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Solve the programming task below in a Python markdown code block. While exploring the old caves, researchers found a book, or more precisely, a stash of mixed pages from a book. Luckily, all of the original pages are present and each page contains its number. Therefore, the researchers can reconstruct the book. After taking a deeper look into the contents of these pages, linguists think that this may be some kind of dictionary. What's interesting is that this ancient civilization used an alphabet which is a subset of the English alphabet, however, the order of these letters in the alphabet is not like the one in the English language. Given the contents of pages that researchers have found, your task is to reconstruct the alphabet of this ancient civilization using the provided pages from the dictionary. Input First-line contains two integers: n and k (1 ≤ n, k ≤ 10^3) — the number of pages that scientists have found and the number of words present at each page. Following n groups contain a line with a single integer p_i (0 ≤ n < 10^3) — the number of i-th page, as well as k lines, each line containing one of the strings (up to 100 characters) written on the page numbered p_i. Output Output a string representing the reconstructed alphabet of this ancient civilization. If the book found is not a dictionary, output "IMPOSSIBLE" without quotes. In case there are multiple solutions, output any of them. Example Input 3 3 2 b b bbac 0 a aca acba 1 ab c ccb Output acb The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Students of Winter Informatics School are going to live in a set of houses connected by underground passages. Teachers are also going to live in some of these houses, but they can not be accommodated randomly. For safety reasons, the following must hold: * All passages between two houses will be closed, if there are no teachers in both of them. All other passages will stay open. * It should be possible to travel between any two houses using the underground passages that are open. * Teachers should not live in houses, directly connected by a passage. Please help the organizers to choose the houses where teachers will live to satisfy the safety requirements or determine that it is impossible. Input The first input line contains a single integer t — the number of test cases (1 ≤ t ≤ 10^5). Each test case starts with two integers n and m (2 ≤ n ≤ 3 ⋅ 10^5, 0 ≤ m ≤ 3 ⋅ 10^5) — the number of houses and the number of passages. Then m lines follow, each of them contains two integers u and v (1 ≤ u, v ≤ n, u ≠ v), describing a passage between the houses u and v. It is guaranteed that there are no two passages connecting the same pair of houses. The sum of values n over all test cases does not exceed 3 ⋅ 10^5, and the sum of values m over all test cases does not exceed 3 ⋅ 10^5. Output For each test case, if there is no way to choose the desired set of houses, output "NO". Otherwise, output "YES", then the total number of houses chosen, and then the indices of the chosen houses in arbitrary order. Examples Input 2 3 2 3 2 2 1 4 2 1 4 2 3 Output YES 2 1 3 NO Input 1 17 27 1 8 2 9 3 10 4 11 5 12 6 13 7 14 8 9 8 14 8 15 9 10 9 15 10 11 10 15 10 17 11 12 11 17 12 13 12 16 12 17 13 14 13 16 14 16 14 15 15 16 15 17 16 17 Output YES 8 1 3 4 5 6 9 14 17 Note The picture below shows the second example test. <image> The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Winters are just damn freezing cold in Nvodsk! That's why a group of n friends prefers to take a taxi, order a pizza and call girls. The phone numbers in the city consist of three pairs of digits (for example, 12-34-56). Each friend has a phonebook of size si (that's the number of phone numbers). We know that taxi numbers consist of six identical digits (for example, 22-22-22), the numbers of pizza deliveries should necessarily be decreasing sequences of six different digits (for example, 98-73-21), all other numbers are the girls' numbers. You are given your friends' phone books. Calculate which friend is best to go to when you are interested in each of those things (who has maximal number of phone numbers of each type). If the phone book of one person contains some number two times, you should count it twice. That is, each number should be taken into consideration the number of times it occurs in the phone book. Input The first line contains an integer n (1 ≤ n ≤ 100) — the number of friends. Then follow n data blocks that describe each friend's phone books. Each block is presented in the following form: first goes the line that contains integer si and string namei (0 ≤ si ≤ 100) — the number of phone numbers in the phone book of the i-th friend and the name of the i-th friend. The name is a non-empty sequence of uppercase and lowercase Latin letters, containing no more than 20 characters. Next si lines contain numbers as "XX-XX-XX", where X is arbitrary digits from 0 to 9. Output In the first line print the phrase "If you want to call a taxi, you should call: ". Then print names of all friends whose phone books contain maximal number of taxi phone numbers. In the second line print the phrase "If you want to order a pizza, you should call: ". Then print names of all friends who have maximal number of pizza phone numbers. In the third line print the phrase "If you want to go to a cafe with a wonderful girl, you should call: ". Then print names of all friends who have maximal number of girls' phone numbers. Print the names in the order in which they are given in the input data. Separate two consecutive names with a comma and a space. Each line should end with exactly one point. For clarifications concerning the output form, see sample tests. It is necessary that you follow the output form strictly. Extra spaces are not allowed. Examples Input 4 2 Fedorov 22-22-22 98-76-54 3 Melnikov 75-19-09 23-45-67 99-99-98 7 Rogulenko 22-22-22 11-11-11 33-33-33 44-44-44 55-55-55 66-66-66 95-43-21 3 Kaluzhin 11-11-11 99-99-99 98-65-32 Output If you want to call a taxi, you should call: Rogulenko. If you want to order a pizza, you should call: Fedorov, Rogulenko, Kaluzhin. If you want to go to a cafe with a wonderful girl, you should call: Melnikov. Input 3 5 Gleb 66-66-66 55-55-55 01-01-01 65-43-21 12-34-56 3 Serega 55-55-55 87-65-43 65-55-21 5 Melnik 12-42-12 87-73-01 36-04-12 88-12-22 82-11-43 Output If you want to call a taxi, you should call: Gleb. If you want to order a pizza, you should call: Gleb, Serega. If you want to go to a cafe with a wonderful girl, you should call: Melnik. Input 3 3 Kulczynski 22-22-22 65-43-21 98-12-00 4 Pachocki 11-11-11 11-11-11 11-11-11 98-76-54 0 Smietanka Output If you want to call a taxi, you should call: Pachocki. If you want to order a pizza, you should call: Kulczynski, Pachocki. If you want to go to a cafe with a wonderful girl, you should call: Kulczynski. Note In the first sample you are given four friends. Fedorov's phone book contains one taxi number and one pizza delivery number, Melnikov's phone book only has 3 numbers of girls, Rogulenko's one has 6 taxi numbers and one pizza delivery number, Kaluzhin's one contains 2 taxi numbers and one pizza delivery number. Thus, if you need to order a taxi, you should obviously call Rogulenko, if you need to order a pizza you should call anybody of the following: Rogulenko, Fedorov, Kaluzhin (each of them has one number). Melnikov has maximal number of phone numbers of girls. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A string s of length n (1 ≤ n ≤ 26) is called alphabetical if it can be obtained using the following algorithm: * first, write an empty string to s (i.e. perform the assignment s := ""); * then perform the next step n times; * at the i-th step take i-th lowercase letter of the Latin alphabet and write it either to the left of the string s or to the right of the string s (i.e. perform the assignment s := c+s or s := s+c, where c is the i-th letter of the Latin alphabet). In other words, iterate over the n first letters of the Latin alphabet starting from 'a' and etc. Each time we prepend a letter to the left of the string s or append a letter to the right of the string s. Strings that can be obtained in that way are alphabetical. For example, the following strings are alphabetical: "a", "ba", "ab", "bac" and "ihfcbadeg". The following strings are not alphabetical: "z", "aa", "ca", "acb", "xyz" and "ddcba". From the given string, determine if it is alphabetical. Input The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow. Each test case is written on a separate line that contains one string s. String s consists of lowercase letters of the Latin alphabet and has a length between 1 and 26, inclusive. Output Output t lines, each of them must contain the answer to the corresponding test case. Output YES if the given string s is alphabetical and NO otherwise. You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive answer). Example Input 11 a ba ab bac ihfcbadeg z aa ca acb xyz ddcba Output YES YES YES YES YES NO NO NO NO NO NO Note The example contains test cases from the main part of the condition. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Hamming distance between strings a and b of equal length (denoted by h(a, b)) is equal to the number of distinct integers i (1 ≤ i ≤ \|a\|), such that ai ≠ bi, where ai is the i-th symbol of string a, bi is the i-th symbol of string b. For example, the Hamming distance between strings "aba" and "bba" equals 1, they have different first symbols. For strings "bbba" and "aaab" the Hamming distance equals 4. John Doe had a paper on which four strings of equal length s1, s2, s3 and s4 were written. Each string si consisted only of lowercase letters "a" and "b". John found the Hamming distances between all pairs of strings he had. Then he lost the paper with the strings but he didn't lose the Hamming distances between all pairs. Help John restore the strings; find some four strings s'1, s'2, s'3, s'4 of equal length that consist only of lowercase letters "a" and "b", such that the pairwise Hamming distances between them are the same as between John's strings. More formally, set s'i must satisfy the condition <image>. To make the strings easier to put down on a piece of paper, you should choose among all suitable sets of strings the one that has strings of minimum length. Input The first line contains space-separated integers h(s1, s2), h(s1, s3), h(s1, s4). The second line contains space-separated integers h(s2, s3) and h(s2, s4). The third line contains the single integer h(s3, s4). All given integers h(si, sj) are non-negative and do not exceed 105. It is guaranteed that at least one number h(si, sj) is positive. Output Print -1 if there's no suitable set of strings. Otherwise print on the first line number len — the length of each string. On the i-th of the next four lines print string s'i. If there are multiple sets with the minimum length of the strings, print any of them. Examples Input 4 4 4 4 4 4 Output 6 aaaabb aabbaa bbaaaa bbbbbb The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A coordinate line has n segments, the i-th segment starts at the position li and ends at the position ri. We will denote such a segment as [li, ri]. You have suggested that one of the defined segments covers all others. In other words, there is such segment in the given set, which contains all other ones. Now you want to test your assumption. Find in the given set the segment which covers all other segments, and print its number. If such a segment doesn't exist, print -1. Formally we will assume that segment [a, b] covers segment [c, d], if they meet this condition a ≤ c ≤ d ≤ b. Input The first line contains integer n (1 ≤ n ≤ 105) — the number of segments. Next n lines contain the descriptions of the segments. The i-th line contains two space-separated integers li, ri (1 ≤ li ≤ ri ≤ 109) — the borders of the i-th segment. It is guaranteed that no two segments coincide. Output Print a single integer — the number of the segment that covers all other segments in the set. If there's no solution, print -1. The segments are numbered starting from 1 in the order in which they appear in the input. Examples Input 3 1 1 2 2 3 3 Output -1 Input 6 1 5 2 3 1 10 7 10 7 7 10 10 Output 3 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. HAI I HAS A TUX GIMMEH TUX I HAS A FOO ITS 0 I HAS A BAR ITS 0 I HAS A BAZ ITS 0 I HAS A QUZ ITS 1 TUX IS NOW A NUMBR IM IN YR LOOP NERFIN YR TUX TIL BOTH SAEM TUX AN 0 I HAS A PUR GIMMEH PUR PUR IS NOW A NUMBR FOO R SUM OF FOO AN PUR BAR R SUM OF BAR AN 1 BOTH SAEM BIGGR OF PRODUKT OF FOO AN QUZ AN PRODUKT OF BAR BAZ AN PRODUKT OF FOO AN QUZ O RLY? YA RLY BAZ R FOO QUZ R BAR OIC IM OUTTA YR LOOP BAZ IS NOW A NUMBAR VISIBLE SMOOSH QUOSHUNT OF BAZ QUZ KTHXBYE Input The input contains between 1 and 10 lines, i-th line contains an integer number xi (0 ≤ xi ≤ 9). Output Output a single real number. