2, ..., an (0 ≤ ai ≤ 600) — participants' scores. It's guaranteed that at least one participant has non-zero score.

Print a single integer — the desired number of ways.

NoteThere are three ways to choose a subset in sample case one.  Only participants with 3 points will get diplomas.  Participants with 2 or 3 points will get diplomas.  Everyone will get a diploma! The only option in sample case two is to award everyone.Note that in sample case three participants with zero scores cannot get anything.


Reca company makes monitors, the most popular of their models is AB999 with the screen size a × b centimeters. Because of some production peculiarities a screen parameters are integer numbers. Recently the screen sides ratio x: y became popular with users. That's why the company wants to reduce monitor AB999 size so that its screen sides ratio becomes x: y, at the same time they want its total area to be maximal of all possible variants. Your task is to find the screen parameters of the reduced size model, or find out that such a reduction can't be performed.

The first line of the input contains 4 integers — a, b, x and y (1 ≤ a, b, x, y ≤ 2·109).

If the answer exists, output 2 positive integers — screen parameters of the reduced size model. Output 0 0 otherwise.


Count the number of distinct sequences a1, a2, ..., an (1 ≤ ai) consisting of positive integers such that gcd(a1, a2, ..., an) = x and . As this number could be large, print the answer modulo 109 + 7.gcd here means the greatest common divisor.

The only line contains two positive integers x and y (1 ≤ x, y ≤ 109).

Print the number of such sequences modulo 109 + 7.

NoteThere are three suitable sequences in the first test: (3, 3, 3), (3, 6), (6, 3).There are no suitable sequences in the second test.


Petya is having a party soon, and he has decided to invite his $$$n$$$ friends.He wants to make invitations in the form of origami. For each invitation, he needs two red sheets, five green sheets, and eight blue sheets. The store sells an infinite number of notebooks of each color, but each notebook consists of only one color with $$$k$$$ sheets. That is, each notebook contains $$$k$$$ sheets of either red, green, or blue.Find the minimum number of notebooks that Petya needs to buy to invite all $$$n$$$ of his friends.

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1\leq n, k\leq 10^8$$$) — the number of Petya's friends and the number of sheets in each notebook respectively.

Print one number — the minimum number of notebooks that Petya needs to buy.

NoteIn the first example, we need $$$2$$$ red notebooks, $$$3$$$ green notebooks, and $$$5$$$ blue notebooks.In the second example, we need $$$5$$$ red notebooks, $$$13$$$ green notebooks, and $$$20$$$ blue notebooks.


The only difference between easy and hard versions is the length of the string.You are given a string $$$s$$$ and a string $$$t$$$, both consisting only of lowercase Latin letters. It is guaranteed that $$$t$$$ can be obtained from $$$s$$$ by removing some (possibly, zero) number of characters (not necessary contiguous) from $$$s$$$ without changing order of remaining characters (in other words, it is guaranteed that $$$t$$$ is a subsequence of $$$s$$$).For example, the strings "test", "tst", "tt", "et" and "" are subsequences of the string "test". But the strings "tset", "se", "contest" are not subsequences of the string "test".You want to remove some substring (contiguous subsequence) from $$$s$$$ of maximum possible length such that after removing this substring $$$t$$$ will remain a subsequence of $$$s$$$.If you want to remove the substring $$$s[l;r]$$$ then the string $$$s$$$ will be transformed to $$$s_1 s_2 \dots s_{l-1} s_{r+1} s_{r+2} \dots s_{|s|-1} s_{|s|}$$$ (where $$$|s|$$$ is the length of $$$s$$$).Your task is to find the maximum possible length of the substring you can remove so that $$$t$$$ is still a subsequence of $$$s$$$.

The first line of the input contains one string $$$s$$$ consisting of at least $$$1$$$ and at most $$$200$$$ lowercase Latin letters. The second line of the input contains one string $$$t$$$ consisting of at least $$$1$$$ and at most $$$200$$$ lowercase Latin letters. It is guaranteed that $$$t$$$ is a subsequence of $$$s$$$.

Print one integer — the maximum possible length of the substring you can remove so that $$$t$$$ is still a subsequence of $$$s$$$.


User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this: << p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >> When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.There are some conditions in the navigation:  If page 1 is in the navigation, the button "<<" must not be printed.  If page n is in the navigation, the button ">>" must not be printed.  If the page number is smaller than 1 or greater than n, it must not be printed.   You can see some examples of the navigations. Make a program that prints the navigation.

The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)

Print the proper navigation. Follow the format of the output from the test samples.


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.


You are given an integer array $$$a_0, a_1, \dots, a_{n - 1}$$$, and an integer $$$k$$$. You perform the following code with it:long long ans = 0; // create a 64-bit signed variable which is initially equal to 0for(int i = 1; i <= k; i++){  int idx = rnd.next(0, n - 1); // generate a random integer between 0 and n - 1, both inclusive                                // each integer from 0 to n - 1 has the same probability of being chosen  ans += a[idx];  a[idx] -= (a[idx] % i);}Your task is to calculate the expected value of the variable ans after performing this code.Note that the input is generated according to special rules (see the input format section).

The only line contains six integers $$$n$$$, $$$a_0$$$, $$$x$$$, $$$y$$$, $$$k$$$ and $$$M$$$ ($$$1 \le n \le 10^7$$$; $$$1 \le a_0, x, y < M \le 998244353$$$; $$$1 \le k \le 17$$$). The array $$$a$$$ in the input is constructed as follows:   $$$a_0$$$ is given in the input;  for every $$$i$$$ from $$$1$$$ to $$$n - 1$$$, the value of $$$a_i$$$ can be calculated as $$$a_i = (a_{i - 1} \cdot x + y) \bmod M$$$.

Let the expected value of the variable ans after performing the code be $$$E$$$. It can be shown that $$$E \cdot n^k$$$ is an integer. You have to output this integer modulo $$$998244353$$$.

NoteThe array in the first example test is $$$[10, 35, 22]$$$. In the second example, it is $$$[15363, 1418543]$$$.


Andrey received a postcard from Irina. It contained only the words "Hello, Andrey!", and a strange string consisting of lowercase Latin letters, snowflakes and candy canes. Andrey thought that this string is an encrypted message, and decided to decrypt it.Andrey noticed that snowflakes and candy canes always stand after the letters, so he supposed that the message was encrypted as follows. Candy cane means that the letter before it can be removed, or can be left. A snowflake means that the letter before it can be removed, left, or repeated several times.For example, consider the following string:   This string can encode the message «happynewyear». For this, candy canes and snowflakes should be used as follows:   candy cane 1: remove the letter w,  snowflake 1: repeat the letter p twice,  candy cane 2: leave the letter n,  snowflake 2: remove the letter w,  snowflake 3: leave the letter e.   Please note that the same string can encode different messages. For example, the string above can encode «hayewyar», «happpppynewwwwwyear», and other messages.Andrey knows that messages from Irina usually have a length of $$$k$$$ letters. Help him to find out if a given string can encode a message of $$$k$$$ letters, and if so, give an example of such a message.

