You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.

The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.  The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.

If such sequence doesn't exist, then print in a single line "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk. If there are multiple possible answers, print any of them.

NoteIn the second sample there are two possible answers: {"aaaca", "s"} and {"aaa", "cas"}.


Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks.What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase.

The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109).

Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4.

NoteIn the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total.In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything.In the fourth example Alyona should buy one pack of one copybook.


A year ago on the bench in public park Leha found an array of n numbers. Leha believes that permutation p is right if for all 1 ≤ i < n condition, that api·api + 1 is not perfect square, holds. Leha wants to find number of right permutations modulo 109 + 7.

First line of input data contains single integer n (1 ≤ n ≤ 300) — length of the array. Next line contains n integers a1, a2, ... , an (1 ≤ ai ≤ 109) — found array.

Output single integer — number of right permutations modulo 109 + 7.

NoteFor first example:[1, 2, 4] — right permutation, because 2 and 8 are not perfect squares.[1, 4, 2] — wrong permutation, because 4 is square of 2.[2, 1, 4] — wrong permutation, because 4 is square of 2.[2, 4, 1] — wrong permutation, because 4 is square of 2.[4, 1, 2] — wrong permutation, because 4 is square of 2.[4, 2, 1] — right permutation, because 8 and 2 are not perfect squares.


You're trying to set the record on your favorite video game. The game consists of N levels, which must be completed sequentially in order to beat the game. You usually complete each level as fast as possible, but sometimes finish a level slower. Specifically, you will complete the i-th level in either Fi seconds or Si seconds, where Fi < Si, and there's a Pi percent chance of completing it in Fi seconds. After completing a level, you may decide to either continue the game and play the next level, or reset the game and start again from the first level. Both the decision and the action are instant.Your goal is to complete all the levels sequentially in at most R total seconds. You want to minimize the expected amount of time playing before achieving that goal. If you continue and reset optimally, how much total time can you expect to spend playing?

The first line of input contains integers N and R , the number of levels and number of seconds you want to complete the game in, respectively. N lines follow. The ith such line contains integers Fi, Si, Pi (1 ≤ Fi < Si ≤ 100, 80 ≤ Pi ≤ 99), the fast time for level i, the slow time for level i, and the probability (as a percentage) of completing level i with the fast time.

Print the total expected time. Your answer must be correct within an absolute or relative error of 10 - 9. Formally, let your answer be a, and the jury's answer be b. Your answer will be considered correct, if .

NoteIn the first example, you never need to reset. There's an 81% chance of completing the level in 2 seconds and a 19% chance of needing 8 seconds, both of which are within the goal time. The expected time is 0.81·2 + 0.19·8 = 3.14.In the second example, you should reset after the first level if you complete it slowly. On average it will take 0.25 slow attempts before your first fast attempt. Then it doesn't matter whether you complete the second level fast or slow. The expected time is 0.25·30 + 20 + 0.85·3 + 0.15·9 = 31.4.


It can be shown that any positive integer x can be uniquely represented as x = 1 + 2 + 4 + ... + 2k - 1 + r, where k and r are integers, k ≥ 0, 0 < r ≤ 2k. Let's call that representation prairie partition of x.For example, the prairie partitions of 12, 17, 7 and 1 are:  12 = 1 + 2 + 4 + 5,17 = 1 + 2 + 4 + 8 + 2,7 = 1 + 2 + 4,1 = 1. Alice took a sequence of positive integers (possibly with repeating elements), replaced every element with the sequence of summands in its prairie partition, arranged the resulting numbers in non-decreasing order and gave them to Borys. Now Borys wonders how many elements Alice's original sequence could contain. Find all possible options!

The first line contains a single integer n (1 ≤ n ≤ 105) — the number of numbers given from Alice to Borys. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1012; a1 ≤ a2 ≤ ... ≤ an) — the numbers given from Alice to Borys.

Output, in increasing order, all possible values of m such that there exists a sequence of positive integers of length m such that if you replace every element with the summands in its prairie partition and arrange the resulting numbers in non-decreasing order, you will get the sequence given in the input. If there are no such values of m, output a single integer -1.

NoteIn the first example, Alice could get the input sequence from [6, 20] as the original sequence.In the second example, Alice's original sequence could be either [4, 5] or [3, 3, 3].


Each of you probably has your personal experience of riding public transportation and buying tickets. After a person buys a ticket (which traditionally has an even number of digits), he usually checks whether the ticket is lucky. Let us remind you that a ticket is lucky if the sum of digits in its first half matches the sum of digits in its second half.But of course, not every ticket can be lucky. Far from it! Moreover, sometimes one look at a ticket can be enough to say right away that the ticket is not lucky. So, let's consider the following unluckiness criterion that can definitely determine an unlucky ticket. We'll say that a ticket is definitely unlucky if each digit from the first half corresponds to some digit from the second half so that each digit from the first half is strictly less than the corresponding digit from the second one or each digit from the first half is strictly more than the corresponding digit from the second one. Each digit should be used exactly once in the comparisons. In other words, there is such bijective correspondence between the digits of the first and the second half of the ticket, that either each digit of the first half turns out strictly less than the corresponding digit of the second half or each digit of the first half turns out strictly more than the corresponding digit from the second half.For example, ticket 2421 meets the following unluckiness criterion and will not be considered lucky (the sought correspondence is 2 > 1 and 4 > 2), ticket 0135 also meets the criterion (the sought correspondence is 0 < 3 and 1 < 5), and ticket 3754 does not meet the criterion. You have a ticket in your hands, it contains 2n digits. Your task is to check whether it meets the unluckiness criterion.

The first line contains an integer n (1 ≤ n ≤ 100). The second line contains a string that consists of 2n digits and defines your ticket.

In the first line print "YES" if the ticket meets the unluckiness criterion. Otherwise, print "NO" (without the quotes).


На координатной прямой сидит n собачек, i-я собачка находится в точке xi. Кроме того, на прямой есть m мисок с едой, для каждой известна её координата на прямой uj и время tj, через которое еда в миске остынет и станет невкусной. Это значит, что если собачка прибежит к миске в момент времени, строго больший tj, то еда уже остынет, и собачка кушать её не станет.Считая, что каждая собачка бежит со скоростью 1, найдите максимальное количество собачек, которые смогут покушать. Считайте, что собачки побегут к тем мискам, на которые вы им укажете. Из одной миски не могут кушать две или более собачки.Собачки могут обгонять друг друга, то есть, если одна из них остановится покушать, другая может пройти мимо неё, чтобы попасть к другой миске.

В первой строке находится пара целых чисел n и m (1 ≤ n, m ≤ 200 000) — количество собачек и мисок соответственно. Во второй строке находятся n целых чисел xi ( - 109 ≤ xi ≤ 109) — координата i-й собачки. В следующих m строках находятся пары целых чисел uj и tj ( - 109 ≤ uj ≤ 109, 1 ≤ tj ≤ 109) — координата j-й миски и время, когда остынет еда в ней, соответственно. Гарантируется, что никакие две собачки не находятся в одной точке. Никакие две миски также не могут находиться в одной точке.

Выведите одно целое число a — максимальное количество собачек, которые смогут покушать.

ПримечаниеВ первом примере первая собачка побежит направо к первой миске, третья собачка сразу начнёт есть из второй миски, четвёртая собачка побежит влево к третьей миске, а пятая собачка побежит влево к четвёртой миске.


Bearland has n cities, numbered 1 through n. There are m bidirectional roads. The i-th road connects two distinct cities ai and bi. No two roads connect the same pair of cities. It's possible to get from any city to any other city (using one or more roads).The distance between cities a and b is defined as the minimum number of roads used to travel between a and b.Limak is a grizzly bear. He is a criminal and your task is to catch him, or at least to try to catch him. You have only two days (today and tomorrow) and after that Limak is going to hide forever.Your main weapon is BCD (Bear Criminal Detector). Where you are in some city, you can use BCD and it tells you the distance between you and a city where Limak currently is. Unfortunately, BCD can be used only once a day.You don't know much about Limak's current location. You assume that he is in one of n cities, chosen uniformly at random (each city with probability ). You decided for the following plan:  Choose one city and use BCD there.   After using BCD you can try to catch Limak (but maybe it isn't a good idea). In this case you choose one city and check it. You win if Limak is there. Otherwise, Limak becomes more careful and you will never catch him (you loose).   Wait 24 hours to use BCD again. You know that Limak will change his location during that time. In detail, he will choose uniformly at random one of roads from his initial city, and he will use the chosen road, going to some other city.  Tomorrow, you will again choose one city and use BCD there.  Finally, you will try to catch Limak. You will choose one city and check it. You will win if Limak is there, and loose otherwise. Each time when you choose one of cities, you can choose any of n cities. Let's say it isn't a problem for you to quickly get somewhere.What is the probability of finding Limak, if you behave optimally?

The first line of the input contains two integers n and m (2 ≤ n ≤ 400, ) — the number of cities and the number of roads, respectively. Then, m lines follow. The i-th of them contains two integers ai and bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — cities connected by the i-th road. No two roads connect the same pair of cities. It's possible to get from any city to any other city.

Print one real number — the probability of finding Limak, if you behave optimally. Your answer will be considered correct if its absolute error does not exceed 10 - 6. Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct if |a - b| ≤ 10 - 6.