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 4. Examples Input 3 0 1 1 Output 0.666667 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In the rush of modern life, people often forget how beautiful the world is. The time to enjoy those around them is so little that some even stand in queues to several rooms at the same time in the clinic, running from one queue to another. (Cultural note: standing in huge and disorganized queues for hours is a native tradition in Russia, dating back to the Soviet period. Queues can resemble crowds rather than lines. Not to get lost in such a queue, a person should follow a strict survival technique: you approach the queue and ask who the last person is, somebody answers and you join the crowd. Now you're the last person in the queue till somebody else shows up. You keep an eye on the one who was last before you as he is your only chance to get to your destination) I'm sure many people have had the problem when a stranger asks who the last person in the queue is and even dares to hint that he will be the last in the queue and then bolts away to some unknown destination. These are the representatives of the modern world, in which the ratio of lack of time is so great that they do not even watch foreign top-rated TV series. Such people often create problems in queues, because the newcomer does not see the last person in the queue and takes a place after the "virtual" link in this chain, wondering where this legendary figure has left. The Smart Beaver has been ill and he's made an appointment with a therapist. The doctor told the Beaver the sad news in a nutshell: it is necessary to do an electrocardiogram. The next day the Smart Beaver got up early, put on the famous TV series on download (three hours till the download's complete), clenched his teeth and bravely went to join a queue to the electrocardiogram room, which is notorious for the biggest queues at the clinic. Having stood for about three hours in the queue, the Smart Beaver realized that many beavers had not seen who was supposed to stand in the queue before them and there was a huge mess. He came up to each beaver in the ECG room queue and asked who should be in front of him in the queue. If the beaver did not know his correct position in the queue, then it might be his turn to go get an ECG, or maybe he should wait for a long, long time... As you've guessed, the Smart Beaver was in a hurry home, so he gave you all the necessary information for you to help him to determine what his number in the queue can be. Input The first line contains two integers n (1 ≤ n ≤ 103) and x (1 ≤ x ≤ n) — the number of beavers that stand in the queue and the Smart Beaver's number, correspondingly. All willing to get to the doctor are numbered from 1 to n. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ n) — the number of the beaver followed by the i-th beaver. If ai = 0, then the i-th beaver doesn't know who is should be in front of him. It is guaranteed that values ai are correct. That is there is no cycles in the dependencies. And any beaver is followed by at most one beaver in the queue. The input limits for scoring 30 points are (subproblem B1): * It is guaranteed that the number of zero elements ai doesn't exceed 20. The input limits for scoring 100 points are (subproblems B1+B2): * The number of zero elements ai is arbitrary. Output Print all possible positions of the Smart Beaver in the line in the increasing order. Examples Input 6 1 2 0 4 0 6 0 Output 2 4 6 Input 6 2 2 3 0 5 6 0 Output 2 5 Input 4 1 0 0 0 0 Output 1 2 3 4 Input 6 2 0 0 1 0 4 5 Output 1 3 4 6 Note <image> Picture for the fourth test. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Little Chris is very keen on his toy blocks. His teacher, however, wants Chris to solve more problems, so he decided to play a trick on Chris. There are exactly s blocks in Chris's set, each block has a unique number from 1 to s. Chris's teacher picks a subset of blocks X and keeps it to himself. He will give them back only if Chris can pick such a non-empty subset Y from the remaining blocks, that the equality holds: <image> "Are you kidding me?", asks Chris. For example, consider a case where s = 8 and Chris's teacher took the blocks with numbers 1, 4 and 5. One way for Chris to choose a set is to pick the blocks with numbers 3 and 6, see figure. Then the required sums would be equal: (1 - 1) + (4 - 1) + (5 - 1) = (8 - 3) + (8 - 6) = 7. <image> However, now Chris has exactly s = 106 blocks. Given the set X of blocks his teacher chooses, help Chris to find the required set Y! Input The first line of input contains a single integer n (1 ≤ n ≤ 5·105), the number of blocks in the set X. The next line contains n distinct space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 106), the numbers of the blocks in X. Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++. Output In the first line of output print a single integer m (1 ≤ m ≤ 106 - n), the number of blocks in the set Y. In the next line output m distinct space-separated integers y1, y2, ..., ym (1 ≤ yi ≤ 106), such that the required equality holds. The sets X and Y should not intersect, i.e. xi ≠ yj for all i, j (1 ≤ i ≤ n; 1 ≤ j ≤ m). It is guaranteed that at least one solution always exists. If there are multiple solutions, output any of them. Examples Input 3 1 4 5 Output 2 999993 1000000 Input 1 1 Output 1 1000000 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players. Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move. Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him. Input The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109). Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters. Output If the player who moves first wins, print "First", otherwise print "Second" (without the quotes). Examples Input 2 3 a b Output First Input 3 1 a b c Output First Input 1 2 ab Output Second The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. User ainta has a permutation p1, p2, ..., pn. As the New Year is coming, he wants to make his permutation as pretty as possible. Permutation a1, a2, ..., an is prettier than permutation b1, b2, ..., bn, if and only if there exists an integer k (1 ≤ k ≤ n) where a1 = b1, a2 = b2, ..., ak - 1 = bk - 1 and ak < bk all holds. As known, permutation p is so sensitive that it could be only modified by swapping two distinct elements. But swapping two elements is harder than you think. Given an n × n binary matrix A, user ainta can swap the values of pi and pj (1 ≤ i, j ≤ n, i ≠ j) if and only if Ai, j = 1. Given the permutation p and the matrix A, user ainta wants to know the prettiest permutation that he can obtain. Input The first line contains an integer n (1 ≤ n ≤ 300) — the size of the permutation p. The second line contains n space-separated integers p1, p2, ..., pn — the permutation p that user ainta has. Each integer between 1 and n occurs exactly once in the given permutation. Next n lines describe the matrix A. The i-th line contains n characters '0' or '1' and describes the i-th row of A. The j-th character of the i-th line Ai, j is the element on the intersection of the i-th row and the j-th column of A. It is guaranteed that, for all integers i, j where 1 ≤ i < j ≤ n, Ai, j = Aj, i holds. Also, for all integers i where 1 ≤ i ≤ n, Ai, i = 0 holds. Output In the first and only line, print n space-separated integers, describing the prettiest permutation that can be obtained. Examples Input 7 5 2 4 3 6 7 1 0001001 0000000 0000010 1000001 0000000 0010000 1001000 Output 1 2 4 3 6 7 5 Input 5 4 2 1 5 3 00100 00011 10010 01101 01010 Output 1 2 3 4 5 Note In the first sample, the swap needed to obtain the prettiest permutation is: (p1, p7). In the second sample, the swaps needed to obtain the prettiest permutation is (p1, p3), (p4, p5), (p3, p4). <image> A permutation p is a sequence of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. The i-th element of the permutation p is denoted as pi. The size of the permutation p is denoted as n. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Anya loves to fold and stick. Today she decided to do just that. Anya has n cubes lying in a line and numbered from 1 to n from left to right, with natural numbers written on them. She also has k stickers with exclamation marks. We know that the number of stickers does not exceed the number of cubes. Anya can stick an exclamation mark on the cube and get the factorial of the number written on the cube. For example, if a cube reads 5, then after the sticking it reads 5!, which equals 120. You need to help Anya count how many ways there are to choose some of the cubes and stick on some of the chosen cubes at most k exclamation marks so that the sum of the numbers written on the chosen cubes after the sticking becomes equal to S. Anya can stick at most one exclamation mark on each cube. Can you do it? Two ways are considered the same if they have the same set of chosen cubes and the same set of cubes with exclamation marks. Input The first line of the input contains three space-separated integers n, k and S (1 ≤ n ≤ 25, 0 ≤ k ≤ n, 1 ≤ S ≤ 1016) — the number of cubes and the number of stickers that Anya has, and the sum that she needs to get. The second line contains n positive integers ai (1 ≤ ai ≤ 109) — the numbers, written on the cubes. The cubes in the input are described in the order from left to right, starting from the first one. Multiple cubes can contain the same numbers. Output Output the number of ways to choose some number of cubes and stick exclamation marks on some of them so that the sum of the numbers became equal to the given number S. Examples Input 2 2 30 4 3 Output 1 Input 2 2 7 4 3 Output 1 Input 3 1 1 1 1 1 Output 6 Note In the first sample the only way is to choose both cubes and stick an exclamation mark on each of them. In the second sample the only way is to choose both cubes but don't stick an exclamation mark on any of them. In the third sample it is possible to choose any of the cubes in three ways, and also we may choose to stick or not to stick the exclamation mark on it. So, the total number of ways is six. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In Ancient Berland there were n cities and m two-way roads of equal length. The cities are numbered with integers from 1 to n inclusively. According to an ancient superstition, if a traveller visits three cities ai, bi, ci in row, without visiting other cities between them, a great disaster awaits him. Overall there are k such city triplets. Each triplet is ordered, which means that, for example, you are allowed to visit the cities in the following order: ai, ci, bi. Vasya wants to get from the city 1 to the city n and not fulfil the superstition. Find out which minimal number of roads he should take. Also you are required to find one of his possible path routes. Input The first line contains three integers n, m, k (2 ≤ n ≤ 3000, 1 ≤ m ≤ 20000, 0 ≤ k ≤ 105) which are the number of cities, the number of roads and the number of the forbidden triplets correspondingly. Then follow m lines each containing two integers xi, yi (1 ≤ xi, yi ≤ n) which are the road descriptions. The road is described by the numbers of the cities it joins. No road joins a city with itself, there cannot be more than one road between a pair of cities. Then follow k lines each containing three integers ai, bi, ci (1 ≤ ai, bi, ci ≤ n) which are the forbidden triplets. Each ordered triplet is listed mo more than one time. All three cities in each triplet are distinct. City n can be unreachable from city 1 by roads. Output If there are no path from 1 to n print -1. Otherwise on the first line print the number of roads d along the shortest path from the city 1 to the city n. On the second line print d + 1 numbers — any of the possible shortest paths for Vasya. The path should start in the city 1 and end in the city n. Examples Input 4 4 1 1 2 2 3 3 4 1 3 1 4 3 Output 2 1 3 4 Input 3 1 0 1 2 Output -1 Input 4 4 2 1 2 2 3 3 4 1 3 1 2 3 1 3 4 Output 4 1 3 2 3 4 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are n sharks who grow flowers for Wet Shark. They are all sitting around the table, such that sharks i and i + 1 are neighbours for all i from 1 to n - 1. Sharks n and 1 are neighbours too. Each shark will grow some number of flowers si. For i-th shark value si is random integer equiprobably chosen in range from li to ri. Wet Shark has it's favourite prime number p, and he really likes it! If for any pair of neighbouring sharks i and j the product si·sj is divisible by p, then Wet Shark becomes happy and gives 1000 dollars to each of these sharks. At the end of the day sharks sum all the money Wet Shark granted to them. Find the expectation of this value. Input The first line of the input contains two space-separated integers n and p (3 ≤ n ≤ 100 000, 2 ≤ p ≤ 109) — the number of sharks and Wet Shark's favourite prime number. It is guaranteed that p is prime. The i-th of the following n lines contains information about i-th shark — two space-separated integers li and ri (1 ≤ li ≤ ri ≤ 109), the range of flowers shark i can produce. Remember that si is chosen equiprobably among all integers from li to ri, inclusive. Output Print a single real number — the expected number of dollars that the sharks receive in total. You answer will be considered correct if its absolute or relative 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 <image>. Examples Input 3 2 1 2 420 421 420420 420421 Output 4500.0 Input 3 5 1 4 2 3 11 14 Output 0.0 Note A prime number is a positive integer number that is divisible only by 1 and itself. 1 is not considered to be prime. Consider the first sample. First shark grows some number of flowers from 1 to 2, second sharks grows from 420 to 421 flowers and third from 420420 to 420421. There are eight cases for the quantities of flowers (s0, s1, s2) each shark grows: 1. (1, 420, 420420): note that s0·s1 = 420, s1·s2 = 176576400, and s2·s0 = 420420. For each pair, 1000 dollars will be awarded to each shark. Therefore, each shark will be awarded 2000 dollars, for a total of 6000 dollars. 2. (1, 420, 420421): now, the product s2·s0 is not divisible by 2. Therefore, sharks s0 and s2 will receive 1000 dollars, while shark s1 will receive 2000. The total is 4000. 3. (1, 421, 420420): total is 4000 4. (1, 421, 420421): total is 0. 5. (2, 420, 420420): total is 6000. 6. (2, 420, 420421): total is 6000. 7. (2, 421, 420420): total is 6000. 8. (2, 421, 420421): total is 4000. The expected value is <image>. In the second sample, no combination of quantities will garner the sharks any money. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. On the planet Mars a year lasts exactly n days (there are no leap years on Mars). But Martians have the same weeks as earthlings — 5 work days and then 2 days off. Your task is to determine the minimum possible and the maximum possible number of days off per year on Mars. Input The first line of the input contains a positive integer n (1 ≤ n ≤ 1 000 000) — the number of days in a year on Mars. Output Print two integers — the minimum possible and the maximum possible number of days off per year on Mars. Examples Input 14 Output 4 4 Input 2 Output 0 2 Note In the first sample there are 14 days in a year on Mars, and therefore independently of the day a year starts with there will be exactly 4 days off . In the second sample there are only 2 days in a year on Mars, and they can both be either work days or days off. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a positive decimal number x. Your task is to convert it to the "simple exponential notation". Let x = a·10b, where 1 ≤ a < 10, then in general case the "simple exponential notation" looks like "aEb". If b equals to zero, the part "Eb" should be skipped. If a is an integer, it should be written without decimal point. Also there should not be extra zeroes in a and b. Input The only line contains the positive decimal number x. The length of the line will not exceed 106. Note that you are given too large number, so you can't use standard built-in data types "float", "double" and other. Output Print the only line — the "simple exponential notation" of the given number x. Examples Input 16 Output 1.6E1 Input 01.23400 Output 1.234 Input .100 Output 1E-1 Input 100. Output 1E2 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1. When ZS the Coder is at level k, he can : 1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k. 2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m. Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5. ZS the Coder needs your help in beating the game — he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level. Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses. Input The first and only line of the input contains a single integer n (1 ≤ n ≤ 100 000), denoting that ZS the Coder wants to reach level n + 1. Output Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i. Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018. It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them. Examples Input 3 Output 14 16 46 Input 2 Output 999999999999999998 44500000000 Input 4 Output 2 17 46 97 Note In the first sample case: On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>. After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>. After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>. Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4. Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution. In the second sample case: On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>. After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000·2 = 9·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>. Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Input The input contains a single integer a (1 ≤ a ≤ 30). Output Output a single integer. Example Input 3 Output 27 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Arpa is researching the Mexican wave. There are n spectators in the stadium, labeled from 1 to n. They start the Mexican wave at time 0. * At time 1, the first spectator stands. * At time 2, the second spectator stands. * ... * At time k, the k-th spectator stands. * At time k + 1, the (k + 1)-th spectator stands and the first spectator sits. * At time k + 2, the (k + 2)-th spectator stands and the second spectator sits. * ... * At time n, the n-th spectator stands and the (n - k)-th spectator sits. * At time n + 1, the (n + 1 - k)-th spectator sits. * ... * At time n + k, the n-th spectator sits. Arpa wants to know how many spectators are standing at time t. Input The first line contains three integers n, k, t (1 ≤ n ≤ 109, 1 ≤ k ≤ n, 1 ≤ t < n + k). Output Print single integer: how many spectators are standing at time t. Examples Input 10 5 3 Output 3 Input 10 5 7 Output 5 Input 10 5 12 Output 3 Note In the following a sitting spectator is represented as -, a standing spectator is represented as ^. * At t = 0 ---------- <image> number of standing spectators = 0. * At t = 1 ^--------- <image> number of standing spectators = 1. * At t = 2 ^^-------- <image> number of standing spectators = 2. * At t = 3 ^^^------- <image> number of standing spectators = 3. * At t = 4 ^^^^------ <image> number of standing spectators = 4. * At t = 5 ^^^^^----- <image> number of standing spectators = 5. * At t = 6 -^^^^^---- <image> number of standing spectators = 5. * At t = 7 --^^^^^--- <image> number of standing spectators = 5. * At t = 8 ---^^^^^-- <image> number of standing spectators = 5. * At t = 9 ----^^^^^- <image> number of standing spectators = 5. * At t = 10 -----^^^^^ <image> number of standing spectators = 5. * At t = 11 ------^^^^ <image> number of standing spectators = 4. * At t = 12 -------^^^ <image> number of standing spectators = 3. * At t = 13 --------^^ <image> number of standing spectators = 2. * At t = 14 ---------^ <image> number of standing spectators = 1. * At t = 15 ---------- <image> number of standing spectators = 0. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You all know that the Library of Bookland is the largest library in the world. There are dozens of thousands of books in the library. Some long and uninteresting story was removed... The alphabet of Bookland is so large that its letters are denoted by positive integers. Each letter can be small or large, the large version of a letter x is denoted by x'. BSCII encoding, which is used everywhere in Bookland, is made in that way so that large letters are presented in the order of the numbers they are denoted by, and small letters are presented in the order of the numbers they are denoted by, but all large letters are before all small letters. For example, the following conditions hold: 2 < 3, 2' < 3', 3' < 2. A word x1, x2, ..., xa is not lexicographically greater than y1, y2, ..., yb if one of the two following conditions holds: * a ≤ b and x1 = y1, ..., xa = ya, i.e. the first word is the prefix of the second word; * there is a position 1 ≤ j ≤ min(a, b), such that x1 = y1, ..., xj - 1 = yj - 1 and xj < yj, i.e. at the first position where the words differ the first word has a smaller letter than the second word has. For example, the word "3' 7 5" is before the word "2 4' 6" in lexicographical order. It is said that sequence of words is in lexicographical order if each word is not lexicographically greater than the next word in the sequence. Denis has a sequence of words consisting of small letters only. He wants to change some letters to large (let's call this process a capitalization) in such a way that the sequence of words is in lexicographical order. However, he soon realized that for some reason he can't change a single letter in a single word. He only can choose a letter and change all of its occurrences in all words to large letters. He can perform this operation any number of times with arbitrary letters of Bookland's alphabet. Help Denis to choose which letters he needs to capitalize (make large) in order to make the sequence of words lexicographically ordered, or determine that it is impossible. Note that some words can be equal. Input The first line contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of words and the number of letters in Bookland's alphabet, respectively. The letters of Bookland's alphabet are denoted by integers from 1 to m. Each of the next n lines contains a description of one word in format li, si, 1, si, 2, ..., si, li (1 ≤ li ≤ 100 000, 1 ≤ si, j ≤ m), where li is the length of the word, and si, j is the sequence of letters in the word. The words are given in the order Denis has them in the sequence. It is guaranteed that the total length of all words is not greater than 100 000. Output In the first line print "Yes" (without quotes), if it is possible to capitalize some set of letters in such a way that the sequence of words becomes lexicographically ordered. Otherwise, print "No" (without quotes). If the required is possible, in the second line print k — the number of letters Denis has to capitalize (make large), and in the third line print k distinct integers — these letters. Note that you don't need to minimize the value k. You can print the letters in any order. If there are multiple answers, print any of them. Examples Input 4 3 1 2 1 1 3 1 3 2 2 1 1 Output Yes 2 2 3 Input 6 5 2 1 2 2 1 2 3 1 2 3 2 1 5 2 4 4 2 4 4 Output Yes 0 Input 4 3 4 3 2 2 1 3 1 1 3 3 2 3 3 2 3 1 Output No Note In the first example after Denis makes letters 2 and 3 large, the sequence looks like the following: * 2' * 1 * 1 3' 2' * 1 1 The condition 2' < 1 holds, so the first word is not lexicographically larger than the second word. The second word is the prefix of the third word, so the are in lexicographical order. As the first letters of the third and the fourth words are the same, and 3' < 1, then the third word is not lexicographically larger than the fourth word. In the second example the words are in lexicographical order from the beginning, so Denis can do nothing. In the third example there is no set of letters such that if Denis capitalizes them, the sequence becomes lexicographically ordered. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vasya writes his own library for building graphical user interface. Vasya called his creation VTK (VasyaToolKit). One of the interesting aspects of this library is that widgets are packed in each other. A widget is some element of graphical interface. Each widget has width and height, and occupies some rectangle on the screen. Any widget in Vasya's library is of type Widget. For simplicity we will identify the widget and its type. Types HBox and VBox are derivatives of type Widget, so they also are types Widget. Widgets HBox and VBox are special. They can store other widgets. Both those widgets can use the pack() method to pack directly in itself some other widget. Widgets of types HBox and VBox can store several other widgets, even several equal widgets — they will simply appear several times. As a result of using the method pack() only the link to the packed widget is saved, that is when the packed widget is changed, its image in the widget, into which it is packed, will also change. We shall assume that the widget a is packed in the widget b if there exists a chain of widgets a = c1, c2, ..., ck = b, k ≥ 2, for which ci is packed directly to ci + 1 for any 1 ≤ i < k. In Vasya's library the situation when the widget a is packed in the widget a (that is, in itself) is not allowed. If you try to pack the widgets into each other in this manner immediately results in an error. Also, the widgets HBox and VBox have parameters border and spacing, which are determined by the methods set_border() and set_spacing() respectively. By default both of these options equal 0. <image> The picture above shows how the widgets are packed into HBox and VBox. At that HBox and VBox automatically change their size depending on the size of packed widgets. As for HBox and VBox, they only differ in that in HBox the widgets are packed horizontally and in VBox — vertically. The parameter spacing sets the distance between adjacent widgets, and border — a frame around all packed widgets of the desired width. Packed widgets are placed exactly in the order in which the pack() method was called for them. If within HBox or VBox there are no packed widgets, their sizes are equal to 0 × 0, regardless of the options border and spacing. The construction of all the widgets is performed using a scripting language VasyaScript. The description of the language can be found in the input data. For the final verification of the code Vasya asks you to write a program that calculates the sizes of all the widgets on the source code in the language of VasyaScript. Input The first line contains an integer n — the number of instructions (1 ≤ n ≤ 100). Next n lines contain instructions in the language VasyaScript — one instruction per line. There is a list of possible instructions below. * "Widget [name]([x],[y])" — create a new widget [name] of the type Widget possessing the width of [x] units and the height of [y] units. * "HBox [name]" — create a new widget [name] of the type HBox. * "VBox [name]" — create a new widget [name] of the type VBox. * "[name1].pack([name2])" — pack the widget [name2] in the widget [name1]. At that, the widget [name1] must be of type HBox or VBox. * "[name].set_border([x])" — set for a widget [name] the border parameter to [x] units. The widget [name] must be of type HBox or VBox. * "[name].set_spacing([x])" — set for a widget [name] the spacing parameter to [x] units. The widget [name] must be of type HBox or VBox. All instructions are written without spaces at the beginning and at the end of the string. The words inside the instruction are separated by exactly one space. There are no spaces directly before the numbers and directly after them. The case matters, for example, "wiDget x" is not a correct instruction. The case of the letters is correct in the input data. All names of the widgets consist of lowercase Latin letters and has the length from 1 to 10 characters inclusive. The names of all widgets are pairwise different. All numbers in the script are integers from 0 to 100 inclusive It is guaranteed that the above-given script is correct, that is that all the operations with the widgets take place after the widgets are created and no widget is packed in itself. It is guaranteed that the script creates at least one widget. Output For each widget print on a single line its name, width and height, separated by spaces. The lines must be ordered lexicographically by a widget's name. Please, do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use cout stream (also you may use %I64d specificator) Examples Input 12 Widget me(50,40) VBox grandpa HBox father grandpa.pack(father) father.pack(me) grandpa.set_border(10) grandpa.set_spacing(20) Widget brother(30,60) father.pack(brother) Widget friend(20,60) Widget uncle(100,20) grandpa.pack(uncle) Output brother 30 60 father 80 60 friend 20 60 grandpa 120 120 me 50 40 uncle 100 20 Input 15 Widget pack(10,10) HBox dummy HBox x VBox y y.pack(dummy) y.set_border(5) y.set_spacing(55) dummy.set_border(10) dummy.set_spacing(20) x.set_border(10) x.set_spacing(10) x.pack(pack) x.pack(dummy) x.pack(pack) x.set_border(0) Output dummy 0 0 pack 10 10 x 40 10 y 10 10 Note In the first sample the widgets are arranged as follows: <image> The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Dima is a beginner programmer. During his working process, he regularly has to repeat the following operation again and again: to remove every second element from the array. One day he has been bored with easy solutions of this problem, and he has come up with the following extravagant algorithm. Let's consider that initially array contains n numbers from 1 to n and the number i is located in the cell with the index 2i - 1 (Indices are numbered starting from one) and other cells of the array are empty. Each step Dima selects a non-empty array cell with the maximum index and moves the number written in it to the nearest empty cell to the left of the selected one. The process continues until all n numbers will appear in the first n cells of the array. For example if n = 4, the array is changing as follows: <image> You have to write a program that allows you to determine what number will be in the cell with index x (1 ≤ x ≤ n) after Dima's algorithm finishes. Input The first line contains two integers n and q (1 ≤ n ≤ 1018, 1 ≤ q ≤ 200 000), the number of elements in the array and the number of queries for which it is needed to find the answer. Next q lines contain integers xi (1 ≤ xi ≤ n), the indices of cells for which it is necessary to output their content after Dima's algorithm finishes. Output For each of q queries output one integer number, the value that will appear in the corresponding array cell after Dima's algorithm finishes. Examples Input 4 3 2 3 4 Output 3 2 4 Input 13 4 10 5 4 8 Output 13 3 8 9 Note The first example is shown in the picture. In the second example the final array is [1, 12, 2, 8, 3, 11, 4, 9, 5, 13, 6, 10, 7]. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm: * if the last digit of the number is non-zero, she decreases the number by one; * if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit). You are given an integer number n. Tanya will subtract one from it k times. Your task is to print the result after all k subtractions. It is guaranteed that the result will be positive integer number. Input The first line of the input contains two integer numbers n and k (2 ≤ n ≤ 10^9, 1 ≤ k ≤ 50) — the number from which Tanya will subtract and the number of subtractions correspondingly. Output Print one integer number — the result of the decreasing n by one k times. It is guaranteed that the result will be positive integer number. Examples Input 512 4 Output 50 Input 1000000000 9 Output 1 Note The first example corresponds to the following sequence: 512 → 511 → 510 → 51 → 50. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. For a vector \vec{v} = (x, y), define \|v\| = √{x^2 + y^2}. Allen had a bit too much to drink at the bar, which is at the origin. There are n vectors \vec{v_1}, \vec{v_2}, ⋅⋅⋅, \vec{v_n}. Allen will make n moves. As Allen's sense of direction is impaired, during the i-th move he will either move in the direction \vec{v_i} or -\vec{v_i}. In other words, if his position is currently p = (x, y), he will either move to p + \vec{v_i} or p - \vec{v_i}. Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position p satisfies \|p\| ≤ 1.5 ⋅ 10^6 so that he can stay safe. Input The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of moves. Each of the following lines contains two space-separated integers x_i and y_i, meaning that \vec{v_i} = (x_i, y_i). We have that \|v_i\| ≤ 10^6 for all i. Output Output a single line containing n integers c_1, c_2, ⋅⋅⋅, c_n, each of which is either 1 or -1. Your solution is correct if the value of p = ∑_{i = 1}^n c_i \vec{v_i}, satisfies \|p\| ≤ 1.5 ⋅ 10^6. It can be shown that a solution always exists under the given constraints. Examples Input 3 999999 0 0 999999 999999 0 Output 1 1 -1 Input 1 -824590 246031 Output 1 Input 8 -67761 603277 640586 -396671 46147 -122580 569609 -2112 400 914208 131792 309779 -850150 -486293 5272 721899 Output 1 1 1 1 1 1 1 -1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Today Oz is playing a new game. He has an array arr[] of N distinct integers . In each turn he is will follow two actions - 1) He select a random number from arr[]. Say value of this element is X. 2) He will remove X from arr[]. if X-1 is present in arr[] then he will remove it. if X+1 is present in arr[] then he will remove it. Oz will make turns until arr[] becomes empty. Oz loves this game so he wants to make maximum number of possible turns. Help Oz to make maximum number of possible turns. Input : The first line contains the number of test cases - T . Each test case consist of two lines. First line will contain a integer N - number of elements in arr[]. Second line will contain N space separated integers. Output : For each test case output maximum number of possible turns that Oz can make. Constraints : 1 ≤ T ≤ 100 1 ≤ N ≤ 100 1 ≤ each element of arr[] ≤ 1000 SAMPLE INPUT 1 6 291 292 295 297 298 299 SAMPLE OUTPUT 4 Explanation One of the possible way to make 4 turns is by choosing the following elements in each turn: 297, 299, 295, 292. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Professor Hatim is researching the sexual behavior of a rare species of lizard. He assumes that they feature two different genders and that they only interact with lizard of the opposite gender. Each lizard has a integer printed on their back. Given the details of lizard interactions, decide whether the experiment supports his assumption of two genders with no homosexual bugs, or if it contains some bug interactions that falsify it. Or simply, you have to print "Suspicious lizard found!" (without quotes), if an interaction of two lizards of same gender is found in the list of interactions, otherwise print "No suspicious lizard found!" (without quotes). Input format: The first line contains an integer T, denoting the number of test cases. The first line of each test case contains two integers N and M, where N denotes the number of lizards and M denotes the number of interactions. Next M lines of each test case contains, two space separated integers, say x and y , denoting the interaction between lizard no. x and lizard no. y. Note: Integers on the back of lizards are numbered from 1 to N. Output format: For each test case ,print a line, saying either “No suspicious lizard found!” if the experiment is consistent with his assumption about the lizard sexual behavior, or “Suspicious lizard found!” if Professor Hatims’s assumption is definitely wrong. Constraints: 1 ≤ T ≤ 5 2 ≤ N ≤ 2000 1 ≤ M ≤ 10^5 SAMPLE INPUT 2 3 3 1 2 2 3 1 3 4 2 1 2 3 4 SAMPLE OUTPUT Suspicious lizards found! No suspicious lizards found! The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There is a street by the name of colorful street in the Pretty Town. The residents of the house have decided that they will paint their houses in either Pink, Orange or Yellow color and not other. They have also decided that no two adjacent houses will have the same color. For house i, i-1 and i+1 are the neighbors and note that the first and the last house are not neighbors. The cost of painting a house in a particular color is different. The cost of painting the first house in color yellow maybe different than what its for painting the second house in the same color. You have to find the minimum of cost of painting the houses which satisfy the given condition. Input Constraints - Number of houses will contain between 1 and 20 elements, inclusive. - Each line of input for houses will have three values for cost of coloring in each color. Each value will be between 1 and 1000. Input Format - The first line will contain the number of test cases - T. - The second line will contain an integer N that will specify how many houses are there. - Each of the following N lines will contain 3 numbers separated by space that represents the cost of painting that house in either pink, orange or yellow color. Output Format Print T lines showing the cost of painting the houses for each test case. SAMPLE INPUT 1 2 11 12 13 14 15 16 SAMPLE OUTPUT 26 Explanation The first house should be painted in pink (11), the second should be painted in orange (15). So the total cost becomes 11+15 = 26 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Xenny had N cubes. Each cube had six faces and each face had a Latin character on each of it's sides. Xenny's friend Asdoc had an interesting activity in mind. He gave Xenny a string S and asked him to use the cubes to form that string. Xenny being a very lazy person, just wanted to randomly roll the cubes and then arrange a subset of them, to form the string S. Xenny relied on probability to get the desired string from the characters on the cubes. Given the character on each face of each of the cubes, find out the the number of ways in which Xenny is able to make string S using the upward facing characters. Input: The first line of input consists of 2 space-separated integers - N and K - the number of cubes and the length of string S respectively. N lines follow. Each line contains 6 space-separated characters, with i^th line representing the characters on the 6 faces of the i^th cube. Last line of input contains string S. Output: Output the required number of ways MOD 10^9 + 7. Constraints: 1 ≤ N ≤ 10 1 ≤ K ≤ N S consists of lower-case Latin characters SAMPLE INPUT 5 4 a a a a a a a a a a a a b b b b b b c c c c c c d d d d d d abcd SAMPLE OUTPUT 2592 Explanation Lets number the cubes: 1. a a a a a a 2. a a a a a a 3. b b b b b b 4. c c c c c c 5. d d d d d d We want to form the string: "abcd" The possible arrangements of cubes are: 1-3-4-5 and 2-3-4-5. In arrangement 1-3-4-5, there are 6 ways to get 'a', 6 ways to get 'b', 6 ways to get 'c' and 6 ways to get 'd'. The same number of ways are possible for the arrangement 2-3-4-5. Hence, total number of ways = 6^4 + 6^4 = 2592. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown. We will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum. Constraints * 1 ≤ K ≤ N ≤ 200000 * 1 ≤ p_i ≤ 1000 * All values in input are integers. Input Input is given from Standard Input in the following format: N K p_1 ... p_N Output Print the maximum possible value of the expected value of the sum of the numbers shown. Your output will be considered correct when its absolute or relative error from our answer is at most 10^{-6}. Examples Input 5 3 1 2 2 4 5 Output 7.000000000000 Input 4 1 6 6 6 6 Output 3.500000000000 Input 10 4 17 13 13 12 15 20 10 13 17 11 Output 32.000000000000 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Takahashi is going to set a 3-character password. How many possible passwords are there if each of its characters must be a digit between 1 and N (inclusive)? Constraints * 1 \leq N \leq 9 * N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of possible passwords. Examples Input 2 Output 8 Input 1 Output 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. An integer X is called a Harshad number if X is divisible by f(X), where f(X) is the sum of the digits in X when written in base 10. Given an integer N, determine whether it is a Harshad number. Constraints * 1?N?10^8 * N is an integer. Input Input is given from Standard Input in the following format: N Output Print `Yes` if N is a Harshad number; print `No` otherwise. Examples Input 12 Output Yes Input 57 Output No Input 148 Output No The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Fennec and Snuke are playing a board game. On the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree. Initially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored. Fennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell. More specifically, each player performs the following action in her/his turn: * Fennec: selects an uncolored cell that is adjacent to a black cell, and paints it black. * Snuke: selects an uncolored cell that is adjacent to a white cell, and paints it white. A player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally. Constraints * 2 \leq N \leq 10^5 * 1 \leq a_i, b_i \leq N * The given graph is a tree. Input Input is given from Standard Input in the following format: N a_1 b_1 : a_{N-1} b_{N-1} Output If Fennec wins, print `Fennec`; if Snuke wins, print `Snuke`. Examples Input 7 3 6 1 2 3 1 7 4 5 7 1 4 Output Fennec Input 4 1 4 4 2 2 3 Output Snuke The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Snuke has decided to play a game using cards. He has a deck consisting of N cards. On the i-th card from the top, an integer A_i is written. He will perform the operation described below zero or more times, so that the values written on the remaining cards will be pairwise distinct. Find the maximum possible number of remaining cards. Here, N is odd, which guarantees that at least one card can be kept. Operation: Take out three arbitrary cards from the deck. Among those three cards, eat two: one with the largest value, and another with the smallest value. Then, return the remaining one card to the deck. Constraints * 3 ≦ N ≦ 10^{5} * N is odd. * 1 ≦ A_i ≦ 10^{5} * A_i is an integer. Input The input is given from Standard Input in the following format: N A_1 A_2 A_3 ... A_{N} Output Print the answer. Examples Input 5 1 2 1 3 7 Output 3 Input 15 1 3 5 2 1 3 2 8 8 6 2 6 11 1 1 Output 7 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Create a program that outputs the surface area S of a square cone with a height of h, with a square with one side x as the base. However, assume that the line segment connecting the apex and the center of the base is orthogonal to the base. Also, x and h are positive integers less than or equal to 100. Input Given multiple datasets. Each dataset is given in the following format: x h When both x and h are 0, it indicates the end of input. Output Output S (real number) on one line for each data set. The output may contain an error of 0.00001 or less. Example Input 6 4 7 9 0 0 Output 96.000000 184.192455 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. A project is underway to build a new viewing tower in Bange town called “Bange Hills Tower” whose selling point will be the gorgeous view of the entire main keep of Wakamatsu Castle from top to bottom. Therefore, the view line from the top of the tower must reach the bottom of the keep without being hindered by any of the buildings in the town. <image> Write a program to calculate the minimum tower height required to view the keep in its entirety based on the following information: the planned location of the tower and the heights and locations of existing buildings. Assume all the buildings, including the keep, are vertical lines without horizontal stretch. “view of the entire keep” means that the view line from the tower top can cover the keep from the bottom to the top without intersecting (contacts at the top are exempted) any of the other vertical lines (i.e., buildings). Input The input is given in the following format. N t x_1 h_1 x_2 h_2 : x_N h_N The first line provides the number of existing buildings N (1≤N≤1000) and the planned location of the tower t (2≤t≤105) in integers. Each of the subsequent N lines provides the information of the i-th building: location x_i (1 ≤ x_i < t) and height from the ground h_i (1 ≤ h_i ≤ 100). All position information is