The first line contains the string received in the postcard. The string consists only of lowercase Latin letters, as well as the characters «*» and «?», meaning snowflake and candy cone, respectively. These characters can only appear immediately after the letter. The length of the string does not exceed $$$200$$$. The second line contains an integer number $$$k$$$ ($$$1 \leq k \leq 200$$$), the required message length.

Print any message of length $$$k$$$ that the given string can encode, or «Impossible» if such a message does not exist.


Ivan's classes at the university have just finished, and now he wants to go to the local CFK cafe and eat some fried chicken.CFK sells chicken chunks in small and large portions. A small portion contains 3 chunks; a large one — 7 chunks. Ivan wants to eat exactly x chunks. Now he wonders whether he can buy exactly this amount of chicken.Formally, Ivan wants to know if he can choose two non-negative integers a and b in such a way that a small portions and b large ones contain exactly x chunks.Help Ivan to answer this question for several values of x!

The first line contains one integer n (1 ≤ n ≤ 100) — the number of testcases. The i-th of the following n lines contains one integer xi (1 ≤ xi ≤ 100) — the number of chicken chunks Ivan wants to eat.

Print n lines, in i-th line output YES if Ivan can buy exactly xi chunks. Otherwise, print NO.

NoteIn the first example Ivan can buy two small portions.In the second example Ivan cannot buy exactly 5 chunks, since one small portion is not enough, but two small portions or one large is too much.


Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?

The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.

Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.

NoteThe least common multiple of some positive integers is the least positive integer which is multiple for each of them.The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.


While swimming at the beach, Mike has accidentally dropped his cellphone into the water. There was no worry as he bought a cheap replacement phone with an old-fashioned keyboard. The keyboard has only ten digital equal-sized keys, located in the following way:  Together with his old phone, he lost all his contacts and now he can only remember the way his fingers moved when he put some number in. One can formally consider finger movements as a sequence of vectors connecting centers of keys pressed consecutively to put in a number. For example, the finger movements for number "586" are the same as finger movements for number "253":    Mike has already put in a number by his "finger memory" and started calling it, so he is now worrying, can he be sure that he is calling the correct number? In other words, is there any other number, that has the same finger movements?

The first line of the input contains the only integer n (1 ≤ n ≤ 9) — the number of digits in the phone number that Mike put in. The second line contains the string consisting of n digits (characters from '0' to '9') representing the number that Mike put in.

If there is no other phone number with the same finger movements and Mike can be sure he is calling the correct number, print "YES" (without quotes) in the only line. Otherwise print "NO" (without quotes) in the first line.

NoteYou can find the picture clarifying the first sample case in the statement above.


Polycarpus has got n candies and m friends (n ≥ m). He wants to make a New Year present with candies to each friend. Polycarpus is planning to present all candies and he wants to do this in the fairest (that is, most equal) manner. He wants to choose such ai, where ai is the number of candies in the i-th friend's present, that the maximum ai differs from the least ai as little as possible.For example, if n is divisible by m, then he is going to present the same number of candies to all his friends, that is, the maximum ai won't differ from the minimum one.

The single line of the input contains a pair of space-separated positive integers n, m (1 ≤ n, m ≤ 100;n ≥ m) — the number of candies and the number of Polycarpus's friends.

Print the required sequence a1, a2, ..., am, where ai is the number of candies in the i-th friend's present. All numbers ai must be positive integers, total up to n, the maximum one should differ from the minimum one by the smallest possible value.

NotePrint ai in any order, separate the numbers by spaces.


Victor tries to write his own text editor, with word correction included. However, the rules of word correction are really strange.Victor thinks that if a word contains two consecutive vowels, then it's kinda weird and it needs to be replaced. So the word corrector works in such a way: as long as there are two consecutive vowels in the word, it deletes the first vowel in a word such that there is another vowel right before it. If there are no two consecutive vowels in the word, it is considered to be correct.You are given a word s. Can you predict what will it become after correction?In this problem letters a, e, i, o, u and y are considered to be vowels.

The first line contains one integer n (1 ≤ n ≤ 100) — the number of letters in word s before the correction. The second line contains a string s consisting of exactly n lowercase Latin letters — the word before the correction.

NoteExplanations of the examples:  There is only one replace: weird  werd; No replace needed since there are no two consecutive vowels; aaeaa  aeaa  aaa  aa  a.


Dima and Inna are doing so great! At the moment, Inna is sitting on the magic lawn playing with a pink pony. Dima wanted to play too. He brought an n × m chessboard, a very tasty candy and two numbers a and b.Dima put the chessboard in front of Inna and placed the candy in position (i, j) on the board. The boy said he would give the candy if it reaches one of the corner cells of the board. He's got one more condition. There can only be actions of the following types:  move the candy from position (x, y) on the board to position (x - a, y - b);  move the candy from position (x, y) on the board to position (x + a, y - b);  move the candy from position (x, y) on the board to position (x - a, y + b);  move the candy from position (x, y) on the board to position (x + a, y + b). Naturally, Dima doesn't allow to move the candy beyond the chessboard borders.Inna and the pony started shifting the candy around the board. They wonder what is the minimum number of allowed actions that they need to perform to move the candy from the initial position (i, j) to one of the chessboard corners. Help them cope with the task!

The first line of the input contains six integers n, m, i, j, a, b (1 ≤ n, m ≤ 106; 1 ≤ i ≤ n; 1 ≤ j ≤ m; 1 ≤ a, b ≤ 106). You can assume that the chessboard rows are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. Position (i, j) in the statement is a chessboard cell on the intersection of the i-th row and the j-th column. You can consider that the corners are: (1, m), (n, 1), (n, m), (1, 1).

In a single line print a single integer — the minimum number of moves needed to get the candy. If Inna and the pony cannot get the candy playing by Dima's rules, print on a single line "Poor Inna and pony!" without the quotes.

NoteNote to sample 1:Inna and the pony can move the candy to position (1 + 2, 3 + 2) = (3, 5), from there they can move it to positions (3 - 2, 5 + 2) = (1, 7) and (3 + 2, 5 + 2) = (5, 7). These positions correspond to the corner squares of the chess board. Thus, the answer to the test sample equals two.