NoteIn the first sample test, there are three cities and there is a road between every pair of cities. Let's analyze one of optimal scenarios.  Use BCD in city 1.   With probability  Limak is in this city and BCD tells you that the distance is 0. You should try to catch him now and you win for sure.  With probability  the distance is 1 because Limak is in city 2 or city 3. In this case you should wait for the second day.   You wait and Limak moves to some other city.   There is probability  that Limak was in city 2 and then went to city 3.   that he went from 2 to 1.   that he went from 3 to 2.   that he went from 3 to 1.   Use BCD again in city 1 (though it's allowed to use it in some other city).   If the distance is 0 then you're sure Limak is in this city (you win).  If the distance is 1 then Limak is in city 2 or city 3. Then you should guess that he is in city 2 (guessing city 3 would be fine too).  You loose only if Limak was in city 2 first and then he moved to city 3. The probability of loosing is . The answer is .


Polycarp is going to participate in the contest. It starts at $$$h_1:m_1$$$ and ends at $$$h_2:m_2$$$. It is guaranteed that the contest lasts an even number of minutes (i.e. $$$m_1 \% 2 = m_2 \% 2$$$, where $$$x \% y$$$ is $$$x$$$ modulo $$$y$$$). It is also guaranteed that the entire contest is held during a single day. And finally it is guaranteed that the contest lasts at least two minutes.Polycarp wants to know the time of the midpoint of the contest. For example, if the contest lasts from $$$10:00$$$ to $$$11:00$$$ then the answer is $$$10:30$$$, if the contest lasts from $$$11:10$$$ to $$$11:12$$$ then the answer is $$$11:11$$$.

The first line of the input contains two integers $$$h_1$$$ and $$$m_1$$$ in the format hh:mm. The second line of the input contains two integers $$$h_2$$$ and $$$m_2$$$ in the same format (hh:mm). It is guaranteed that $$$0 \le h_1, h_2 \le 23$$$ and $$$0 \le m_1, m_2 \le 59$$$. It is guaranteed that the contest lasts an even number of minutes (i.e. $$$m_1 \% 2 = m_2 \% 2$$$, where $$$x \% y$$$ is $$$x$$$ modulo $$$y$$$). It is also guaranteed that the entire contest is held during a single day. And finally it is guaranteed that the contest lasts at least two minutes.

Print two integers $$$h_3$$$ and $$$m_3$$$ ($$$0 \le h_3 \le 23, 0 \le m_3 \le 59$$$) corresponding to the midpoint of the contest in the format hh:mm. Print each number as exactly two digits (prepend a number with leading zero if needed), separate them with ':'.


Moamen and Ezzat are playing a game. They create an array $$$a$$$ of $$$n$$$ non-negative integers where every element is less than $$$2^k$$$.Moamen wins if $$$a_1 \,\&\, a_2 \,\&\, a_3 \,\&\, \ldots \,\&\, a_n \ge a_1 \oplus a_2 \oplus a_3 \oplus \ldots \oplus a_n$$$.Here $$$\&$$$ denotes the bitwise AND operation, and $$$\oplus$$$ denotes the bitwise XOR operation.Please calculate the number of winning for Moamen arrays $$$a$$$.As the result may be very large, print the value modulo $$$1\,000\,000\,007$$$ ($$$10^9 + 7$$$).

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 5$$$)— the number of test cases.  Each test case consists of one line containing two integers $$$n$$$ and $$$k$$$ ($$$1 \le n\le 2\cdot 10^5$$$, $$$0 \le k \le 2\cdot 10^5$$$).

For each test case, print a single value — the number of different arrays that Moamen wins with. Print the result modulo $$$1\,000\,000\,007$$$ ($$$10^9 + 7$$$).


Ralph has a magic field which is divided into n × m blocks. That is to say, there are n rows and m columns on the field. Ralph can put an integer in each block. However, the magic field doesn't always work properly. It works only if the product of integers in each row and each column equals to k, where k is either 1 or -1.Now Ralph wants you to figure out the number of ways to put numbers in each block in such a way that the magic field works properly. Two ways are considered different if and only if there exists at least one block where the numbers in the first way and in the second way are different. You are asked to output the answer modulo 1000000007 = 109 + 7.Note that there is no range of the numbers to put in the blocks, but we can prove that the answer is not infinity.

The only line contains three integers n, m and k (1 ≤ n, m ≤ 1018, k is either 1 or -1).

Print a single number denoting the answer modulo 1000000007.

NoteIn the first example the only way is to put -1 into the only block.In the second example the only way is to put 1 into every block.


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 $$$s$$$.


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

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

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


You are given a set of n points on the plane. A line containing the origin is called good, if projection of the given set to this line forms a symmetric multiset of points. Find the total number of good lines.Multiset is a set where equal elements are allowed.Multiset is called symmetric, if there is a point P on the plane such that the multiset is centrally symmetric in respect of point P.

The first line contains a single integer n (1 ≤ n ≤ 2000) — the number of points in the set. Each of the next n lines contains two integers xi and yi ( - 106  ≤  xi,  yi  ≤  106) — the coordinates of the points. It is guaranteed that no two points coincide.

If there are infinitely many good lines, print -1. Otherwise, print single integer — the number of good lines.

NotePicture to the first sample test: In the second sample, any line containing the origin is good.


Polycarp has interviewed Oleg and has written the interview down without punctuation marks and spaces to save time. Thus, the interview is now a string s consisting of n lowercase English letters.There is a filler word ogo in Oleg's speech. All words that can be obtained from ogo by adding go several times to the end of it are also considered to be fillers. For example, the words ogo, ogogo, ogogogo are fillers, but the words go, og, ogog, ogogog and oggo are not fillers.The fillers have maximal size, for example, for ogogoo speech we can't consider ogo a filler and goo as a normal phrase. We should consider ogogo as a filler here.To print the interview, Polycarp has to replace each of the fillers with three asterisks. Note that a filler word is replaced with exactly three asterisks regardless of its length.Polycarp has dealt with this problem in no time. Can you do the same? The clock is ticking!

The first line contains a positive integer n (1 ≤ n ≤ 100) — the length of the interview. The second line contains the string s of length n, consisting of lowercase English letters.

Print the interview text after the replacement of each of the fillers with "***". It is allowed for the substring "***" to have several consecutive occurences.

NoteThe first sample contains one filler word ogogo, so the interview for printing is "a***b".The second sample contains two fillers ogo and ogogogo. Thus, the interview is transformed to "***gmg***".


Kitahara Haruki has bought n apples for Touma Kazusa and Ogiso Setsuna. Now he wants to divide all the apples between the friends.Each apple weights 100 grams or 200 grams. Of course Kitahara Haruki doesn't want to offend any of his friend. Therefore the total weight of the apples given to Touma Kazusa must be equal to the total weight of the apples given to Ogiso Setsuna.But unfortunately Kitahara Haruki doesn't have a knife right now, so he cannot split any apple into some parts. Please, tell him: is it possible to divide all the apples in a fair way between his friends?

The first line contains an integer n (1 ≤ n ≤ 100) — the number of apples. The second line contains n integers w1, w2, ..., wn (wi = 100 or wi = 200), where wi is the weight of the i-th apple.

In a single line print "YES" (without the quotes) if it is possible to divide all the apples between his friends. Otherwise print "NO" (without the quotes).

NoteIn the first test sample Kitahara Haruki can give the first and the last apple to Ogiso Setsuna and the middle apple to Touma Kazusa.


Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:  a1 = xyz;  a2 = xzy;  a3 = (xy)z;  a4 = (xz)y;  a5 = yxz;  a6 = yzx;  a7 = (yx)z;  a8 = (yz)x;  a9 = zxy;  a10 = zyx;  a11 = (zx)y;  a12 = (zy)x. Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac.

The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.

Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.  xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity).


After a probationary period in the game development company of IT City Petya was included in a group of the programmers that develops a new turn-based strategy game resembling the well known "Heroes of Might & Magic". A part of the game is turn-based fights of big squadrons of enemies on infinite fields where every cell is in form of a hexagon.Some of magic effects are able to affect several field cells at once, cells that are situated not farther than n cells away from the cell in which the effect was applied. The distance between cells is the minimum number of cell border crosses on a path from one cell to another.It is easy to see that the number of cells affected by a magic effect grows rapidly when n increases, so it can adversely affect the game performance. That's why Petya decided to write a program that can, given n, determine the number of cells that should be repainted after effect application, so that game designers can balance scale of the effects and the game performance. Help him to do it. Find the number of hexagons situated not farther than n cells away from a given cell.

The only line of the input contains one integer n (0 ≤ n ≤ 109).

Output one integer — the number of hexagons situated not farther than n cells away from a given cell.


Barney is standing in a bar and starring at a pretty girl. He wants to shoot her with his heart arrow but he needs to know the distance between him and the girl to make his shot accurate.  Barney asked the bar tender Carl about this distance value, but Carl was so busy talking to the customers so he wrote the distance value (it's a real number) on a napkin. The problem is that he wrote it in scientific notation. The scientific notation of some real number x is the notation of form AeB, where A is a real number and B is an integer and x = A × 10B is true. In our case A is between 0 and 9 and B is non-negative.Barney doesn't know anything about scientific notation (as well as anything scientific at all). So he asked you to tell him the distance value in usual decimal representation with minimal number of digits after the decimal point (and no decimal point if it is an integer). See the output format for better understanding.

The first and only line of input contains a single string of form a.deb where a, d and b are integers and e is usual character 'e' (0 ≤ a ≤ 9, 0 ≤ d < 10100, 0 ≤ b ≤ 100) — the scientific notation of the desired distance value. a and b contain no leading zeros and d contains no trailing zeros (but may be equal to 0). Also, b can not be non-zero if a is zero.

Print the only real number x (the desired distance value) in the only line in its decimal notation.  Thus if x is an integer, print it's integer value without decimal part and decimal point and without leading zeroes.  Otherwise print x in a form of p.q such that p is an integer that have no leading zeroes (but may be equal to zero), and q is an integer that have no trailing zeroes (and may not be equal to zero).