one-dimensional along the ground line whose origin coincides with the Keep location. No more than one building is located in the same location (i.e. if i ≠ j, then x_i ≠ x_j). Output Output the required height as a real number. No limits on the number of decimal places as long as the error does not exceed ± 10-3. Example Input 3 10 6 4 4 2 3 2 Output 6.666667 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Once upon a time, there was a traveler. He plans to travel using stagecoaches (horse wagons). His starting point and destination are fixed, but he cannot determine his route. Your job in this problem is to write a program which determines the route for him. There are several cities in the country, and a road network connecting them. If there is a road between two cities, one can travel by a stagecoach from one of them to the other. A coach ticket is needed for a coach ride. The number of horses is specified in each of the tickets. Of course, with more horses, the coach runs faster. At the starting point, the traveler has a number of coach tickets. By considering these tickets and the information on the road network, you should find the best possible route that takes him to the destination in the shortest time. The usage of coach tickets should be taken into account. The following conditions are assumed. * A coach ride takes the traveler from one city to another directly connected by a road. In other words, on each arrival to a city, he must change the coach. * Only one ticket can be used for a coach ride between two cities directly connected by a road. * Each ticket can be used only once. * The time needed for a coach ride is the distance between two cities divided by the number of horses. * The time needed for the coach change should be ignored. Input The input consists of multiple datasets, each in the following format. The last dataset is followed by a line containing five zeros (separated by a space). > n m p a b > t1 t2 ... tn > x1 y1 z1 > x2 y2 z2 > ... > xp yp zp > Every input item in a dataset is a non-negative integer. If a line contains two or more input items, they are separated by a space. n is the number of coach tickets. You can assume that the number of tickets is between 1 and 8. m is the number of cities in the network. You can assume that the number of cities is between 2 and 30. p is the number of roads between cities, which may be zero. a is the city index of the starting city. b is the city index of the destination city. a is not equal to b. You can assume that all city indices in a dataset (including the above two) are between 1 and m. The second line of a dataset gives the details of coach tickets. ti is the number of horses specified in the i-th coach ticket (1<=i<=n). You can assume that the number of horses is between 1 and 10. The following p lines give the details of roads between cities. The i-th road connects two cities with city indices xi and yi, and has a distance zi (1<=i<=p). You can assume that the distance is between 1 and 100. No two roads connect the same pair of cities. A road never connects a city with itself. Each road can be traveled in both directions. Output For each dataset in the input, one line should be output as specified below. An output line should not contain extra characters such as spaces. If the traveler can reach the destination, the time needed for the best route (a route with the shortest time) should be printed. The answer should not have an error greater than 0.001. You may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied. If the traveler cannot reach the destination, the string "`Impossible`" should be printed. One cannot reach the destination either when there are no routes leading to the destination, or when the number of tickets is not sufficient. Note that the first letter of "`Impossible`" is in uppercase, while the other letters are in lowercase. Example Input 3 4 3 1 4 3 1 2 1 2 10 2 3 30 3 4 20 2 4 4 2 1 3 1 2 3 3 1 3 3 4 1 2 4 2 5 2 4 3 4 1 5 5 1 2 10 2 3 10 3 4 10 1 2 0 1 2 1 8 5 10 1 5 2 7 1 8 4 5 6 3 1 2 5 2 3 4 3 4 7 4 5 3 1 3 25 2 4 23 3 5 22 1 4 45 2 5 51 1 5 99 0 0 0 0 0 Output 30.000 3.667 Impossible Impossible 2.856 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given an undirected weighted graph G, you should find one of spanning trees specified as follows. The graph G is an ordered pair (V, E), where V is a set of vertices {v1, v2, ... , vn} and E is a set of undirected edges {e1, e2, ... , em}. Each edge e ∈ E has its weight w(e). A spanning tree T is a tree (a connected subgraph without cycles) which connects all the n vertices with n - 1 edges. The slimness of a spanning tree T is defined as the difference between the largest weight and the smallest weight among the n - 1 edges of T. <image> Figure 5: A graph G and the weights of the edges For example, a graph G in Figure 5(a) has four vertices {v1, v2, v3, v4} and five undirected edges {e1, e2, e3, e4, e5}. The weights of the edges are w(e1) = 3, w(e2) = 5, w(e3) = 6, w(e4) = 6, w(e5) = 7 as shown in Figure 5(b). <image> Figure 6: Examples of the spanning trees of G There are several spanning trees for G. Four of them are depicted in Figure 6(a)-(d). The spanning tree Ta in Figure 6(a) has three edges whose weights are 3, 6 and 7. The largest weight is 7 and the smallest weight is 3 so that the slimness of the tree Ta is 4. The slimnesses of spanning trees Tb , Tc and Td shown in Figure 6(b), (c) and (d) are 3, 2 and 1, respectively. You can easily see the slimness of any other spanning tree is greater than or equal to 1, thus the spanning tree Td in Figure 6(d) is one of the slimmest spanning trees whose slimness is 1. Your job is to write a program that computes the smallest slimness. Input The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset has the following format. n m a1 b1 w1 . . . am bm wm Every input item in a dataset is a non-negative integer. Items in a line are separated by a space. n is the number of the vertices and m the number of the edges. You can assume 2 ≤ n ≤ 100 and 0 ≤ m ≤ n(n - 1)/2. ak and bk (k = 1, ... , m) are positive integers less than or equal to n, which represent the two vertices vak and vbk connected by the kth edge ek. wk is a positive integer less than or equal to 10000, which indicates the weight of ek . You can assume that the graph G = (V, E) is simple, that is, there are no self-loops (that connect the same vertex) nor parallel edges (that are two or more edges whose both ends are the same two vertices). Output For each dataset, if the graph has spanning trees, the smallest slimness among them should be printed. Otherwise, -1 should be printed. An output should not contain extra characters. Example Input 4 5 1 2 3 1 3 5 1 4 6 2 4 6 3 4 7 4 6 1 2 10 1 3 100 1 4 90 2 3 20 2 4 80 3 4 40 2 1 1 2 1 3 0 3 1 1 2 1 3 3 1 2 2 2 3 5 1 3 6 5 10 1 2 110 1 3 120 1 4 130 1 5 120 2 3 110 2 4 120 2 5 130 3 4 120 3 5 110 4 5 120 5 10 1 2 9384 1 3 887 1 4 2778 1 5 6916 2 3 7794 2 4 8336 2 5 5387 3 4 493 3 5 6650 4 5 1422 5 8 1 2 1 2 3 100 3 4 100 4 5 100 1 5 50 2 5 50 3 5 50 4 1 150 0 0 Output 1 20 0 -1 -1 1 0 1686 50 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. At University A, there were many mistakes in entering IDs. Therefore, University A decided to issue a new ID to prevent typos. There is a way to check if the new ID is correct to prevent typos. ・ Calculate the sum of all digits. ・ However, the number of even-numbered digits is doubled, with the rightmost digit as the first digit. -When the number becomes 10 or more by doubling, the number obtained by adding the 1st digit and the 10th digit is used as the digit number. ・ If the sum is divisible by 10, the ID is correct, otherwise it is incorrect. As an example, check the ID 53579. Since the sum of all digits is calculated, 5 + 3 + 5 + 7 + 9 However, since the number of even-numbered digits is doubled, 5 + 6 + 5 + 14 + 9 When the number becomes 10 or more by doubling, the number obtained by adding the ones digit and the tens digit is the digit number. 5 + 6 + 5 + (1 + 4) + 9 From the above, the total sum is 30. Since 30 is divisible by 10, 53579 is the correct ID. Mr. B is a college student at University A and was issued a new ID, but he forgot some digits of the ID. However, I succeeded in narrowing down some candidates as to what kind of numbers will be included in the forgotten part. Your job is to find out how many correct combinations of B's IDs are available. Input The input is given in the following format. n ID m a0 a1 ... am-1 n is the number of digits in the ID. Each digit of the ID contains a number from 0 to 9 or the letter'' to indicate that it is a forgotten digit. m is the number of candidate numbers in the''. ai is a candidate for numbers in''. Input meets the following constraints 1 ≤ n ≤ 100,000 1 ≤ m ≤ 10 0 ≤ ai ≤ 9 Number of 1 ≤'' ≤ 7 Output Output the answer value on one line Examples Input 5 557 2 3 9 Output 1 Input 15 2**9261199* 9 0 1 2 3 4 6 7 8 9 Output 478297 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Problem Ghosts line up in a straight line from left to right with $ N $ people. At first, the $ i $ th ghost from the left is facing left if $ U_i $ is'L', and facing right if it is'R'. They are so timid that I don't want to see scary ghosts as much as possible. You can instruct each ghost to look back. It's scary to look back, so once the $ i $ th ghost looks back, it creates a fear of $ A_i $. When the ghost looking to the left looks back, it turns to the right. When the ghost looking to the right looks back, it turns to the left. For $ i <j $, if the $ i $ th ghost is pointing to the right and the $ j $ th ghost is pointing to the left, then the $ i $ th ghost and the $ j $ th ghost are pointing to the left. Is defined as facing each other. The following constraints are given in $ M $. The $ S_i $ th ghost is scared of the $ T_i $ th ghost. In the final state, if the $ S_i $ th ghost and the $ T_i $ th ghost face each other, a fear level of $ B_i $ will occur. Find the minimum value of the total fear that occurs when you give the optimal instructions. Constraints The input satisfies the following conditions. * $ 1 \ le N \ le 500 $ * $ 0 \ le M \ le \ min (N \ times (N-1), 1000) $ * $ \| U \| = N $ * $ U_i = $'L' or'R' * $ 1 \ le A_i \ le 1000 $ * $ 1 \ le B_i \ le 1000 $ * $ 1 \ le S_i, T_i \ le N $ * $ (S_i, T_i) \ ne (S_j, T_j), $ if $ i \ ne j $ * $ S_i \ ne T_i $ Input The input is given in the following format. $ N $ $ M $ $ U $ $ A_1 $ $ A_2 $ $ ... $ $ A_N $ $ S_1 $ $ T_1 $ $ B_1 $ $ S_2 $ $ T_2 $ $ B_2 $ $ \ vdots $ $ S_M $ $ T_M $ $ B_M $ All inputs are given as integers. Output Output the minimum value of the total fear level. Examples Input 3 1 RRL 5 5 1 3 1 10 Output 1 Input 5 5 RLRLL 9 5 1 3 10 1 3 5 2 4 9 4 2 16 1 5 2 3 5 10 Output 8 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. For a given polygon g, computes the area of the polygon. g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of g. The line segment connecting pn and p1 is also a side of the polygon. Note that the polygon is not necessarily convex. Constraints * 3 ≤ n ≤ 100 * -10000 ≤ xi, yi ≤ 10000 * No point will occur more than once. * Two sides can intersect only at a common endpoint. Input The input consists of coordinates of the points p1,..., pn in the following format: n x1 y1 x2 y2 : xn yn The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Output Print the area of the polygon in a line. The area should be printed with one digit to the right of the decimal