Dante is engaged in a fight with "The Savior". Before he can fight it with his sword, he needs to break its shields. He has two guns, Ebony and Ivory, each of them is able to perform any non-negative number of shots.For every bullet that hits the shield, Ebony deals a units of damage while Ivory deals b units of damage. In order to break the shield Dante has to deal exactly c units of damage. Find out if this is possible.

The first line of the input contains three integers a, b, c (1 ≤ a, b ≤ 100, 1 ≤ c ≤ 10 000) — the number of units of damage dealt by Ebony gun and Ivory gun, and the total number of damage required to break the shield, respectively.

Print "Yes" (without quotes) if Dante can deal exactly c damage to the shield and "No" (without quotes) otherwise.

NoteIn the second sample, Dante can fire 1 bullet from Ebony and 2 from Ivory to deal exactly 1·3 + 2·2 = 7 damage. In the third sample, Dante can fire 1 bullet from ebony and no bullets from ivory to do 1·6 + 0·11 = 6 damage.


A long time ago (probably even in the first book), Nicholas Flamel, a great alchemist and the creator of the Philosopher's Stone, taught Harry Potter three useful spells. The first one allows you to convert a grams of sand into b grams of lead, the second one allows you to convert c grams of lead into d grams of gold and third one allows you to convert e grams of gold into f grams of sand. When Harry told his friends about these spells, Ron Weasley was amazed. After all, if they succeed in turning sand into lead, lead into gold, and then turning part of the gold into sand again and so on, then it will be possible to start with a small amount of sand and get huge amounts of gold! Even an infinite amount of gold! Hermione Granger, by contrast, was skeptical about that idea. She argues that according to the law of conservation of matter getting an infinite amount of matter, even using magic, is impossible. On the contrary, the amount of matter may even decrease during transformation, being converted to magical energy. Though Hermione's theory seems convincing, Ron won't believe her. As far as Ron is concerned, Hermione made up her law of conservation of matter to stop Harry and Ron wasting their time with this nonsense, and to make them go and do homework instead. That's why Ron has already collected a certain amount of sand for the experiments. A quarrel between the friends seems unavoidable...Help Harry to determine which one of his friends is right, and avoid the quarrel after all. To do this you have to figure out whether it is possible to get the amount of gold greater than any preassigned number from some finite amount of sand.

The first line contains 6 integers a, b, c, d, e, f (0 ≤ a, b, c, d, e, f ≤ 1000).

Print "Ron", if it is possible to get an infinitely large amount of gold having a certain finite amount of sand (and not having any gold and lead at all), i.e., Ron is right. Otherwise, print "Hermione".

Ron Hermione Hermione Hermione Ron Hermione Ron

NoteConsider the first sample. Let's start with the 500 grams of sand. Apply the first spell 5 times and turn the sand into 1000 grams of lead. Then apply the second spell 4 times to get 600 grams of gold. Let’s take 400 grams from the resulting amount of gold turn them back into sand. We get 500 grams of sand and 200 grams of gold. If we apply the same operations to 500 grams of sand again, we can get extra 200 grams of gold every time. Thus, you can get 200, 400, 600 etc. grams of gold, i.e., starting with a finite amount of sand (500 grams), you can get the amount of gold which is greater than any preassigned number.In the forth sample it is impossible to get sand, or lead, or gold, applying the spells.In the fifth sample an infinitely large amount of gold can be obtained by using only the second spell, which allows you to receive 1 gram of gold out of nothing. Note that if such a second spell is available, then the first and the third one do not affect the answer at all.The seventh sample is more interesting. We can also start with a zero amount of sand there. With the aid of the third spell you can get sand out of nothing. We get 10000 grams of sand in this manner. Let's get 100 grams of lead using the first spell 100 times. Then make 1 gram of gold from them. We managed to receive 1 gram of gold, starting with a zero amount of sand! Clearly, in this manner you can get an infinitely large amount of gold.


Each evening after the dinner the SIS's students gather together to play the game of Sport Mafia. For the tournament, Alya puts candies into the box, which will serve as a prize for a winner. To do that, she performs $$$n$$$ actions. The first action performed is to put a single candy into the box. For each of the remaining moves she can choose from two options:  the first option, in case the box contains at least one candy, is to take exactly one candy out and eat it. This way the number of candies in the box decreased by $$$1$$$;  the second option is to put candies in the box. In this case, Alya will put $$$1$$$ more candy, than she put in the previous time. Thus, if the box is empty, then it can only use the second option.For example, one possible sequence of Alya's actions look as follows:  put one candy into the box;  put two candies into the box;  eat one candy from the box;  eat one candy from the box;  put three candies into the box;  eat one candy from the box;  put four candies into the box;  eat one candy from the box;  put five candies into the box; This way she will perform $$$9$$$ actions, the number of candies at the end will be $$$11$$$, while Alya will eat $$$4$$$ candies in total.You know the total number of actions $$$n$$$ and the number of candies at the end $$$k$$$. You need to find the total number of sweets Alya ate. That is the number of moves of the first option. It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer always exists.Please note, that during an action of the first option, Alya takes out and eats exactly one candy.

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^9$$$; $$$0 \le k \le 10^9$$$) — the total number of moves and the number of candies in the box at the end.  It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer exists.

Print a single integer — the number of candies, which Alya ate. Please note, that in this problem there aren't multiple possible answers — the answer is unique for any input data.

NoteIn the first example, Alya has made one move only. According to the statement, the first move is always putting one candy in the box. Hence Alya ate $$$0$$$ candies.In the second example the possible sequence of Alya's actions looks as follows:   put $$$1$$$ candy,  put $$$2$$$ candies,  eat a candy,  eat a candy,  put $$$3$$$ candies,  eat a candy,  put $$$4$$$ candies,  eat a candy,  put $$$5$$$ candies.  This way, she will make exactly $$$n=9$$$ actions and in the end the box will contain $$$1+2-1-1+3-1+4-1+5=11$$$ candies. The answer is $$$4$$$, since she ate $$$4$$$ candies in total.


Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?

The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.

Print a single integer — the minimum sum in rubles that Ann will need to spend.

NoteIn the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.


Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.

A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.

In a single line print the number of times Manao has to push a button in the worst-case scenario.

NoteConsider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes.


Drazil is playing a math game with Varda.Let's define  for positive integer x as a product of factorials of its digits. For example, .First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:1. x doesn't contain neither digit 0 nor digit 1.2.  = .Help friends find such number.

The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a. The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.

Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.