You are given a string s consisting of n lowercase Latin letters. You have to type this string using your keyboard.Initially, you have an empty string. Until you type the whole string, you may perform the following operation:  add a character to the end of the string. Besides, at most once you may perform one additional operation: copy the string and append it to itself.For example, if you have to type string abcabca, you can type it in 7 operations if you type all the characters one by one. However, you can type it in 5 operations if you type the string abc first and then copy it and type the last character.If you have to type string aaaaaaaaa, the best option is to type 4 characters one by one, then copy the string, and then type the remaining character.Print the minimum number of operations you need to type the given string.

The first line of the input containing only one integer number n (1 ≤ n ≤ 100) — the length of the string you have to type. The second line containing the string s consisting of n lowercase Latin letters.

Print one integer number — the minimum number of operations you need to type the given string.

NoteThe first test described in the problem statement.In the second test you can only type all the characters one by one.


Good job! Now that Heidi is able to distinguish between Poisson and uniform distributions, she is in a good position to actually estimate the populations.Can you help Heidi estimate each village's population?

Output one line per village, in the same order as provided in the input, containing your (integer) population estimate. Your answer is considered correct if it is an integer that falls into the interval , where P is the real population of the village, used to create the distribution (either Poisson or uniform) from which the marmots drew their answers.


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.


Valera the horse lives on a plane. The Cartesian coordinate system is defined on this plane. Also an infinite spiral is painted on the plane. The spiral consists of segments: [(0, 0), (1, 0)], [(1, 0), (1, 1)], [(1, 1), ( - 1, 1)], [( - 1, 1), ( - 1,  - 1)], [( - 1,  - 1), (2,  - 1)], [(2,  - 1), (2, 2)] and so on. Thus, this infinite spiral passes through each integer point of the plane.Valera the horse lives on the plane at coordinates (0, 0). He wants to walk along the spiral to point (x, y). Valera the horse has four legs, so he finds turning very difficult. Count how many times he will have to turn if he goes along a spiral from point (0, 0) to point (x, y).

The first line contains two space-separated integers x and y (|x|, |y| ≤ 100).

Print a single integer, showing how many times Valera has to turn.


Fedya loves problems involving data structures. Especially ones about different queries on subsegments. Fedya had a nice array $$$a_1, a_2, \ldots a_n$$$ and a beautiful data structure. This data structure, given $$$l$$$ and $$$r$$$, $$$1 \le l \le r \le n$$$, could find the greatest integer $$$d$$$, such that $$$d$$$ divides each of $$$a_l$$$, $$$a_{l+1}$$$, ..., $$$a_{r}$$$. Fedya really likes this data structure, so he applied it to every non-empty contiguous subarray of array $$$a$$$, put all answers into the array and sorted it. He called this array $$$b$$$. It's easy to see that array $$$b$$$ contains $$$n(n+1)/2$$$ elements.After that, Fedya implemented another cool data structure, that allowed him to find sum $$$b_l + b_{l+1} + \ldots + b_r$$$ for given $$$l$$$ and $$$r$$$, $$$1 \le l \le r \le n(n+1)/2$$$. Surely, Fedya applied this data structure to every contiguous subarray of array $$$b$$$, called the result $$$c$$$ and sorted it. Help Fedya find the lower median of array $$$c$$$.Recall that for a sorted array of length $$$k$$$ the lower median is an element at position $$$\lfloor \frac{k + 1}{2} \rfloor$$$, if elements of the array are enumerated starting from $$$1$$$. For example, the lower median of array $$$(1, 1, 2, 3, 6)$$$ is $$$2$$$, and the lower median of $$$(0, 17, 23, 96)$$$ is $$$17$$$.

First line contains a single integer $$$n$$$ — number of elements in array $$$a$$$ ($$$1 \le n \le 50\,000$$$).  Second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ — elements of the array ($$$1 \le a_i \le 100\,000$$$).

Print a single integer — the lower median of array $$$c$$$.

NoteIn the first sample array $$$b$$$ is equal to $$${3, 3, 6}$$$, then array $$$c$$$ is equal to $$${3, 3, 6, 6, 9, 12}$$$, so the lower median is $$$6$$$.In the second sample $$$b$$$ is $$${8, 8, 8}$$$, $$$c$$$ is $$${8, 8, 8, 16, 16, 24}$$$, so the lower median is $$$8$$$.


You might have heard about the next game in Lara Croft series coming out this year. You also might have watched its trailer. Though you definitely missed the main idea about its plot, so let me lift the veil of secrecy.Lara is going to explore yet another dangerous dungeon. Game designers decided to use good old 2D environment. The dungeon can be represented as a rectangle matrix of n rows and m columns. Cell (x, y) is the cell in the x-th row in the y-th column. Lara can move between the neighbouring by side cells in all four directions.Moreover, she has even chosen the path for herself to avoid all the traps. She enters the dungeon in cell (1, 1), that is top left corner of the matrix. Then she goes down all the way to cell (n, 1) — the bottom left corner. Then she starts moving in the snake fashion — all the way to the right, one cell up, then to the left to the cell in 2-nd column, one cell up. She moves until she runs out of non-visited cells. n and m given are such that she always end up in cell (1, 2).Lara has already moved to a neighbouring cell k times. Can you determine her current position?

The only line contains three integers n, m and k (2 ≤ n, m ≤ 109, n is always even, 0 ≤ k < n·m). Note that k doesn't fit into 32-bit integer type!

Print the cell (the row and the column where the cell is situated) where Lara ends up after she moves k times.


Polycarp has a cat and his cat is a real gourmet! Dependent on a day of the week he eats certain type of food:  on Mondays, Thursdays and Sundays he eats fish food;  on Tuesdays and Saturdays he eats rabbit stew;  on other days of week he eats chicken stake. Polycarp plans to go on a trip and already packed his backpack. His backpack contains:  $$$a$$$ daily rations of fish food;  $$$b$$$ daily rations of rabbit stew;  $$$c$$$ daily rations of chicken stakes. Polycarp has to choose such day of the week to start his trip that his cat can eat without additional food purchases as long as possible. Print the maximum number of days the cat can eat in a trip without additional food purchases, if Polycarp chooses the day of the week to start his trip optimally.

The first line of the input contains three positive integers $$$a$$$, $$$b$$$ and $$$c$$$ ($$$1 \le a, b, c \le 7\cdot10^8$$$) — the number of daily rations of fish food, rabbit stew and chicken stakes in Polycarps backpack correspondingly.

NoteIn the first example the best day for start of the trip is Sunday. In this case, during Sunday and Monday the cat will eat fish food, during Tuesday — rabbit stew and during Wednesday — chicken stake. So, after four days of the trip all food will be eaten.In the second example Polycarp can start his trip in any day of the week. In any case there are food supplies only for one week in Polycarps backpack.In the third example Polycarp can start his trip in any day, excluding Wednesday, Saturday and Sunday. In this case, the cat will eat three different dishes in three days. Nevertheless that after three days of a trip there will be $$$99$$$ portions of rabbit stew in a backpack, can cannot eat anything in fourth day of a trip.


To celebrate the opening of the Winter Computer School the organizers decided to buy in n liters of cola. However, an unexpected difficulty occurred in the shop: it turned out that cola is sold in bottles 0.5, 1 and 2 liters in volume. At that, there are exactly a bottles 0.5 in volume, b one-liter bottles and c of two-liter ones. The organizers have enough money to buy any amount of cola. What did cause the heated arguments was how many bottles of every kind to buy, as this question is pivotal for the distribution of cola among the participants (and organizers as well).Thus, while the organizers are having the argument, discussing different variants of buying cola, the Winter School can't start. Your task is to count the number of all the possible ways to buy exactly n liters of cola and persuade the organizers that this number is too large, and if they keep on arguing, then the Winter Computer School will have to be organized in summer.All the bottles of cola are considered indistinguishable, i.e. two variants of buying are different from each other only if they differ in the number of bottles of at least one kind.

The first line contains four integers — n, a, b, c (1 ≤ n ≤ 10000, 0 ≤ a, b, c ≤ 5000).

Print the unique number — the solution to the problem. If it is impossible to buy exactly n liters of cola, print 0.


Vasily the bear has a favorite rectangle, it has one vertex at point (0, 0), and the opposite vertex at point (x, y). Of course, the sides of Vasya's favorite rectangle are parallel to the coordinate axes. Vasya also loves triangles, if the triangles have one vertex at point B = (0, 0). That's why today he asks you to find two points A = (x1, y1) and C = (x2, y2), such that the following conditions hold:  the coordinates of points: x1, x2, y1, y2 are integers. Besides, the following inequation holds: x1 < x2;  the triangle formed by point A, B and C is rectangular and isosceles ( is right);  all points of the favorite rectangle are located inside or on the border of triangle ABC;  the area of triangle ABC is as small as possible. Help the bear, find the required points. It is not so hard to proof that these points are unique.

The first line contains two integers x, y ( - 109 ≤ x, y ≤ 109, x ≠ 0, y ≠ 0).

Print in the single line four integers x1, y1, x2, y2 — the coordinates of the required points.


Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal).

The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn.

Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise.

NoteIn the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row.In the second example it wasn't possible to win by making single turn.In the third example Ilya could have won by placing X in the last row between two existing Xs.In the fourth example it wasn't possible to win by making single turn.


Golorps are mysterious creatures who feed on variables. Golorp's name is a program in some programming language. Some scientists believe that this language is Befunge; golorps are tantalizingly silent.Variables consumed by golorps can take values from 0 to 9, inclusive. For each golorp its daily diet is defined by its name. Some golorps are so picky that they can't be fed at all. Besides, all golorps are very health-conscious and try to eat as little as possible. Given a choice of several valid sequences of variable values, each golorp will choose lexicographically smallest one.For the purposes of this problem you can assume that a golorp consists of jaws and a stomach. The number of variables necessary to feed a golorp is defined by the shape of its jaws. Variables can get to the stomach only via the jaws.A hungry golorp is visiting you. You know its name; feed it or figure out that it's impossible.

The input is a single string (between 13 and 1024 characters long) — the name of the visiting golorp. All names are similar and will resemble the ones given in the samples. The name is guaranteed to be valid.

Output lexicographically smallest sequence of variable values fit for feeding this golorp. Values should be listed in the order in which they get into the jaws. If the golorp is impossible to feed, output "false".


You have $$$c_1$$$ letters 'a', $$$c_2$$$ letters 'b', ..., $$$c_{26}$$$ letters 'z'. You want to build a beautiful string of length $$$n$$$ from them (obviously, you cannot use the $$$i$$$-th letter more than $$$c_i$$$ times). Each $$$c_i$$$ is greater than $$$\frac{n}{3}$$$.A string is called beautiful if there are no palindromic contiguous substrings of odd length greater than $$$1$$$ in it. For example, the string "abacaba" is not beautiful, it has several palindromic substrings of odd length greater than $$$1$$$ (for example, "aca"). Another example: the string "abcaa" is beautiful.Calculate the number of different strings you can build, and print the answer modulo $$$998244353$$$.

Print one integer — the number of strings you can build, taken modulo $$$998244353$$$.


Doctor prescribed medicine to his patient. The medicine is represented by pills. Each pill consists of a shell and healing powder. The shell consists of two halves; each half has one of four colors — blue, red, white or yellow.The doctor wants to put 28 pills in a rectangular box 7 × 8 in size. Besides, each pill occupies exactly two neighboring cells and any cell contains exactly one half of a pill. Thus, the result is a four colored picture 7 × 8 in size.The doctor thinks that a patient will recover sooner if the picture made by the pills will be special. Unfortunately, putting the pills in the box so as to get the required picture is not a very easy task. That's why doctor asks you to help. Doctor has some amount of pills of each of 10 painting types. They all contain the same medicine, that's why it doesn't matter which 28 of them will be stored inside the box.Place the pills in the box so that the required picture was formed. If it is impossible to place the pills in the required manner, then place them so that the number of matching colors in all 56 cells in the final arrangement and the doctor's picture were maximum.

First 7 lines contain the doctor's picture. Each line contains 8 characters, each character can be "B", "R", "W" and "Y" that stands for blue, red, white and yellow colors correspondingly. Next four lines contain 10 numbers that stand for, correspondingly, the number of pills painted: "BY" "BW" "BR" "BB" "RY" "RW" "RR" "WY" "WW" "YY" Those numbers lie within range from 0 to 28 inclusively. It is guaranteed that the total number of pills in no less than 28.

Print on the first line the maximal number cells for which the colors match. Then print 13 lines each containing 15 characters — the pills' position in the optimal arrangement. The intersections of odd lines and odd columns should contain characters "B", "R", "W" and "Y". All other positions should contain characters ".", "-" and "|". Use "-" and "|" to show which halves belong to one pill. See the samples for more clarification. If there are several possible solutions, print any of them.

WWWBBWWW
WWWBBWWW
YYWBBWWW
YYWBBWRR
YYWBBWRR
YYWBBWRR
YYWBBWRR
0 0 0 8
0 1 5
1 10
5

WWWWWWWW
WBYWRBBY
BRYRBWYY
WWBRYWBB
BWWRWBYW
RBWRBWYY
WWWWWWWW
0 0 0 1
0 0 1
0 1
25


InputThe only line of input contains three integers a1, a2, a3 (1 ≤ a1, a2, a3 ≤ 20), separated by spaces.OutputOutput a single integer.ExamplesInput2 3 2Output5Input13 14 1Output14Input14 5 9Output464Input17 18 3Output53


In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 × 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone — neither any other statues, nor Anna, nor Maria.Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is — to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.

You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one — for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is ".". If a cell has Maria, then it is represented by character "M". If a cell has Anna, it is represented by the character "A". If a cell has a statue, then the cell is represented by character "S". It is guaranteed that the last character of the first row is always "A", the first character of the last line is always "M". The remaining characters are "." or "S".

If Maria wins, print string "WIN". If the statues win, print string "LOSE".


Vasya has n pairs of socks. In the morning of each day Vasya has to put on a pair of socks before he goes to school. When he comes home in the evening, Vasya takes off the used socks and throws them away. Every m-th day (at days with numbers m, 2m, 3m, ...) mom buys a pair of socks to Vasya. She does it late in the evening, so that Vasya cannot put on a new pair of socks before the next day. How many consecutive days pass until Vasya runs out of socks?

The single line contains two integers n and m (1 ≤ n ≤ 100; 2 ≤ m ≤ 100), separated by a space.

Print a single integer — the answer to the problem.

NoteIn the first sample Vasya spends the first two days wearing the socks that he had initially. Then on day three he puts on the socks that were bought on day two.In the second sample Vasya spends the first nine days wearing the socks that he had initially. Then he spends three days wearing the socks that were bought on the third, sixth and ninth days. Than he spends another day wearing the socks that were bought on the twelfth day.


A sweet little monster Om Nom loves candies very much. One day he found himself in a rather tricky situation that required him to think a bit in order to enjoy candies the most. Would you succeed with the same task if you were on his place?  One day, when he came to his friend Evan, Om Nom didn't find him at home but he found two bags with candies. The first was full of blue candies and the second bag was full of red candies. Om Nom knows that each red candy weighs Wr grams and each blue candy weighs Wb grams. Eating a single red candy gives Om Nom Hr joy units and eating a single blue candy gives Om Nom Hb joy units.Candies are the most important thing in the world, but on the other hand overeating is not good. Om Nom knows if he eats more than C grams of candies, he will get sick. Om Nom thinks that it isn't proper to leave candy leftovers, so he can only eat a whole candy. Om Nom is a great mathematician and he quickly determined how many candies of what type he should eat in order to get the maximum number of joy units. Can you repeat his achievement? You can assume that each bag contains more candies that Om Nom can eat.

The single line contains five integers C, Hr, Hb, Wr, Wb (1 ≤ C, Hr, Hb, Wr, Wb ≤ 109).

Print a single integer — the maximum number of joy units that Om Nom can get.

NoteIn the sample test Om Nom can eat two candies of each type and thus get 16 joy units.


In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence BDF is a subsequence of ABCDEF. A substring of a string is a continuous subsequence of the string. For example, BCD is a substring of ABCDEF.You are given two strings s1, s2 and another string called virus. Your task is to find the longest common subsequence of s1 and s2, such that it doesn't contain virus as a substring.

The input contains three strings in three separate lines: s1, s2 and virus (1 ≤ |s1|, |s2|, |virus| ≤ 100). Each string consists only of uppercase English letters.

Output the longest common subsequence of s1 and s2 without virus as a substring. If there are multiple answers, any of them will be accepted.  If there is no valid common subsequence, output 0.


Polycarpus loves lucky numbers. Everybody knows that lucky numbers are positive integers, whose decimal representation (without leading zeroes) contain only the lucky digits x and y. For example, if x = 4, and y = 7, then numbers 47, 744, 4 are lucky.Let's call a positive integer a undoubtedly lucky, if there are such digits x and y (0 ≤ x, y ≤ 9), that the decimal representation of number a (without leading zeroes) contains only digits x and y.Polycarpus has integer n. He wants to know how many positive integers that do not exceed n, are undoubtedly lucky. Help him, count this number.

The first line contains a single integer n (1 ≤ n ≤ 109) — Polycarpus's number.

Print a single integer that says, how many positive integers that do not exceed n are undoubtedly lucky.

NoteIn the first test sample all numbers that do not exceed 10 are undoubtedly lucky.In the second sample numbers 102, 103, 104, 105, 106, 107, 108, 109, 120, 123 are not undoubtedly lucky.


You are given an undirected graph where each edge has one of two colors: black or red.Your task is to assign a real number to each node so that:   for each black edge the sum of values at its endpoints is $$$1$$$;  for each red edge the sum of values at its endpoints is $$$2$$$;  the sum of the absolute values of all assigned numbers is the smallest possible. Otherwise, if it is not possible, report that there is no feasible assignment of the numbers.

The first line contains two integers $$$N$$$ ($$$1 \leq N \leq 100\,000$$$) and $$$M$$$ ($$$0 \leq M \leq 200\,000$$$): the number of nodes and the number of edges, respectively. The nodes are numbered by consecutive integers: $$$1, 2, \ldots, N$$$. The next $$$M$$$ lines describe the edges. Each line contains three integers $$$a$$$, $$$b$$$ and $$$c$$$ denoting that there is an edge between nodes $$$a$$$ and $$$b$$$ ($$$1 \leq a, b \leq N$$$) with color $$$c$$$ ($$$1$$$ denotes black, $$$2$$$ denotes red).

If there is a solution, the first line should contain the word "YES" and the second line should contain $$$N$$$ space-separated numbers. For each $$$i$$$ ($$$1 \le i \le N$$$), the $$$i$$$-th number should be the number assigned to the node $$$i$$$. Output should be such that:    the sum of the numbers at the endpoints of each edge differs from the precise value by less than $$$10^{-6}$$$;  the sum of the absolute values of all assigned numbers differs from the smallest possible by less than $$$10^{-6}$$$.  If there are several valid solutions, output any of them. If there is no solution, the only line should contain the word "NO".

NoteNote that in the second example the solution is not unique.