Greg is a beginner bodybuilder. Today the gym coach gave him the training plan. All it had was n integers a1, a2, ..., an. These numbers mean that Greg needs to do exactly n exercises today. Besides, Greg should repeat the i-th in order exercise ai times.Greg now only does three types of exercises: "chest" exercises, "biceps" exercises and "back" exercises. Besides, his training is cyclic, that is, the first exercise he does is a "chest" one, the second one is "biceps", the third one is "back", the fourth one is "chest", the fifth one is "biceps", and so on to the n-th exercise.Now Greg wonders, which muscle will get the most exercise during his training. We know that the exercise Greg repeats the maximum number of times, trains the corresponding muscle the most. Help Greg, determine which muscle will get the most training.

The first line contains integer n (1 ≤ n ≤ 20). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 25) — the number of times Greg repeats the exercises.

Print word "chest" (without the quotes), if the chest gets the most exercise, "biceps" (without the quotes), if the biceps gets the most exercise and print "back" (without the quotes) if the back gets the most exercise. It is guaranteed that the input is such that the answer to the problem is unambiguous.

NoteIn the first sample Greg does 2 chest, 8 biceps and zero back exercises, so the biceps gets the most exercises.In the second sample Greg does 5 chest, 1 biceps and 10 back exercises, so the back gets the most exercises.In the third sample Greg does 18 chest, 12 biceps and 8 back exercises, so the chest gets the most exercise.


Vus the Cossack holds a programming competition, in which $$$n$$$ people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly $$$m$$$ pens and $$$k$$$ notebooks.Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.

The first line contains three integers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$1 \leq n, m, k \leq 100$$$) — the number of participants, the number of pens, and the number of notebooks respectively.

Print "Yes" if it possible to reward all the participants. Otherwise, print "No". You can print each letter in any case (upper or lower).

NoteIn the first example, there are $$$5$$$ participants. The Cossack has $$$8$$$ pens and $$$6$$$ notebooks. Therefore, he has enough pens and notebooks.In the second example, there are $$$3$$$ participants. The Cossack has $$$9$$$ pens and $$$3$$$ notebooks. He has more than enough pens but only the minimum needed number of notebooks.In the third example, there are $$$8$$$ participants but only $$$5$$$ pens. Since the Cossack does not have enough pens, the answer is "No".


Vector Willman and Array Bolt are the two most famous athletes of Byteforces. They are going to compete in a race with a distance of L meters today.  Willman and Bolt have exactly the same speed, so when they compete the result is always a tie. That is a problem for the organizers because they want a winner. While watching previous races the organizers have noticed that Willman can perform only steps of length equal to w meters, and Bolt can perform only steps of length equal to b meters. Organizers decided to slightly change the rules of the race. Now, at the end of the racetrack there will be an abyss, and the winner will be declared the athlete, who manages to run farther from the starting point of the the racetrack (which is not the subject to change by any of the athletes). Note that none of the athletes can run infinitely far, as they both will at some moment of time face the point, such that only one step further will cause them to fall in the abyss. In other words, the athlete will not fall into the abyss if the total length of all his steps will be less or equal to the chosen distance L.Since the organizers are very fair, the are going to set the length of the racetrack as an integer chosen randomly and uniformly in range from 1 to t (both are included). What is the probability that Willman and Bolt tie again today?

The first line of the input contains three integers t, w and b (1 ≤ t, w, b ≤ 5·1018) — the maximum possible length of the racetrack, the length of Willman's steps and the length of Bolt's steps respectively.

Print the answer to the problem as an irreducible fraction . Follow the format of the samples output. The fraction  (p and q are integers, and both p ≥ 0 and q > 0 holds) is called irreducible, if there is no such integer d > 1, that both p and q are divisible by d.

NoteIn the first sample Willman and Bolt will tie in case 1, 6 or 7 are chosen as the length of the racetrack.


wHAT DO WE NEED cAPS LOCK FOR?Caps lock is a computer keyboard key. Pressing it sets an input mode in which typed letters are capital by default. If it is pressed by accident, it leads to accidents like the one we had in the first passage. Let's consider that a word has been typed with the Caps lock key accidentally switched on, if:   either it only contains uppercase letters;  or all letters except for the first one are uppercase. In this case we should automatically change the case of all letters. For example, the case of the letters that form words "hELLO", "HTTP", "z" should be changed.Write a program that applies the rule mentioned above. If the rule cannot be applied, the program should leave the word unchanged.

The first line of the input data contains a word consisting of uppercase and lowercase Latin letters. The word's length is from 1 to 100 characters, inclusive.

Print the result of the given word's processing.


Misha and Vanya have played several table tennis sets. Each set consists of several serves, each serve is won by one of the players, he receives one point and the loser receives nothing. Once one of the players scores exactly k points, the score is reset and a new set begins.Across all the sets Misha scored a points in total, and Vanya scored b points. Given this information, determine the maximum number of sets they could have played, or that the situation is impossible.Note that the game consisted of several complete sets.

The first line contains three space-separated integers k, a and b (1 ≤ k ≤ 109, 0 ≤ a, b ≤ 109, a + b > 0).

If the situation is impossible, print a single number -1. Otherwise, print the maximum possible number of sets.

NoteNote that the rules of the game in this problem differ from the real table tennis game, for example, the rule of "balance" (the winning player has to be at least two points ahead to win a set) has no power within the present problem.


A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).Consider a permutation $$$p$$$ of length $$$n$$$, we build a graph of size $$$n$$$ using it as follows:   For every $$$1 \leq i \leq n$$$, find the largest $$$j$$$ such that $$$1 \leq j < i$$$ and $$$p_j > p_i$$$, and add an undirected edge between node $$$i$$$ and node $$$j$$$  For every $$$1 \leq i \leq n$$$, find the smallest $$$j$$$ such that $$$i < j \leq n$$$ and $$$p_j > p_i$$$, and add an undirected edge between node $$$i$$$ and node $$$j$$$ In cases where no such $$$j$$$ exists, we make no edges. Also, note that we make edges between the corresponding indices, not the values at those indices.For clarity, consider as an example $$$n = 4$$$, and $$$p = [3,1,4,2]$$$; here, the edges of the graph are $$$(1,3),(2,1),(2,3),(4,3)$$$.A permutation $$$p$$$ is cyclic if the graph built using $$$p$$$ has at least one simple cycle. Given $$$n$$$, find the number of cyclic permutations of length $$$n$$$. Since the number may be very large, output it modulo $$$10^9+7$$$.Please refer to the Notes section for the formal definition of a simple cycle

The first and only line contains a single integer $$$n$$$ ($$$3 \le n \le 10^6$$$).

Output a single integer $$$0 \leq x < 10^9+7$$$, the number of cyclic permutations of length $$$n$$$ modulo $$$10^9+7$$$.