SIHanatsuka - EMber SIHanatsuka - ATONEMENTBack in time, the seven-year-old Nora used to play lots of games with her creation ROBO_Head-02, both to have fun and enhance his abilities.One day, Nora's adoptive father, Phoenix Wyle, brought Nora $$$n$$$ boxes of toys. Before unpacking, Nora decided to make a fun game for ROBO.She labelled all $$$n$$$ boxes with $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$ and asked ROBO to do the following action several (possibly zero) times:  Pick three distinct indices $$$i$$$, $$$j$$$ and $$$k$$$, such that $$$a_i \mid a_j$$$ and $$$a_i \mid a_k$$$. In other words, $$$a_i$$$ divides both $$$a_j$$$ and $$$a_k$$$, that is $$$a_j \bmod a_i = 0$$$, $$$a_k \bmod a_i = 0$$$.  After choosing, Nora will give the $$$k$$$-th box to ROBO, and he will place it on top of the box pile at his side. Initially, the pile is empty.  After doing so, the box $$$k$$$ becomes unavailable for any further actions. Being amused after nine different tries of the game, Nora asked ROBO to calculate the number of possible different piles having the largest amount of boxes in them. Two piles are considered different if there exists a position where those two piles have different boxes.Since ROBO was still in his infant stages, and Nora was still too young to concentrate for a long time, both fell asleep before finding the final answer. Can you help them?As the number of such piles can be very large, you should print the answer modulo $$$10^9 + 7$$$.

The first line contains an integer $$$n$$$ ($$$3 \le n \le 60$$$), denoting the number of boxes. The second line contains $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 60$$$), where $$$a_i$$$ is the label of the $$$i$$$-th box.

Print the number of distinct piles having the maximum number of boxes that ROBO_Head can have, modulo $$$10^9 + 7$$$.

NoteLet's illustrate the box pile as a sequence $$$b$$$, with the pile's bottommost box being at the leftmost position.In the first example, there are $$$2$$$ distinct piles possible:   $$$b = [6]$$$ ($$$[2, \mathbf{6}, 8] \xrightarrow{(1, 3, 2)} [2, 8]$$$)  $$$b = [8]$$$ ($$$[2, 6, \mathbf{8}] \xrightarrow{(1, 2, 3)} [2, 6]$$$) In the second example, there are $$$4$$$ distinct piles possible:   $$$b = [9, 12]$$$ ($$$[2, 3, 4, \mathbf{9}, 12] \xrightarrow{(2, 5, 4)} [2, 3, 4, \mathbf{12}] \xrightarrow{(1, 3, 4)} [2, 3, 4]$$$)  $$$b = [4, 12]$$$ ($$$[2, 3, \mathbf{4}, 9, 12] \xrightarrow{(1, 5, 3)} [2, 3, 9, \mathbf{12}] \xrightarrow{(2, 3, 4)} [2, 3, 9]$$$)  $$$b = [4, 9]$$$ ($$$[2, 3, \mathbf{4}, 9, 12] \xrightarrow{(1, 5, 3)} [2, 3, \mathbf{9}, 12] \xrightarrow{(2, 4, 3)} [2, 3, 12]$$$)  $$$b = [9, 4]$$$ ($$$[2, 3, 4, \mathbf{9}, 12] \xrightarrow{(2, 5, 4)} [2, 3, \mathbf{4}, 12] \xrightarrow{(1, 4, 3)} [2, 3, 12]$$$) In the third sequence, ROBO can do nothing at all. Therefore, there is only $$$1$$$ valid pile, and that pile is empty.


We'll define S(n) for positive integer n as follows: the number of the n's digits in the decimal base. For example, S(893) = 3, S(114514) = 6.You want to make a consecutive integer sequence starting from number m (m, m + 1, ...). But you need to pay S(n)·k to add the number n to the sequence.You can spend a cost up to w, and you want to make the sequence as long as possible. Write a program that tells sequence's maximum length.

The first line contains three integers w (1 ≤ w ≤ 1016), m (1 ≤ m ≤ 1016), k (1 ≤ k ≤ 109). Please, do not write 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.

The first line should contain a single integer — the answer to the problem.


The year 2015 is almost over.Limak is a little polar bear. He has recently learnt about the binary system. He noticed that the passing year has exactly one zero in its representation in the binary system — 201510 = 111110111112. Note that he doesn't care about the number of zeros in the decimal representation.Limak chose some interval of years. He is going to count all years from this interval that have exactly one zero in the binary representation. Can you do it faster?Assume that all positive integers are always written without leading zeros.

The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 1018) — the first year and the last year in Limak's interval respectively.

Print one integer – the number of years Limak will count in his chosen interval.

NoteIn the first sample Limak's interval contains numbers 510 = 1012, 610 = 1102, 710 = 1112, 810 = 10002, 910 = 10012 and 1010 = 10102. Two of them (1012 and 1102) have the described property.


Johnny has a younger sister Anne, who is very clever and smart. As she came home from the kindergarten, she told his brother about the task that her kindergartener asked her to solve. The task was just to construct a triangle out of four sticks of different colours. Naturally, one of the sticks is extra. It is not allowed to break the sticks or use their partial length. Anne has perfectly solved this task, now she is asking Johnny to do the same.The boy answered that he would cope with it without any difficulty. However, after a while he found out that different tricky things can occur. It can happen that it is impossible to construct a triangle of a positive area, but it is possible to construct a degenerate triangle. It can be so, that it is impossible to construct a degenerate triangle even. As Johnny is very lazy, he does not want to consider such a big amount of cases, he asks you to help him.

The first line of the input contains four space-separated positive integer numbers not exceeding 100 — lengthes of the sticks.

Output TRIANGLE if it is possible to construct a non-degenerate triangle. Output SEGMENT if the first case cannot take place and it is possible to construct a degenerate triangle. Output IMPOSSIBLE if it is impossible to construct any triangle. Remember that you are to use three sticks. It is not allowed to break the sticks or use their partial length.


Attention: we lost all the test cases for this problem, so instead of solving the problem, we need you to generate test cases. We're going to give you the answer, and you need to print a test case that produces the given answer. The original problem is in the following paragraph.People don't use cash as often as they used to. Having a credit card solves some of the hassles of cash, such as having to receive change when you can't form the exact amount of money needed to purchase an item. Typically cashiers will give you as few coins as possible in change, but they don't have to. For example, if your change is 30 cents, a cashier could give you a 5 cent piece and a 25 cent piece, or they could give you three 10 cent pieces, or ten 1 cent pieces, two 5 cent pieces, and one 10 cent piece. Altogether there are 18 different ways to make 30 cents using only 1 cent pieces, 5 cent pieces, 10 cent pieces, and 25 cent pieces. Two ways are considered different if they contain a different number of at least one type of coin. Given the denominations of the coins and an amount of change to be made, how many different ways are there to make change?As we mentioned before, we lost all the test cases for this problem, so we're actually going to give you the number of ways, and want you to produce a test case for which the number of ways is the given number. There could be many ways to achieve this (we guarantee there's always at least one), so you can print any, as long as it meets the constraints described below.

Input will consist of a single integer A (1 ≤ A ≤ 105), the desired number of ways.

In the first line print integers N and M (1 ≤ N ≤ 106, 1 ≤ M ≤ 10), the amount of change to be made, and the number of denominations, respectively. Then print M integers D1, D2, ..., DM (1 ≤ Di ≤ 106), the denominations of the coins. All denominations must be distinct: for any i ≠ j we must have Di ≠ Dj. If there are multiple tests, print any of them. You can print denominations in atbitrary order.


Once upon a time in the Kingdom of Far Far Away lived Sam the Farmer. Sam had a cow named Dawn and he was deeply attached to her. Sam would spend the whole summer stocking hay to feed Dawn in winter. Sam scythed hay and put it into haystack. As Sam was a bright farmer, he tried to make the process of storing hay simpler and more convenient to use. He collected the hay into cubical hay blocks of the same size. Then he stored the blocks in his barn. After a summer spent in hard toil Sam stored A·B·C hay blocks and stored them in a barn as a rectangular parallelepiped A layers high. Each layer had B rows and each row had C blocks.At the end of the autumn Sam came into the barn to admire one more time the hay he'd been stacking during this hard summer. Unfortunately, Sam was horrified to see that the hay blocks had been carelessly scattered around the barn. The place was a complete mess. As it turned out, thieves had sneaked into the barn. They completely dissembled and took away a layer of blocks from the parallelepiped's front, back, top and sides. As a result, the barn only had a parallelepiped containing (A - 1) × (B - 2) × (C - 2) hay blocks. To hide the evidence of the crime, the thieves had dissembled the parallelepiped into single 1 × 1 × 1 blocks and scattered them around the barn. After the theft Sam counted n hay blocks in the barn but he forgot numbers A, B и C.Given number n, find the minimally possible and maximally possible number of stolen hay blocks.

The only line contains integer n from the problem's statement (1 ≤ n ≤ 109).

Print space-separated minimum and maximum number of hay blocks that could have been stolen by the thieves. Note that the answer to the problem can be large enough, so you must use the 64-bit integer type for calculations. Please, do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

NoteLet's consider the first sample test. If initially Sam has a parallelepiped consisting of 32 = 2 × 4 × 4 hay blocks in his barn, then after the theft the barn has 4 = (2 - 1) × (4 - 2) × (4 - 2) hay blocks left. Thus, the thieves could have stolen 32 - 4 = 28 hay blocks. If Sam initially had a parallelepiped consisting of 45 = 5 × 3 × 3 hay blocks in his barn, then after the theft the barn has 4 = (5 - 1) × (3 - 2) × (3 - 2) hay blocks left. Thus, the thieves could have stolen 45 - 4 = 41 hay blocks. No other variants of the blocks' initial arrangement (that leave Sam with exactly 4 blocks after the theft) can permit the thieves to steal less than 28 or more than 41 blocks.


The Duck songFor simplicity, we'll assume that there are only three types of grapes: green grapes, purple grapes and black grapes.Andrew, Dmitry and Michal are all grapes' lovers, however their preferences of grapes are different. To make all of them happy, the following should happen: Andrew, Dmitry and Michal should eat at least $$$x$$$, $$$y$$$ and $$$z$$$ grapes, respectively. Andrew has an extreme affinity for green grapes, thus he will eat green grapes and green grapes only. On the other hand, Dmitry is not a fan of black grapes — any types of grapes except black would do for him. In other words, Dmitry can eat green and purple grapes. Michal has a common taste — he enjoys grapes in general and will be pleased with any types of grapes, as long as the quantity is sufficient.Knowing that his friends are so fond of grapes, Aki decided to host a grape party with them. He has prepared a box with $$$a$$$ green grapes, $$$b$$$ purple grapes and $$$c$$$ black grapes.However, Aki isn't sure if the box he prepared contains enough grapes to make everyone happy. Can you please find out whether it's possible to distribute grapes so that everyone is happy or Aki has to buy some more grapes?It is not required to distribute all the grapes, so it's possible that some of them will remain unused.

The first line contains three integers $$$x$$$, $$$y$$$ and $$$z$$$ ($$$1 \le x, y, z \le 10^5$$$) — the number of grapes Andrew, Dmitry and Michal want to eat. The second line contains three integers $$$a$$$, $$$b$$$, $$$c$$$ ($$$1 \le a, b, c \le 10^5$$$) — the number of green, purple and black grapes in the box.

If there is a grape distribution that allows everyone to be happy, print "YES", otherwise print "NO".

NoteIn the first example, there is only one possible distribution:Andrew should take $$$1$$$ green grape, Dmitry should take $$$3$$$ remaining green grapes and $$$3$$$ purple grapes, and Michal will take $$$2$$$ out of $$$3$$$ available black grapes.In the second test, there is no possible distribution, since Andrew is not be able to eat enough green grapes. :(


Catherine has a deck of n cards, each of which is either red, green, or blue. As long as there are at least two cards left, she can do one of two actions:   take any two (not necessarily adjacent) cards with different colors and exchange them for a new card of the third color;  take any two (not necessarily adjacent) cards with the same color and exchange them for a new card with that color. She repeats this process until there is only one card left. What are the possible colors for the final card?

The first line of the input contains a single integer n (1 ≤ n ≤ 200) — the total number of cards. The next line contains a string s of length n — the colors of the cards. s contains only the characters 'B', 'G', and 'R', representing blue, green, and red, respectively.

Print a single string of up to three characters — the possible colors of the final card (using the same symbols as the input) in alphabetical order.

NoteIn the first sample, Catherine has one red card and one blue card, which she must exchange for a green card.In the second sample, Catherine has two green cards and one red card. She has two options: she can exchange the two green cards for a green card, then exchange the new green card and the red card for a blue card. Alternatively, she can exchange a green and a red card for a blue card, then exchange the blue card and remaining green card for a red card.In the third sample, Catherine only has blue cards, so she can only exchange them for more blue cards.


It's tough to be a superhero. And it's twice as tough to resist the supervillain who is cool at math. Suppose that you're an ordinary Batman in an ordinary city of Gotham. Your enemy Joker mined the building of the city administration and you only have several minutes to neutralize the charge. To do that you should enter the cancel code on the bomb control panel.However, that mad man decided to give you a hint. This morning the mayor found a playing card under his pillow. There was a line written on the card:The bomb has a note saying "J(x) = A", where A is some positive integer. You suspect that the cancel code is some integer x that meets the equation J(x) = A. Now in order to decide whether you should neutralize the bomb or run for your life, you've got to count how many distinct positive integers x meet this equation.

The single line of the input contains a single integer A (1 ≤ A ≤ 1012).

Print the number of solutions of the equation J(x) = A.

NoteRecord x|n means that number n divides number x. is defined as the largest positive integer that divides both a and b.In the first sample test the only suitable value of x is 2. Then J(2) = 1 + 2.In the second sample test the following values of x match:  x = 14, J(14) = 1 + 2 + 7 + 14 = 24  x = 15, J(15) = 1 + 3 + 5 + 15 = 24  x = 23, J(23) = 1 + 23 = 24


There are $$$n$$$ students in a school class, the rating of the $$$i$$$-th student on Codehorses is $$$a_i$$$. You have to form a team consisting of $$$k$$$ students ($$$1 \le k \le n$$$) such that the ratings of all team members are distinct.If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print $$$k$$$ distinct numbers which should be the indices of students in the team you form. If there are multiple answers, print any of them.

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 100$$$) — the number of students and the size of the team you have to form. The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 100$$$), where $$$a_i$$$ is the rating of $$$i$$$-th student.

If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print $$$k$$$ distinct integers from $$$1$$$ to $$$n$$$ which should be the indices of students in the team you form. All the ratings of the students in the team should be distinct. You may print the indices in any order. If there are multiple answers, print any of them. Assume that the students are numbered from $$$1$$$ to $$$n$$$.

NoteAll possible answers for the first example:   {1 2 5}  {2 3 5}  {2 4 5} Note that the order does not matter.


n children are standing in a circle and playing a game. Children's numbers in clockwise order form a permutation a1, a2, ..., an of length n. It is an integer sequence such that each integer from 1 to n appears exactly once in it.The game consists of m steps. On each step the current leader with index i counts out ai people in clockwise order, starting from the next person. The last one to be pointed at by the leader becomes the new leader.You are given numbers l1, l2, ..., lm — indices of leaders in the beginning of each step. Child with number l1 is the first leader in the game. Write a program which will restore a possible permutation a1, a2, ..., an. If there are multiple solutions then print any of them. If there is no solution then print -1.

The first line contains two integer numbers n, m (1 ≤ n, m ≤ 100). The second line contains m integer numbers l1, l2, ..., lm (1 ≤ li ≤ n) — indices of leaders in the beginning of each step.

Print such permutation of n numbers a1, a2, ..., an that leaders in the game will be exactly l1, l2, ..., lm if all the rules are followed. If there are multiple solutions print any of them.  If there is no permutation which satisfies all described conditions print -1.

NoteLet's follow leadership in the first example:   Child 2 starts.  Leadership goes from 2 to 2 + a2 = 3.  Leadership goes from 3 to 3 + a3 = 5. As it's greater than 4, it's going in a circle to 1.  Leadership goes from 1 to 1 + a1 = 4.  Leadership goes from 4 to 4 + a4 = 8. Thus in circle it still remains at 4.


Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states: XX   XX   .X   X.X.   .X   XX   XX Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square. Vasya has a board with $$$2\times n$$$ squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.

The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols "0" (zero) that denote the empty squares and symbols "X" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed $$$100$$$.

Output a single integer — the maximum amount of bishwocks that can be placed onto the given board.


The bear decided to store some raspberry for the winter. He cunningly found out the price for a barrel of honey in kilos of raspberry for each of the following n days. According to the bear's data, on the i-th (1 ≤ i ≤ n) day, the price for one barrel of honey is going to is xi kilos of raspberry.Unfortunately, the bear has neither a honey barrel, nor the raspberry. At the same time, the bear's got a friend who is ready to lend him a barrel of honey for exactly one day for c kilograms of raspberry. That's why the bear came up with a smart plan. He wants to choose some day d (1 ≤ d < n), lent a barrel of honey and immediately (on day d) sell it according to a daily exchange rate. The next day (d + 1) the bear wants to buy a new barrel of honey according to a daily exchange rate (as he's got some raspberry left from selling the previous barrel) and immediately (on day d + 1) give his friend the borrowed barrel of honey as well as c kilograms of raspberry for renting the barrel.The bear wants to execute his plan at most once and then hibernate. What maximum number of kilograms of raspberry can he earn? Note that if at some point of the plan the bear runs out of the raspberry, then he won't execute such a plan.

The first line contains two space-separated integers, n and c (2 ≤ n ≤ 100, 0 ≤ c ≤ 100), — the number of days and the number of kilos of raspberry that the bear should give for borrowing the barrel. The second line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi ≤ 100), the price of a honey barrel on day i.

Print a single integer — the answer to the problem.

NoteIn the first sample the bear will lend a honey barrel at day 3 and then sell it for 7. Then the bear will buy a barrel for 3 and return it to the friend. So, the profit is (7 - 3 - 1) = 3.In the second sample bear will lend a honey barrel at day 1 and then sell it for 100. Then the bear buy the barrel for 1 at the day 2. So, the profit is (100 - 1 - 2) = 97.


Vasily has a number a, which he wants to turn into a number b. For this purpose, he can do two types of operations:  multiply the current number by 2 (that is, replace the number x by 2·x);  append the digit 1 to the right of current number (that is, replace the number x by 10·x + 1). You need to help Vasily to transform the number a into the number b using only the operations described above, or find that it is impossible.Note that in this task you are not required to minimize the number of operations. It suffices to find any way to transform a into b.

The first line contains two positive integers a and b (1 ≤ a < b ≤ 109) — the number which Vasily has and the number he wants to have.

If there is no way to get b from a, print "NO" (without quotes). Otherwise print three lines. On the first line print "YES" (without quotes). The second line should contain single integer k — the length of the transformation sequence. On the third line print the sequence of transformations x1, x2, ..., xk, where:   x1 should be equal to a,  xk should be equal to b,  xi should be obtained from xi - 1 using any of two described operations (1 < i ≤ k).  If there are multiple answers, print any of them.