NoteThere are $$$16$$$ cyclic permutations for $$$n = 4$$$. $$$[4,2,1,3]$$$ is one such permutation, having a cycle of length four: $$$4 \rightarrow 3 \rightarrow 2 \rightarrow 1 \rightarrow 4$$$.Nodes $$$v_1$$$, $$$v_2$$$, $$$\ldots$$$, $$$v_k$$$ form a simple cycle if the following conditions hold:   $$$k \geq 3$$$.  $$$v_i \neq v_j$$$ for any pair of indices $$$i$$$ and $$$j$$$. ($$$1 \leq i < j \leq k$$$)  $$$v_i$$$ and $$$v_{i+1}$$$ share an edge for all $$$i$$$ ($$$1 \leq i < k$$$), and $$$v_1$$$ and $$$v_k$$$ share an edge.


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.


Yet another Armageddon is coming! This time the culprit is the Julya tribe calendar. The beavers in this tribe knew math very well. Smart Beaver, an archaeologist, got a sacred plate with a magic integer on it. The translation from Old Beaverish is as follows: "May the Great Beaver bless you! May your chacres open and may your third eye never turn blind from beholding the Truth! Take the magic number, subtract a digit from it (the digit must occur in the number) and get a new magic number. Repeat this operation until a magic number equals zero. The Earth will stand on Three Beavers for the time, equal to the number of subtractions you perform!"Distinct subtraction sequences can obviously get you different number of operations. But the Smart Beaver is ready to face the worst and is asking you to count the minimum number of operations he needs to reduce the magic number to zero.

The single line contains the magic integer n, 0 ≤ n.   to get 20 points, you need to solve the problem with constraints: n ≤ 106 (subproblem C1);  to get 40 points, you need to solve the problem with constraints: n ≤ 1012 (subproblems C1+C2);  to get 100 points, you need to solve the problem with constraints: n ≤ 1018 (subproblems C1+C2+C3).

Print a single integer — the minimum number of subtractions that turns the magic number to a zero.

NoteIn the first test sample the minimum number of operations can be reached by the following sequence of subtractions:  24 → 20 → 18 → 10 → 9 → 0


Kavi has $$$2n$$$ points lying on the $$$OX$$$ axis, $$$i$$$-th of which is located at $$$x = i$$$.Kavi considers all ways to split these $$$2n$$$ points into $$$n$$$ pairs. Among those, he is interested in good pairings, which are defined as follows:Consider $$$n$$$ segments with ends at the points in correspondent pairs. The pairing is called good, if for every $$$2$$$ different segments $$$A$$$ and $$$B$$$ among those, at least one of the following holds:  One of the segments $$$A$$$ and $$$B$$$ lies completely inside the other.  $$$A$$$ and $$$B$$$ have the same length. Consider the following example:  $$$A$$$ is a good pairing since the red segment lies completely inside the blue segment.$$$B$$$ is a good pairing since the red and the blue segment have the same length.$$$C$$$ is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo $$$998244353$$$.Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.

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

Print the number of good pairings modulo $$$998244353$$$.

NoteThe good pairings for the second example are:   In the third example, the good pairings are:


You are given an array a with n distinct integers. Construct an array b by permuting a such that for every non-empty subset of indices S = {x1, x2, ..., xk} (1 ≤ xi ≤ n, 0 < k < n) the sums of elements on that positions in a and b are different, i. e.

The first line contains one integer n (1 ≤ n ≤ 22) — the size of the array. The second line contains n space-separated distinct integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the elements of the array.

If there is no such array b, print -1. Otherwise in the only line print n space-separated integers b1, b2, ..., bn. Note that b must be a permutation of a. If there are multiple answers, print any of them.

NoteAn array x is a permutation of y, if we can shuffle elements of y such that it will coincide with x.Note that the empty subset and the subset containing all indices are not counted.


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".


The tram in Berland goes along a straight line from the point 0 to the point s and back, passing 1 meter per t1 seconds in both directions. It means that the tram is always in the state of uniform rectilinear motion, instantly turning around at points x = 0 and x = s.Igor is at the point x1. He should reach the point x2. Igor passes 1 meter per t2 seconds. Your task is to determine the minimum time Igor needs to get from the point x1 to the point x2, if it is known where the tram is and in what direction it goes at the moment Igor comes to the point x1.Igor can enter the tram unlimited number of times at any moment when his and the tram's positions coincide. It is not obligatory that points in which Igor enter and exit the tram are integers. Assume that any boarding and unboarding happens instantly. Igor can move arbitrary along the line (but not faster than 1 meter per t2 seconds). He can also stand at some point for some time.

The first line contains three integers s, x1 and x2 (2 ≤ s ≤ 1000, 0 ≤ x1, x2 ≤ s, x1 ≠ x2) — the maximum coordinate of the point to which the tram goes, the point Igor is at, and the point he should come to. The second line contains two integers t1 and t2 (1 ≤ t1, t2 ≤ 1000) — the time in seconds in which the tram passes 1 meter and the time in seconds in which Igor passes 1 meter. The third line contains two integers p and d (1 ≤ p ≤ s - 1, d is either 1 or ) — the position of the tram in the moment Igor came to the point x1 and the direction of the tram at this moment. If , the tram goes in the direction from the point s to the point 0. If d = 1, the tram goes in the direction from the point 0 to the point s.

Print the minimum time in seconds which Igor needs to get from the point x1 to the point x2.

NoteIn the first example it is profitable for Igor to go by foot and not to wait the tram. Thus, he has to pass 2 meters and it takes 8 seconds in total, because he passes 1 meter per 4 seconds. In the second example Igor can, for example, go towards the point x2 and get to the point 1 in 6 seconds (because he has to pass 3 meters, but he passes 1 meters per 2 seconds). At that moment the tram will be at the point 1, so Igor can enter the tram and pass 1 meter in 1 second. Thus, Igor will reach the point x2 in 7 seconds in total.


On the way to Rio de Janeiro Ostap kills time playing with a grasshopper he took with him in a special box. Ostap builds a line of length n such that some cells of this line are empty and some contain obstacles. Then, he places his grasshopper to one of the empty cells and a small insect in another empty cell. The grasshopper wants to eat the insect.Ostap knows that grasshopper is able to jump to any empty cell that is exactly k cells away from the current (to the left or to the right). Note that it doesn't matter whether intermediate cells are empty or not as the grasshopper makes a jump over them. For example, if k = 1 the grasshopper can jump to a neighboring cell only, and if k = 2 the grasshopper can jump over a single cell.Your goal is to determine whether there is a sequence of jumps such that grasshopper will get from his initial position to the cell with an insect.

The first line of the input contains two integers n and k (2 ≤ n ≤ 100, 1 ≤ k ≤ n - 1) — the number of cells in the line and the length of one grasshopper's jump. The second line contains a string of length n consisting of characters '.', '#', 'G' and 'T'. Character '.' means that the corresponding cell is empty, character '#' means that the corresponding cell contains an obstacle and grasshopper can't jump there. Character 'G' means that the grasshopper starts at this position and, finally, 'T' means that the target insect is located at this cell. It's guaranteed that characters 'G' and 'T' appear in this line exactly once.

If there exists a sequence of jumps (each jump of length k), such that the grasshopper can get from his initial position to the cell with the insect, print "YES" (without quotes) in the only line of the input. Otherwise, print "NO" (without quotes).

NoteIn the first sample, the grasshopper can make one jump to the right in order to get from cell 2 to cell 4.In the second sample, the grasshopper is only able to jump to neighboring cells but the way to the insect is free — he can get there by jumping left 5 times.In the third sample, the grasshopper can't make a single jump.In the fourth sample, the grasshopper can only jump to the cells with odd indices, thus he won't be able to reach the insect.


When new students come to the Specialized Educational and Scientific Centre (SESC) they need to start many things from the beginning. Sometimes the teachers say (not always unfairly) that we cannot even count. So our teachers decided to teach us arithmetics from the start. And what is the best way to teach students add and subtract? — That's right, using counting sticks! An here's our new task: An expression of counting sticks is an expression of type:[ A sticks][sign +][B sticks][sign =][C sticks] (1 ≤ A, B, C).  Sign + consists of two crossed sticks: one vertical and one horizontal. Sign = consists of two horizontal sticks. The expression is arithmetically correct if A + B = C.We've got an expression that looks like A + B = C given by counting sticks. Our task is to shift at most one stick (or we can shift nothing) so that the expression became arithmetically correct. Note that we cannot remove the sticks from the expression, also we cannot shift the sticks from the signs + and =.We really aren't fabulous at arithmetics. Can you help us?

The single line contains the initial expression. It is guaranteed that the expression looks like A + B = C, where 1 ≤ A, B, C ≤ 100.

If there isn't a way to shift the stick so the expression becomes correct, print on a single line "Impossible" (without the quotes). If there is a way, print the resulting expression. Follow the format of the output from the test samples. Don't print extra space characters. If there are multiple correct answers, print any of them. For clarifications, you are recommended to see the test samples.

NoteIn the first sample we can shift stick from the third group of sticks to the first one.In the second sample we cannot shift vertical stick from + sign to the second group of sticks. So we cannot make a - sign.There is no answer in the third sample because we cannot remove sticks from the expression.In the forth sample the initial expression is already arithmetically correct and that is why we don't have to shift sticks.


Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if  and , where k is some integer number in range [1, a].By  we denote the quotient of integer division of x and y. By  we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?

The single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).

Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).

NoteFor the first sample, there are no nice integers because  is always zero.For the second sample, the set of nice integers is {3, 5}.


Winnie-the-Pooh likes honey very much! That is why he decided to visit his friends. Winnie has got three best friends: Rabbit, Owl and Eeyore, each of them lives in his own house. There are winding paths between each pair of houses. The length of a path between Rabbit's and Owl's houses is a meters, between Rabbit's and Eeyore's house is b meters, between Owl's and Eeyore's house is c meters.For enjoying his life and singing merry songs Winnie-the-Pooh should have a meal n times a day. Now he is in the Rabbit's house and has a meal for the first time. Each time when in the friend's house where Winnie is now the supply of honey is about to end, Winnie leaves that house. If Winnie has not had a meal the required amount of times, he comes out from the house and goes to someone else of his two friends. For this he chooses one of two adjacent paths, arrives to the house on the other end and visits his friend. You may assume that when Winnie is eating in one of his friend's house, the supply of honey in other friend's houses recover (most probably, they go to the supply store).Winnie-the-Pooh does not like physical activity. He wants to have a meal n times, traveling minimum possible distance. Help him to find this distance.

First line contains an integer n (1 ≤ n ≤ 100) — number of visits. Second line contains an integer a (1 ≤ a ≤ 100) — distance between Rabbit's and Owl's houses. Third line contains an integer b (1 ≤ b ≤ 100) — distance between Rabbit's and Eeyore's houses. Fourth line contains an integer c (1 ≤ c ≤ 100) — distance between Owl's and Eeyore's houses.

Output one number — minimum distance in meters Winnie must go through to have a meal n times.

NoteIn the first test case the optimal path for Winnie is the following: first have a meal in Rabbit's house, then in Owl's house, then in Eeyore's house. Thus he will pass the distance 2 + 1 = 3.In the second test case Winnie has a meal in Rabbit's house and that is for him. So he doesn't have to walk anywhere at all.


Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm:  if the last digit of the number is non-zero, she decreases the number by one;  if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit). You are given an integer number $$$n$$$. Tanya will subtract one from it $$$k$$$ times. Your task is to print the result after all $$$k$$$ subtractions.It is guaranteed that the result will be positive integer number.

The first line of the input contains two integer numbers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 10^9$$$, $$$1 \le k \le 50$$$) — the number from which Tanya will subtract and the number of subtractions correspondingly.

Print one integer number — the result of the decreasing $$$n$$$ by one $$$k$$$ times. It is guaranteed that the result will be positive integer number.

NoteThe first example corresponds to the following sequence: $$$512 \rightarrow 511 \rightarrow 510 \rightarrow 51 \rightarrow 50$$$.


Numbers k-bonacci (k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows:  F(k, n) = 0, for integer n, 1 ≤ n < k;  F(k, k) = 1;  F(k, n) = F(k, n - 1) + F(k, n - 2) + ... + F(k, n - k), for integer n, n > k. Note that we determine the k-bonacci numbers, F(k, n), only for integer values of n and k.You've got a number s, represent it as a sum of several (at least two) distinct k-bonacci numbers.

The first line contains two integers s and k (1 ≤ s, k ≤ 109; k > 1).

In the first line print an integer m (m ≥ 2) that shows how many numbers are in the found representation. In the second line print m distinct integers a1, a2, ..., am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s. It is guaranteed that the answer exists. If there are several possible answers, print any of them.


Every summer Vitya comes to visit his grandmother in the countryside. This summer, he got a huge wart. Every grandma knows that one should treat warts when the moon goes down. Thus, Vitya has to catch the moment when the moon is down.Moon cycle lasts 30 days. The size of the visible part of the moon (in Vitya's units) for each day is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and then cycle repeats, thus after the second 1 again goes 0.As there is no internet in the countryside, Vitya has been watching the moon for n consecutive days and for each of these days he wrote down the size of the visible part of the moon. Help him find out whether the moon will be up or down next day, or this cannot be determined by the data he has.