The Little Elephant is playing with the Cartesian coordinates' system. Most of all he likes playing with integer points. The Little Elephant defines an integer point as a pair of integers (x; y), such that 0 ≤ x ≤ w and 0 ≤ y ≤ h. Thus, the Little Elephant knows only (w + 1)·(h + 1) distinct integer points.The Little Elephant wants to paint a triangle with vertexes at integer points, the triangle's area must be a positive integer. For that, he needs to find the number of groups of three points that form such triangle. At that, the order of points in a group matters, that is, the group of three points (0;0), (0;2), (2;2) isn't equal to the group (0;2), (0;0), (2;2).Help the Little Elephant to find the number of groups of three integer points that form a nondegenerate triangle with integer area.

A single line contains two integers w and h (1 ≤ w, h ≤ 4000).

In a single output line print an integer — the remainder of dividing the answer to the problem by 1000000007 (109 + 7).


Limak is going to participate in a contest on the last day of the 2016. The contest will start at 20:00 and will last four hours, exactly until midnight. There will be n problems, sorted by difficulty, i.e. problem 1 is the easiest and problem n is the hardest. Limak knows it will take him 5·i minutes to solve the i-th problem.Limak's friends organize a New Year's Eve party and Limak wants to be there at midnight or earlier. He needs k minutes to get there from his house, where he will participate in the contest first.How many problems can Limak solve if he wants to make it to the party?

The only line of the input contains two integers n and k (1 ≤ n ≤ 10, 1 ≤ k ≤ 240) — the number of the problems in the contest and the number of minutes Limak needs to get to the party from his house.

Print one integer, denoting the maximum possible number of problems Limak can solve so that he could get to the party at midnight or earlier.

NoteIn the first sample, there are 3 problems and Limak needs 222 minutes to get to the party. The three problems require 5, 10 and 15 minutes respectively. Limak can spend 5 + 10 = 15 minutes to solve first two problems. Then, at 20:15 he can leave his house to get to the party at 23:57 (after 222 minutes). In this scenario Limak would solve 2 problems. He doesn't have enough time to solve 3 problems so the answer is 2.In the second sample, Limak can solve all 4 problems in 5 + 10 + 15 + 20 = 50 minutes. At 20:50 he will leave the house and go to the party. He will get there exactly at midnight.In the third sample, Limak needs only 1 minute to get to the party. He has enough time to solve all 7 problems.


Nick likes strings very much, he likes to rotate them, sort them, rearrange characters within a string... Once he wrote a random string of characters a, b, c on a piece of paper and began to perform the following operations:   to take two adjacent characters and replace the second character with the first one,  to take two adjacent characters and replace the first character with the second one To understand these actions better, let's take a look at a string «abc». All of the following strings can be obtained by performing one of the described operations on «abc»: «bbc», «abb», «acc». Let's denote the frequency of a character for each of the characters a, b and c as the number of occurrences of this character in the string. For example, for string «abc»: |a| = 1, |b| = 1, |c| = 1, and for string «bbc»: |a| = 0, |b| = 2, |c| = 1. While performing the described operations, Nick sometimes got balanced strings. Let's say that a string is balanced, if the frequencies of each character differ by at most 1. That is  - 1 ≤ |a| - |b| ≤ 1,  - 1 ≤ |a| - |c| ≤ 1 и  - 1 ≤ |b| - |c| ≤ 1. Would you help Nick find the number of different balanced strings that can be obtained by performing the operations described above, perhaps multiple times, on the given string s. This number should be calculated modulo 51123987.

The first line contains integer n (1 ≤ n ≤ 150) — the length of the given string s. Next line contains the given string s. The initial string can be balanced as well, in this case it should be counted too. The given string s consists only of characters a, b and c.

Output the only number — the number of different balanced strings that can be obtained by performing the described operations, perhaps multiple times, on the given string s, modulo 51123987.

NoteIn the first sample it is possible to get 51 different strings through the described operations, but only 7 of them are balanced: «abca», «bbca», «bcca», «bcaa», «abcc», «abbc», «aabc». In the second sample: «abbc», «aabc», «abcc». In the third sample there is only one balanced string — «ab» itself.


Polycarpus has a ribbon, its length is n. He wants to cut the ribbon in a way that fulfils the following two conditions:   After the cutting each ribbon piece should have length a, b or c.  After the cutting the number of ribbon pieces should be maximum. Help Polycarpus and find the number of ribbon pieces after the required cutting.

The first line contains four space-separated integers n, a, b and c (1 ≤ n, a, b, c ≤ 4000) — the length of the original ribbon and the acceptable lengths of the ribbon pieces after the cutting, correspondingly. The numbers a, b and c can coincide.

Print a single number — the maximum possible number of ribbon pieces. It is guaranteed that at least one correct ribbon cutting exists.

NoteIn the first example Polycarpus can cut the ribbon in such way: the first piece has length 2, the second piece has length 3.In the second example Polycarpus can cut the ribbon in such way: the first piece has length 5, the second piece has length 2.


Two participants are each given a pair of distinct numbers from 1 to 9 such that there's exactly one number that is present in both pairs. They want to figure out the number that matches by using a communication channel you have access to without revealing it to you.Both participants communicated to each other a set of pairs of numbers, that includes the pair given to them. Each pair in the communicated sets comprises two different numbers.Determine if you can with certainty deduce the common number, or if you can determine with certainty that both participants know the number but you do not.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 12$$$) — the number of pairs the first participant communicated to the second and vice versa. The second line contains $$$n$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, — pairs of numbers communicated from first participant to the second. The third line contains $$$m$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, — pairs of numbers communicated from the second participant to the first. All pairs within each set are distinct (in particular, if there is a pair $$$(1,2)$$$, there will be no pair $$$(2,1)$$$ within the same set), and no pair contains the same number twice. It is guaranteed that the two sets do not contradict the statements, in other words, there is pair from the first set and a pair from the second set that share exactly one number.

If you can deduce the shared number with certainty, print that number. If you can with certainty deduce that both participants know the shared number, but you do not know it, print $$$0$$$. Otherwise print $$$-1$$$.

NoteIn the first example the first participant communicated pairs $$$(1,2)$$$ and $$$(3,4)$$$, and the second communicated $$$(1,5)$$$, $$$(3,4)$$$. Since we know that the actual pairs they received share exactly one number, it can't be that they both have $$$(3,4)$$$. Thus, the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, and at this point you already know the shared number is $$$1$$$.In the second example either the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, or the first has $$$(3,4)$$$ and the second has $$$(6,4)$$$. In the first case both of them know the shared number is $$$1$$$, in the second case both of them know the shared number is $$$4$$$. You don't have enough information to tell $$$1$$$ and $$$4$$$ apart.In the third case if the first participant was given $$$(1,2)$$$, they don't know what the shared number is, since from their perspective the second participant might have been given either $$$(1,3)$$$, in which case the shared number is $$$1$$$, or $$$(2,3)$$$, in which case the shared number is $$$2$$$. While the second participant does know the number with certainty, neither you nor the first participant do, so the output is $$$-1$$$.


Apart from Nian, there is a daemon named Sui, which terrifies children and causes them to become sick. Parents give their children money wrapped in red packets and put them under the pillow, so that when Sui tries to approach them, it will be driven away by the fairies inside.Big Banban is hesitating over the amount of money to give out. He considers loops to be lucky since it symbolizes unity and harmony.He would like to find a positive integer n not greater than 1018, such that there are exactly k loops in the decimal representation of n, or determine that such n does not exist.A loop is a planar area enclosed by lines in the digits' decimal representation written in Arabic numerals. For example, there is one loop in digit 4, two loops in 8 and no loops in 5. Refer to the figure below for all exact forms.

The first and only line contains an integer k (1 ≤ k ≤ 106) — the desired number of loops.

Output an integer — if no such n exists, output -1; otherwise output any such n. In the latter case, your output should be a positive decimal integer not exceeding 1018.


Simon and Antisimon play a game. Initially each player receives one fixed positive integer that doesn't change throughout the game. Simon receives number a and Antisimon receives number b. They also have a heap of n stones. The players take turns to make a move and Simon starts. During a move a player should take from the heap the number of stones equal to the greatest common divisor of the fixed number he has received and the number of stones left in the heap. A player loses when he cannot take the required number of stones (i. e. the heap has strictly less stones left than one needs to take). Your task is to determine by the given a, b and n who wins the game.

The only string contains space-separated integers a, b and n (1 ≤ a, b, n ≤ 100) — the fixed numbers Simon and Antisimon have received correspondingly and the initial number of stones in the pile.

If Simon wins, print "0" (without the quotes), otherwise print "1" (without the quotes).

NoteThe greatest common divisor of two non-negative integers a and b is such maximum positive integer k, that a is divisible by k without remainder and similarly, b is divisible by k without remainder. Let gcd(a, b) represent the operation of calculating the greatest common divisor of numbers a and b. Specifically, gcd(x, 0) = gcd(0, x) = x.In the first sample the game will go like that: Simon should take gcd(3, 9) = 3 stones from the heap. After his move the heap has 6 stones left. Antisimon should take gcd(5, 6) = 1 stone from the heap. After his move the heap has 5 stones left. Simon should take gcd(3, 5) = 1 stone from the heap. After his move the heap has 4 stones left. Antisimon should take gcd(5, 4) = 1 stone from the heap. After his move the heap has 3 stones left. Simon should take gcd(3, 3) = 3 stones from the heap. After his move the heap has 0 stones left. Antisimon should take gcd(5, 0) = 5 stones from the heap. As 0 < 5, it is impossible and Antisimon loses.In the second sample each player during each move takes one stone from the heap. As n is even, Antisimon takes the last stone and Simon can't make a move after that.