The first line of the input contains a single integer n (1 ≤ n ≤ 92) — the number of consecutive days Vitya was watching the size of the visible part of the moon.  The second line contains n integers ai (0 ≤ ai ≤ 15) — Vitya's records. It's guaranteed that the input data is consistent.

If Vitya can be sure that the size of visible part of the moon on day n + 1 will be less than the size of the visible part on day n, then print "DOWN" at the only line of the output. If he might be sure that the size of the visible part will increase, then print "UP". If it's impossible to determine what exactly will happen with the moon, print -1.

NoteIn the first sample, the size of the moon on the next day will be equal to 8, thus the answer is "UP".In the second sample, the size of the moon on the next day will be 11, thus the answer is "DOWN".In the third sample, there is no way to determine whether the size of the moon on the next day will be 7 or 9, thus the answer is -1.


Mishka started participating in a programming contest. There are $$$n$$$ problems in the contest. Mishka's problem-solving skill is equal to $$$k$$$.Mishka arranges all problems from the contest into a list. Because of his weird principles, Mishka only solves problems from one of the ends of the list. Every time, he chooses which end (left or right) he will solve the next problem from. Thus, each problem Mishka solves is either the leftmost or the rightmost problem in the list.Mishka cannot solve a problem with difficulty greater than $$$k$$$. When Mishka solves the problem, it disappears from the list, so the length of the list decreases by $$$1$$$. Mishka stops when he is unable to solve any problem from any end of the list.How many problems can Mishka solve?

The first line of input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 100$$$) — the number of problems in the contest and Mishka's problem-solving skill. The second line of input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 100$$$), where $$$a_i$$$ is the difficulty of the $$$i$$$-th problem. The problems are given in order from the leftmost to the rightmost in the list.

Print one integer — the maximum number of problems Mishka can solve.

NoteIn the first example, Mishka can solve problems in the following order: $$$[4, 2, 3, 1, 5, 1, 6, 4] \rightarrow [2, 3, 1, 5, 1, 6, 4] \rightarrow [2, 3, 1, 5, 1, 6] \rightarrow [3, 1, 5, 1, 6] \rightarrow [1, 5, 1, 6] \rightarrow [5, 1, 6]$$$, so the number of solved problems will be equal to $$$5$$$.In the second example, Mishka can't solve any problem because the difficulties of problems from both ends are greater than $$$k$$$.In the third example, Mishka's solving skill is so amazing that he can solve all the problems.


Being a nonconformist, Volodya is displeased with the current state of things, particularly with the order of natural numbers (natural number is positive integer number). He is determined to rearrange them. But there are too many natural numbers, so Volodya decided to start with the first n. He writes down the following sequence of numbers: firstly all odd integers from 1 to n (in ascending order), then all even integers from 1 to n (also in ascending order). Help our hero to find out which number will stand at the position number k.

The only line of input contains integers n and k (1 ≤ k ≤ n ≤ 1012). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Print the number that will stand at the position number k after Volodya's manipulations.

NoteIn the first sample Volodya's sequence will look like this: {1, 3, 5, 7, 9, 2, 4, 6, 8, 10}. The third place in the sequence is therefore occupied by the number 5.


Sereja showed an interesting game to his friends. The game goes like that. Initially, there is a table with an empty cup and n water mugs on it. Then all players take turns to move. During a move, a player takes a non-empty mug of water and pours all water from it into the cup. If the cup overfills, then we assume that this player lost.As soon as Sereja's friends heard of the game, they wanted to play it. Sereja, on the other hand, wanted to find out whether his friends can play the game in such a way that there are no losers. You are given the volumes of all mugs and the cup. Also, you know that Sereja has (n - 1) friends. Determine if Sereja's friends can play the game so that nobody loses.

The first line contains integers n and s (2 ≤ n ≤ 100; 1 ≤ s ≤ 1000) — the number of mugs and the volume of the cup. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 10). Number ai means the volume of the i-th mug.

In a single line, print "YES" (without the quotes) if his friends can play in the described manner, and "NO" (without the quotes) otherwise.


You have a fraction . You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.

The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).

Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.

NoteThe fraction in the first example has the following decimal notation: . The first zero stands on second position.The fraction in the second example has the following decimal notation: . There is no digit 7 in decimal notation of the fraction.


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 apply to the given integer $$$n$$$ to make from it the square of some positive integer or report that it is impossible.An integer $$$x$$$ is the square of some positive integer if and only if $$$x=y^2$$$ for some positive integer $$$y$$$.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^{9}$$$). The number is given without leading zeroes.

If it is impossible to make the square of some positive integer from $$$n$$$, print -1. In the other case, print the minimal number of operations required to do it.

NoteIn the first example we should delete from $$$8314$$$ the digits $$$3$$$ and $$$4$$$. After that $$$8314$$$ become equals to $$$81$$$, which is the square of the integer $$$9$$$.In the second example the given $$$625$$$ is the square of the integer $$$25$$$, so you should not delete anything. In the third example it is impossible to make the square from $$$333$$$, so the answer is -1.


Malek lives in an apartment block with 100 floors numbered from 0 to 99. The apartment has an elevator with a digital counter showing the floor that the elevator is currently on. The elevator shows each digit of a number with 7 light sticks by turning them on or off. The picture below shows how the elevator shows each digit.One day when Malek wanted to go from floor 88 to floor 0 using the elevator he noticed that the counter shows number 89 instead of 88. Then when the elevator started moving the number on the counter changed to 87. After a little thinking Malek came to the conclusion that there is only one explanation for this: One of the sticks of the counter was broken. Later that day Malek was thinking about the broken stick and suddenly he came up with the following problem.Suppose the digital counter is showing number n. Malek calls an integer x (0 ≤ x ≤ 99) good if it's possible that the digital counter was supposed to show x but because of some(possibly none) broken sticks it's showing n instead. Malek wants to know number of good integers for a specific n. So you must write a program that calculates this number. Please note that the counter always shows two digits.

The only line of input contains exactly two digits representing number n (0 ≤ n ≤ 99). Note that n may have a leading zero.

In the only line of the output print the number of good integers.

NoteIn the first sample the counter may be supposed to show 88 or 89.In the second sample the good integers are 00, 08, 80 and 88.In the third sample the good integers are 03, 08, 09, 33, 38, 39, 73, 78, 79, 83, 88, 89, 93, 98, 99.