Since next season are coming, you'd like to form a team from two or three participants. There are $$$n$$$ candidates, the $$$i$$$-th candidate has rank $$$a_i$$$. But you have weird requirements for your teammates: if you have rank $$$v$$$ and have chosen the $$$i$$$-th and $$$j$$$-th candidate, then $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$ must be met.You are very experienced, so you can change your rank to any non-negative integer but $$$X$$$ and $$$Y$$$ are tied with your birthdate, so they are fixed.Now you want to know, how many are there pairs $$$(i, j)$$$ such that there exists an integer $$$v$$$ meeting the following constraints: $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$. It's possible that $$$i = j$$$ and you form a team of two.$$$GCD$$$ is the greatest common divisor of two number, $$$LCM$$$ — the least common multiple.

First line contains three integers $$$n$$$, $$$X$$$ and $$$Y$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le X \le Y \le 10^{18}$$$) — the number of candidates and corresponding constants. Second line contains $$$n$$$ space separated integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^{18}$$$) — ranks of candidates.

Print the only integer — the number of pairs $$$(i, j)$$$ such that there exists an integer $$$v$$$ meeting the following constraints: $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$. It's possible that $$$i = j$$$.


Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.

The first line contains a non-empty string s — the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters "+". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.


Let's call an array a of size n coprime iff gcd(a1, a2, ..., an) = 1, where gcd is the greatest common divisor of the arguments.You are given two numbers n and k. For each i (1 ≤ i ≤ k) you have to determine the number of coprime arrays a of size n such that for every j (1 ≤ j ≤ n) 1 ≤ aj ≤ i. Since the answers can be very large, you have to calculate them modulo 109 + 7.

The first line contains two integers n and k (1 ≤ n, k ≤ 2·106) — the size of the desired arrays and the maximum upper bound on elements, respectively.

Since printing 2·106 numbers may take a lot of time, you have to output the answer in such a way: Let bi be the number of coprime arrays with elements in range [1, i], taken modulo 109 + 7. You have to print , taken modulo 109 + 7. Here  denotes bitwise xor operation (^ in C++ or Java, xor in Pascal).

NoteExplanation of the example:Since the number of coprime arrays is large, we will list the arrays that are non-coprime, but contain only elements in range [1, i]:For i = 1, the only array is coprime. b1 = 1.For i = 2, array [2, 2, 2] is not coprime. b2 = 7.For i = 3, arrays [2, 2, 2] and [3, 3, 3] are not coprime. b3 = 25.For i = 4, arrays [2, 2, 2], [3, 3, 3], [2, 2, 4], [2, 4, 2], [2, 4, 4], [4, 2, 2], [4, 2, 4], [4, 4, 2] and [4, 4, 4] are not coprime. b4 = 55.


One hot summer day Pete and his friend Billy decided to buy a watermelon. They chose the biggest and the ripest one, in their opinion. After that the watermelon was weighed, and the scales showed w kilos. They rushed home, dying of thirst, and decided to divide the berry, however they faced a hard problem.Pete and Billy are great fans of even numbers, that's why they want to divide the watermelon in such a way that each of the two parts weighs even number of kilos, at the same time it is not obligatory that the parts are equal. The boys are extremely tired and want to start their meal as soon as possible, that's why you should help them and find out, if they can divide the watermelon in the way they want. For sure, each of them should get a part of positive weight.

The first (and the only) input line contains integer number w (1 ≤ w ≤ 100) — the weight of the watermelon bought by the boys.

Print YES, if the boys can divide the watermelon into two parts, each of them weighing even number of kilos; and NO in the opposite case.

NoteFor example, the boys can divide the watermelon into two parts of 2 and 6 kilos respectively (another variant — two parts of 4 and 4 kilos).


Let's denote a function $$$f(x)$$$ in such a way: we add $$$1$$$ to $$$x$$$, then, while there is at least one trailing zero in the resulting number, we remove that zero. For example,   $$$f(599) = 6$$$: $$$599 + 1 = 600 \rightarrow 60 \rightarrow 6$$$;  $$$f(7) = 8$$$: $$$7 + 1 = 8$$$;  $$$f(9) = 1$$$: $$$9 + 1 = 10 \rightarrow 1$$$;  $$$f(10099) = 101$$$: $$$10099 + 1 = 10100 \rightarrow 1010 \rightarrow 101$$$. We say that some number $$$y$$$ is reachable from $$$x$$$ if we can apply function $$$f$$$ to $$$x$$$ some (possibly zero) times so that we get $$$y$$$ as a result. For example, $$$102$$$ is reachable from $$$10098$$$ because $$$f(f(f(10098))) = f(f(10099)) = f(101) = 102$$$; and any number is reachable from itself.You are given a number $$$n$$$; your task is to count how many different numbers are reachable from $$$n$$$.

The first line contains one integer $$$n$$$ ($$$1 \le n \le 10^9$$$).

Print one integer: the number of different numbers that are reachable from $$$n$$$.


One day Misha and Andrew were playing a very simple game. First, each player chooses an integer in the range from 1 to n. Let's assume that Misha chose number m, and Andrew chose number a.Then, by using a random generator they choose a random integer c in the range between 1 and n (any integer from 1 to n is chosen with the same probability), after which the winner is the player, whose number was closer to c. The boys agreed that if m and a are located on the same distance from c, Misha wins.Andrew wants to win very much, so he asks you to help him. You know the number selected by Misha, and number n. You need to determine which value of a Andrew must choose, so that the probability of his victory is the highest possible.More formally, you need to find such integer a (1 ≤ a ≤ n), that the probability that  is maximal, where c is the equiprobably chosen integer from 1 to n (inclusive).

The first line contains two integers n and m (1 ≤ m ≤ n ≤ 109) — the range of numbers in the game, and the number selected by Misha respectively.

Print a single number — such value a, that probability that Andrew wins is the highest. If there are multiple such values, print the minimum of them.

NoteIn the first sample test: Andrew wins if c is equal to 2 or 3. The probability that Andrew wins is 2 / 3. If Andrew chooses a = 3, the probability of winning will be 1 / 3. If a = 1, the probability of winning is 0.In the second sample test: Andrew wins if c is equal to 1 and 2. The probability that Andrew wins is 1 / 2. For other choices of a the probability of winning is less.


Jabber ID on the national Berland service «Babber» has a form <username>@<hostname>[/resource], where   <username> — is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters «_», the length of <username> is between 1 and 16, inclusive.  <hostname> — is a sequence of word separated by periods (characters «.»), where each word should contain only characters allowed for <username>, the length of each word is between 1 and 16, inclusive. The length of <hostname> is between 1 and 32, inclusive.  <resource> — is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters «_», the length of <resource> is between 1 and 16, inclusive. The content of square brackets is optional — it can be present or can be absent.There are the samples of correct Jabber IDs: mike@codeforces.com, 007@en.codeforces.com/contest.Your task is to write program which checks if given string is a correct Jabber ID.

The input contains of a single line. The line has the length between 1 and 100 characters, inclusive. Each characters has ASCII-code between 33 and 127, inclusive.


Today is Wednesday, the third day of the week. What's more interesting is that tomorrow is the last day of the year 2015.Limak is a little polar bear. He enjoyed this year a lot. Now, he is so eager to the coming year 2016.Limak wants to prove how responsible a bear he is. He is going to regularly save candies for the entire year 2016! He considers various saving plans. He can save one candy either on some fixed day of the week or on some fixed day of the month.Limak chose one particular plan. He isn't sure how many candies he will save in the 2016 with his plan. Please, calculate it and tell him.

The only line of the input is in one of the following two formats:    "x of week" where x (1 ≤ x ≤ 7) denotes the day of the week. The 1-st day is Monday and the 7-th one is Sunday.  "x of month" where x (1 ≤ x ≤ 31) denotes the day of the month.

Print one integer — the number of candies Limak will save in the year 2016.

NotePolar bears use the Gregorian calendar. It is the most common calendar and you likely use it too. You can read about it on Wikipedia if you want to – https://en.wikipedia.org/wiki/Gregorian_calendar. The week starts with Monday.In the first sample Limak wants to save one candy on each Thursday (the 4-th day of the week). There are 52 Thursdays in the 2016. Thus, he will save 52 candies in total.In the second sample Limak wants to save one candy on the 30-th day of each month. There is the 30-th day in exactly 11 months in the 2016 — all months but February. It means that Limak will save 11 candies in total.


Petr stands in line of n people, but he doesn't know exactly which position he occupies. He can say that there are no less than a people standing in front of him and no more than b people standing behind him. Find the number of different positions Petr can occupy.

The only line contains three integers n, a and b (0 ≤ a, b < n ≤ 100).

Print the single number — the number of the sought positions.

NoteThe possible positions in the first sample are: 2 and 3 (if we number the positions starting with 1).In the second sample they are 3, 4 and 5.


One day Vasya the Hipster decided to count how many socks he had. It turned out that he had a red socks and b blue socks.According to the latest fashion, hipsters should wear the socks of different colors: a red one on the left foot, a blue one on the right foot.Every day Vasya puts on new socks in the morning and throws them away before going to bed as he doesn't want to wash them.Vasya wonders, what is the maximum number of days when he can dress fashionable and wear different socks, and after that, for how many days he can then wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got.Can you help him?

The single line of the input contains two positive integers a and b (1 ≤ a, b ≤ 100) — the number of red and blue socks that Vasya's got.

Print two space-separated integers — the maximum number of days when Vasya can wear different socks and the number of days when he can wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got. Keep in mind that at the end of the day Vasya throws away the socks that he's been wearing on that day.

NoteIn the first sample Vasya can first put on one pair of different socks, after that he has two red socks left to wear on the second day.