Certainly, everyone is familiar with tic-tac-toe game. The rules are very simple indeed. Two players take turns marking the cells in a 3 × 3 grid (one player always draws crosses, the other — noughts). The player who succeeds first in placing three of his marks in a horizontal, vertical or diagonal line wins, and the game is finished. The player who draws crosses goes first. If the grid is filled, but neither Xs, nor 0s form the required line, a draw is announced.You are given a 3 × 3 grid, each grid cell is empty, or occupied by a cross or a nought. You have to find the player (first or second), whose turn is next, or print one of the verdicts below:   illegal — if the given board layout can't appear during a valid game;  the first player won — if in the given board layout the first player has just won;  the second player won — if in the given board layout the second player has just won;  draw — if the given board layout has just let to a draw.

The input consists of three lines, each of the lines contains characters ".", "X" or "0" (a period, a capital letter X, or a digit zero).

Print one of the six verdicts: first, second, illegal, the first player won, the second player won or draw.


Mislove had an array $$$a_1$$$, $$$a_2$$$, $$$\cdots$$$, $$$a_n$$$ of $$$n$$$ positive integers, but he has lost it. He only remembers the following facts about it: The number of different numbers in the array is not less than $$$l$$$ and is not greater than $$$r$$$; For each array's element $$$a_i$$$ either $$$a_i = 1$$$ or $$$a_i$$$ is even and there is a number $$$\dfrac{a_i}{2}$$$ in the array.For example, if $$$n=5$$$, $$$l=2$$$, $$$r=3$$$ then an array could be $$$[1,2,2,4,4]$$$ or $$$[1,1,1,1,2]$$$; but it couldn't be $$$[1,2,2,4,8]$$$ because this array contains $$$4$$$ different numbers; it couldn't be $$$[1,2,2,3,3]$$$ because $$$3$$$ is odd and isn't equal to $$$1$$$; and it couldn't be $$$[1,1,2,2,16]$$$ because there is a number $$$16$$$ in the array but there isn't a number $$$\frac{16}{2} = 8$$$.According to these facts, he is asking you to count the minimal and the maximal possible sums of all elements in an array.

The only input line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$1 \leq n \leq 1\,000$$$, $$$1 \leq l \leq r \leq \min(n, 20)$$$) — an array's size, the minimal number and the maximal number of distinct elements in an array.

Output two numbers — the minimal and the maximal possible sums of all elements in an array.

NoteIn the first example, an array could be the one of the following: $$$[1,1,1,2]$$$, $$$[1,1,2,2]$$$ or $$$[1,2,2,2]$$$. In the first case the minimal sum is reached and in the last case the maximal sum is reached.In the second example, the minimal sum is reached at the array $$$[1,1,1,1,1]$$$, and the maximal one is reached at the array $$$[1,2,4,8,16]$$$.


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.


You have a plate and you want to add some gilding to it. The plate is a rectangle that we split into $$$w\times h$$$ cells. There should be $$$k$$$ gilded rings, the first one should go along the edge of the plate, the second one — $$$2$$$ cells away from the edge and so on. Each ring has a width of $$$1$$$ cell. Formally, the $$$i$$$-th of these rings should consist of all bordering cells on the inner rectangle of size $$$(w - 4(i - 1))\times(h - 4(i - 1))$$$.  The picture corresponds to the third example. Your task is to compute the number of cells to be gilded.

The only line contains three integers $$$w$$$, $$$h$$$ and $$$k$$$ ($$$3 \le w, h \le 100$$$, $$$1 \le k \le \left\lfloor \frac{min(n, m) + 1}{4}\right\rfloor$$$, where $$$\lfloor x \rfloor$$$ denotes the number $$$x$$$ rounded down) — the number of rows, columns and the number of rings, respectively.

Print a single positive integer — the number of cells to be gilded.

NoteThe first example is shown on the picture below.  The second example is shown on the picture below.  The third example is shown in the problem description.


Consider the infinite sequence of integers: 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5.... The sequence is built in the following way: at first the number 1 is written out, then the numbers from 1 to 2, then the numbers from 1 to 3, then the numbers from 1 to 4 and so on. Note that the sequence contains numbers, not digits. For example number 10 first appears in the sequence in position 55 (the elements are numerated from one).Find the number on the n-th position of the sequence.

The only line contains integer n (1 ≤ n ≤ 1014) — the position of the number to find. Note that the given number is too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Print the element in the n-th position of the sequence (the elements are numerated from one).


Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints. A color hint goes like that: a player names some color and points at all the cards of this color. Similarly goes the value hint. A player names some value and points at all the cards that contain the value.Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.

The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.

Print a single integer — the minimum number of hints that the other players should make.

NoteIn the first sample Borya already knows for each card that it is a green three.In the second sample we can show all fours and all red cards.In the third sample you need to make hints about any four colors.


Bizon the Champion isn't just charming, he also is very smart.While some of us were learning the multiplication table, Bizon the Champion had fun in his own manner. Bizon the Champion painted an n × m multiplication table, where the element on the intersection of the i-th row and j-th column equals i·j (the rows and columns of the table are numbered starting from 1). Then he was asked: what number in the table is the k-th largest number? Bizon the Champion always answered correctly and immediately. Can you repeat his success?Consider the given multiplication table. If you write out all n·m numbers from the table in the non-decreasing order, then the k-th number you write out is called the k-th largest number.

The single line contains integers n, m and k (1 ≤ n, m ≤ 5·105; 1 ≤ k ≤ n·m).

Print the k-th largest number in a n × m multiplication table.

NoteA 2 × 3 multiplication table looks like this:1 2 32 4 6


Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly one lowercase English letter into s to make it a palindrome. A palindrome is a string that reads the same forward and backward. For example, "noon", "testset" and "a" are all palindromes, while "test" and "kitayuta" are not.You can choose any lowercase English letter, and insert it to any position of s, possibly to the beginning or the end of s. You have to insert a letter even if the given string is already a palindrome.If it is possible to insert one lowercase English letter into s so that the resulting string will be a palindrome, print the string after the insertion. Otherwise, print "NA" (without quotes, case-sensitive). In case there is more than one palindrome that can be obtained, you are allowed to print any of them.

The only line of the input contains a string s (1 ≤ |s| ≤ 10). Each character in s is a lowercase English letter.

If it is possible to turn s into a palindrome by inserting one lowercase English letter, print the resulting string in a single line. Otherwise, print "NA" (without quotes, case-sensitive). In case there is more than one solution, any of them will be accepted.

NoteFor the first sample, insert 'r' to the end of "revive" to obtain a palindrome "reviver".For the second sample, there is more than one solution. For example, "eve" will also be accepted.For the third sample, it is not possible to turn "kitayuta" into a palindrome by just inserting one letter.