point. Examples Input 3 0 0 2 2 -1 1 Output 2.0 Input 4 0 0 1 1 1 2 0 2 Output 1.5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Write a program which reads a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and rotate specified elements by a list of the following operation: * rotate($b, m, e$): For each integer $k$ ($0 \leq k < (e - b)$), move element $b + k$ to the place of element $b + ((k + (e - m)) \mod (e - b))$. Constraints * $1 \leq n \leq 1,000$ * $-1,000,000,000 \leq a_i \leq 1,000,000,000$ * $1 \leq q \leq 1,000$ * $0 \leq b_i \leq m_i < e_i \leq n$ Input The input is given in the following format. $n$ $a_0 \; a_1 \; ...,\; a_{n-1}$ $q$ $b_1 \; m_1 \; e_1$ $b_2 \; m_2 \; e_2$ : $b_{q} \; m_{q} \; e_{q}$ In the first line, $n$ (the number of elements in $A$) is given. In the second line, $a_i$ (each element in $A$) are given. In the third line, the number of queries $q$ is given and each query is given by three integers $b_i \; m_i \; e_i$ in the following $q$ lines. Output Print all elements of $A$ in a line after performing the given operations. Put a single space character between adjacency elements and a newline at the end of the last element. Example Input 11 1 2 3 4 5 6 7 8 9 10 11 1 2 6 9 Output 1 2 7 8 9 3 4 5 6 10 11 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given two strings s and t. The string s consists of lowercase Latin letters and at most one wildcard character '', the string t consists only of lowercase Latin letters. The length of the string s equals n, the length of the string t equals m. The wildcard character '' in the string s (if any) can be replaced with an arbitrary sequence (possibly empty) of lowercase Latin letters. No other character of s can be replaced with anything. If it is possible to replace a wildcard character '' in s to obtain a string t, then the string t matches the pattern s. For example, if s="abaaba" then the following strings match it "abaaba", "abacaba" and "abazzzaba", but the following strings do not match: "ababa", "abcaaba", "codeforces", "aba1aba", "aba?aba". If the given string t matches the given string s, print "YES", otherwise print "NO". Input The first line contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5) — the length of the string s and the length of the string t, respectively. The second line contains string s of length n, which consists of lowercase Latin letters and at most one wildcard character ''. The third line contains string t of length m, which consists only of lowercase Latin letters. Output Print "YES" (without quotes), if you can obtain the string t from the string s. Otherwise print "NO" (without quotes). Examples Input 6 10 codes codeforces Output YES Input 6 5 vkcup vkcup Output YES Input 1 1 v k Output NO Input 9 6 gfgfgfgf gfgfgf Output NO Note In the first example a wildcard character '' can be replaced with a string "force". So the string s after this replacement is "codeforces" and the answer is "YES". In the second example a wildcard character '' can be replaced with an empty string. So the string s after this replacement is "vkcup" and the answer is "YES". There is no wildcard character '' in the third example and the strings "v" and "k" are different so the answer is "NO". In the fourth example there is no such replacement of a wildcard character '' that you can obtain the string t so the answer is "NO". The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are playing a strange game with Li Chen. You have a tree with n nodes drawn on a piece of paper. All nodes are unlabeled and distinguishable. Each of you independently labeled the vertices from 1 to n. Neither of you know the other's labelling of the tree. You and Li Chen each chose a subtree (i.e., a connected subgraph) in that tree. Your subtree consists of the vertices labeled x_1, x_2, …, x_{k_1} in your labeling, Li Chen's subtree consists of the vertices labeled y_1, y_2, …, y_{k_2} in his labeling. The values of x_1, x_2, …, x_{k_1} and y_1, y_2, …, y_{k_2} are known to both of you. <image> The picture shows two labelings of a possible tree: yours on the left and Li Chen's on the right. The selected trees are highlighted. There are two common nodes. You want to determine whether your subtrees have at least one common vertex. Luckily, your friend Andrew knows both labelings of the tree. You can ask Andrew at most 5 questions, each of which is in one of the following two forms: * A x: Andrew will look at vertex x in your labeling and tell you the number of this vertex in Li Chen's labeling. * B y: Andrew will look at vertex y in Li Chen's labeling and tell you the number of this vertex in your labeling. Determine whether the two subtrees have at least one common vertex after asking some questions. If there is at least one common vertex, determine one of your labels for any of the common vertices. Interaction Each test consists of several test cases. The first line of input contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. For each testcase, your program should interact in the following format. The first line contains a single integer n (1 ≤ n ≤ 1 000) — the number of nodes in the tree. Each of the next n-1 lines contains two integers a_i and b_i (1≤ a_i, b_i≤ n) — the edges of the tree, indicating an edge between node a_i and b_i according to your labeling of the nodes. The next line contains a single integer k_1 (1 ≤ k_1 ≤ n) — the number of nodes in your subtree. The next line contains k_1 distinct integers x_1,x_2,…,x_{k_1} (1 ≤ x_i ≤ n) — the indices of the nodes in your subtree, according to your labeling. It is guaranteed that these vertices form a subtree. The next line contains a single integer k_2 (1 ≤ k_2 ≤ n) — the number of nodes in Li Chen's subtree. The next line contains k_2 distinct integers y_1, y_2, …, y_{k_2} (1 ≤ y_i ≤ n) — the indices (according to Li Chen's labeling) of the nodes in Li Chen's subtree. It is guaranteed that these vertices form a subtree according to Li Chen's labelling of the tree's nodes. Test cases will be provided one by one, so you must complete interacting with the previous test (i.e. by printing out a common node or -1 if there is not such node) to start receiving the next one. You can ask the Andrew two different types of questions. * You can print "A x" (1 ≤ x ≤ n). Andrew will look at vertex x in your labeling and respond to you with the number of this vertex in Li Chen's labeling. * You can print "B y" (1 ≤ y ≤ n). Andrew will look at vertex y in Li Chen's labeling and respond to you with the number of this vertex in your labeling. You may only ask at most 5 questions per tree. When you are ready to answer, print "C s", where s is your label of a vertex that is common to both subtrees, or -1, if no such vertex exists. Printing the answer does not count as a question. Remember to flush your answer to start receiving the next test case. After printing a question do not forget to print end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use: * fflush(stdout) or cout.flush() in C++; * System.out.flush() in Java; * flush(output) in Pascal; * stdout.flush() in Python; * see documentation for other languages. If the judge responds with -1, it means that you asked more queries than allowed, or asked an invalid query. Your program should immediately terminate (for example, by calling exit(0)). You will receive Wrong Answer; it means that you asked more queries than allowed, or asked an invalid query. If you ignore this, you can get other verdicts since your program will continue to read from a closed stream. Hack Format To hack, use the following format. Note that you can only hack with one test case. The first line should contain a single integer t (t=1). The second line should contain a single integer n (1 ≤ n ≤ 1 000). The third line should contain n integers p_1, p_2, …, p_n (1≤ p_i≤ n) — a permutation of 1 to n. This encodes the labels that Li Chen chose for his tree. In particular, Li Chen chose label p_i for the node you labeled i. Each of the next n-1 lines should contain two integers a_i and b_i (1≤ a_i, b_i≤ n). These edges should form a tree. The next line should contain a single integer k_1 (1 ≤ k_1 ≤ n). The next line should contain k_1 distinct integers x_1,x_2,…,x_{k_1} (1 ≤ x_i ≤ n). These vertices should form a subtree. The next line should contain a single integer k_2 (1 ≤ k_2 ≤ n). The next line should contain k_2 distinct integers y_1, y_2, …, y_{k_2} (1 ≤ y_i ≤ n). These vertices should form a subtree in Li Chen's tree according to the permutation above. Examples Input 1 3 1 2 2 3 1 1 1 2 2 1 Output A 1 B 2 C 1 Input 2 6 1 2 1 3 1 4 4 5 4 6 4 1 3 4 5 3 3 5 2 3 6 1 2 1 3 1 4 4 5 4 6 3 1 2 3 3 4 1 6 5 Output B 2 C 1 A 1 C -1 Note For the first sample, Li Chen's hidden permutation is [2, 3, 1], and for the second, his hidden permutation is [5, 3, 2, 4, 1, 6] for both cases. In the first sample, there is a tree with three nodes in a line. On the top, is how you labeled the tree and the subtree you chose, and the bottom is how Li Chen labeled the tree and the subtree he chose: <image> In the first question, you ask Andrew to look at node 1 in your labelling and tell you the label of it in Li Chen's labelling. Andrew responds with 2. At this point, you know that both of your subtrees contain the same node (i.e. node 1 according to your labeling), so you can output "C 1" and finish. However, you can also ask Andrew to look at node 2 in Li Chen's labelling and tell you the label of it in your labelling. Andrew responds with 1 (this step was given with the only reason — to show you how to ask questions). For the second sample, there are two test cases. The first looks is the one from the statement: <image> We first ask "B 2", and Andrew will tell us 3. In this case, we know 3 is a common vertex, and moreover, any subtree with size 3 that contains node 3 must contain node 1 as well, so we can output either "C 1" or "C 3" as our answer. In the second case in the second sample, the situation looks as follows: <image> In this case, you know that the only subtree of size 3 that doesn't contain node 1 is subtree 4,5,6. You ask Andrew for the label of node 1 in Li Chen's labelling and Andrew says 5. In this case, you know that Li Chen's subtree doesn't contain node 1, so his subtree must be consist of the nodes 4,5,6 (in your labelling), thus the two subtrees have no common nodes. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Ivan unexpectedly saw a present from one of his previous birthdays. It is array of n numbers from 1 to 200. Array is old and some numbers are hard to read. Ivan remembers that for all elements at least one of its neighbours ls not less than it, more formally: a_{1} ≤ a_{2}, a_{n} ≤ a_{n-1} and a_{i} ≤ max(a_{i-1}, a_{i+1}) for all i from 2 to n-1. Ivan does not remember the array and asks to find the number of ways to restore it. Restored elements also should be integers from 1 to 200. Since the number of ways can be big, print it modulo 998244353. Input First line of input contains one integer n (2 ≤ n ≤ 10^{5}) — size of the array. Second line of input contains n integers a_{i} — elements of array. Either a_{i} = -1 or 1 ≤ a_{i} ≤ 200. a_{i} = -1 means that i-th element can't be read. Output Print number of ways to restore the array modulo 998244353. Examples Input 3 1 -1 2 Output 1 Input 2 -1 -1 Output 200 Note In the first example, only possible value of a_{2} is 2. In the second example, a_{1} = a_{2} so there are 200 different values because all restored elements should be integers between 1 and 200. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Arkady invited Anna for a dinner to a sushi restaurant. The restaurant is a bit unusual: it offers n pieces of sushi aligned in a row, and a customer has to choose a continuous subsegment of these sushi to buy. The pieces of sushi are of two types: either with tuna or with eel. Let's denote the type of the i-th from the left sushi as t_i, where t_i = 1 means it is with tuna, and t_i = 2 means it is with eel. Arkady does not like tuna, Anna does not like eel. Arkady wants to choose such a continuous subsegment of sushi that it has equal number of sushi of each type and each half of the subsegment has only sushi of one type. For example, subsegment [2, 2, 2, 1, 1, 1] is valid, but subsegment [1, 2, 1, 2, 1, 2] is not, because both halves contain both types of sushi. Find the length of the longest continuous subsegment of sushi Arkady can buy. Input The first line contains a single integer n (2 ≤ n ≤ 100 000) — the number of pieces of sushi. The second line contains n integers t_1, t_2, ..., t_n (t_i = 1, denoting a sushi with tuna or t_i = 2, denoting a sushi with eel), representing the types of sushi from left to right. It is guaranteed that there is at least one piece of sushi of each type. Note that it means that there is at least one valid continuous segment. Output Print a single integer — the maximum length of a valid continuous segment. Examples Input 7 2 2 2 1 1 2 2 Output 4 Input 6 1 2 1 2 1 2 Output 2 Input 9 2 2 1 1 1 2 2 2 2 Output 6 Note In the first example Arkady can choose the subsegment [2, 2, 1, 1] or the subsegment [1, 1, 2, 2] with length 4. In the second example there is no way but to choose one of the subsegments [2, 1] or [1, 2] with length 2. In the third example Arkady's best choice is the subsegment [1, 1, 1, 2, 2, 2]. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a set of points x_1, x_2, ..., x_n on the number line. Two points i and j can be matched with each other if the following conditions hold: * neither i nor j is matched with any other point; * \|x_i - x_j\| ≥ z. What is the maximum number of pairs of points you can match with each other? Input The first line contains two integers n and z (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ z ≤ 10^9) — the number of points and the constraint on the distance between matched points, respectively. The second line contains n integers x_1, x_2, ..., x_n (1 ≤ x_i ≤ 10^9). Output Print one integer — the maximum number of pairs of points you can match with each other. Examples Input 4 2 1 3 3 7 Output 2 Input 5 5 10 9 5 8 7 Output 1 Note In the first example, you may match point 1 with point 2 (\|3 - 1\| ≥ 2), and point 3 with point 4 (\|7 - 3\| ≥ 2). In the second example, you may match point 1 with point 3 (\|5 - 10\| ≥ 5). The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given two integers b and w. You have a chessboard of size 10^9 × 10^9 with the top left cell at (1; 1), the cell (1; 1) is painted white. Your task is to find a connected component on this chessboard that contains exactly b black cells and exactly w white cells. Two cells are called connected if they share a side (i.e. for the cell (x, y) there are at most four connected cells: (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)). A set of cells is called a connected component if for every pair of cells C_1 and C_2 from this set, there exists a sequence of cells c_1, c_2, ..., c_k such that c_1 = C_1, c_k = C_2, all c_i from 1 to k are belong to this set of cells and for every i ∈ [1, k - 1], cells c_i and c_{i + 1} are connected. Obviously, it can be impossible to find such component. In this case print "NO". Otherwise, print "YES" and any suitable connected component. You have to answer q independent queries. Input The first line of the input contains one integer q (1 ≤ q ≤ 10^5) — the number of queries. Then q queries follow. The only line of the query contains two integers b and w (1 ≤ b, w ≤ 10^5) — the number of black cells required and the number of white cells required. It is guaranteed that the sum of numbers of cells does not exceed 2 ⋅ 10^5 (∑ w + ∑ b ≤ 2 ⋅ 10^5). Output For each query, print the answer to it. If it is impossible to find the required component, print "NO" on the first line. Otherwise, print "YES" on the first line. In the next b + w lines print coordinates of cells of your component in any order. There should be exactly b black cells and w white cells in your answer. The printed component should be connected. If there are several answers, you can print any. All coordinates in the answer should be in the range [1; 10^9]. Example Input 3 1 1 1 4 2 5 Output YES 2 2 1 2 YES 2 3 1 3 3 3 2 2 2 4 YES 2 3 2 4 2 5 1 3 1 5 3 3 3 5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Hanh lives in a shared apartment. There are n people (including Hanh) living there, each has a private fridge. n fridges are secured by several steel chains. Each steel chain connects two different fridges and is protected by a digital lock. The owner of a fridge knows passcodes of all chains connected to it. A fridge can be open only if all chains connected to it are unlocked. For example, if a fridge has no chains connected to it at all, then any of n people can open it. <image> For exampe, in the picture there are n=4 people and 5 chains. The first person knows passcodes of two chains: 1-4 and 1-2. The fridge 1 can be open by its owner (the person 1), also two people 2 and 4 (acting together) can open it. The weights of these fridges are a_1, a_2, …, a_n. To make a steel chain connecting fridges u and v, you have to pay a_u + a_v dollars. Note that the landlord allows you to create multiple chains connecting the same pair of fridges. Hanh's apartment landlord asks you to create exactly m steel chains so that all fridges are private. A fridge is private if and only if, among n people living in the apartment, only the owner can open it (i.e. no other person acting alone can do it). In other words, the fridge i is not private if there exists the person j (i ≠ j) that the person j can open the fridge i. For example, in the picture all the fridges are private. On the other hand, if there are n=2 fridges and only one chain (which connects them) then both fridges are not private (both fridges can be open not only by its owner but also by another person). Of course, the landlord wants to minimize the total cost of all steel chains to fulfill his request. Determine whether there exists any way to make exactly m chains, and if yes, output any solution that minimizes the total cost. Input Each test contains multiple test cases. The first line contains the number of test cases T (1 ≤ T ≤ 10). Then the descriptions of the test cases follow. The first line of each test case contains two integers n, m (2 ≤ n ≤ 1000, 1 ≤ m ≤ n) — the number of people living in Hanh's apartment and the number of steel chains that the landlord requires, respectively. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^4) — weights of all fridges. Output For each test case: * If there is no solution, print a single integer -1. * Otherwise, print a single integer c — the minimum total cost. The i-th of the next m lines contains two integers u_i and v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i), meaning that the i-th steel chain connects fridges u_i and v_i. An arbitrary number of chains can be between a pair of fridges. If there are multiple answers, print any. Example Input 3 4 4 1 1 1 1 3 1 1 2 3 3 3 1 2 3 Output 8 1 2 4 3 3 2 4 1 -1 12 3 2 1 2 3 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Polycarp is sad — New Year is coming in few days but there is still no snow in his city. To bring himself New Year mood, he decided to decorate his house with some garlands. The local store introduced a new service this year, called "Build your own garland". So you can buy some red, green and blue lamps, provide them and the store workers will solder a single garland of them. The resulting garland will have all the lamps you provided put in a line. Moreover, no pair of lamps of the same color will be adjacent to each other in this garland! For example, if you provide 3 red, 3 green and 3 blue lamps, the resulting garland can look like this: "RGBRBGBGR" ("RGB" being the red, green and blue color, respectively). Note that it's ok to have lamps of the same color on the ends of the garland. However, if you provide, say, 1 red, 10 green and 2 blue lamps then the store workers won't be able to build any garland of them. Any garland consisting of these lamps will have at least one pair of lamps of the same color adjacent to each other. Note that the store workers should use all the lamps you provided. So Polycarp has bought some sets of lamps and now he wants to know if the store workers can build a garland from each of them. Input The first line contains a single integer t (1 ≤ t ≤ 100) — the number of sets of lamps Polycarp has bought. Each of the next t lines contains three integers r, g and b (1 ≤ r, g, b ≤ 10^9) — the number of red, green and blue lamps in the set, respectively. Output Print t lines — for each set of lamps print "Yes" if the store workers can build a garland from them and "No" otherwise. Example Input 3 3 3 3 1 10 2 2 1 1 Output Yes No Yes Note The first two sets are desribed in the statement. The third set produces garland "RBRG", for example. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Catherine received an array of integers as a gift for March 8. Eventually she grew bored with it, and she started calculated various useless characteristics for it. She succeeded to do it for each one she came up with. But when she came up with another one — xor of all pairwise sums of elements in the array, she realized that she couldn't compute it for a very large array, thus she asked for your help. Can you do it? Formally, you need to compute $$$ (a_1 + a_2) ⊕ (a_1 + a_3) ⊕ … ⊕ (a_1 + a_n) \\\ ⊕ (a_2 + a_3) ⊕ … ⊕ (a_2 + a_n) \\\ … \\\ ⊕ (a_{n-1} + a_n) \\\ $$$ Here x ⊕ y is a bitwise XOR operation (i.e. x ^ y in many modern programming languages). You can read about it in Wikipedia: <https://en.wikipedia.org/wiki/Exclusive_or#Bitwise_operation>. Input The first line contains a single integer n (2 ≤ n ≤ 400 000) — the number of integers in the array. The second line contains integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7). Output Print a single integer — xor of all pairwise sums of integers in the given array. Examples Input 2 1 2 Output 3 Input 3 1 2 3 Output 2 Note In the first sample case there is only one sum 1 + 2 = 3. In the second sample case there are three sums: 1 + 2 = 3, 1 + 3 = 4, 2 + 3 = 5. In binary they are represented as 011_2 ⊕ 100_2 ⊕ 101_2 = 010_2, thus the answer is 2. ⊕ is the bitwise xor operation. To define x ⊕ y, consider binary representations of integers x and y. We put the i-th bit of the result to be 1 when exactly one of the i-th bits of x and y is 1. Otherwise, the i-th bit of the result is put to be 0. For example, 0101_2 ⊕ 0011_2 = 0110_2. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Nastya just made a huge mistake and dropped a whole package of rice on the floor. Mom will come soon. If she sees this, then Nastya will be punished. In total, Nastya dropped n grains. Nastya read that each grain weighs some integer number of grams from a - b to a + b, inclusive (numbers a and b are known), and the whole package of n grains weighs from c - d to c + d grams, inclusive (numbers c and d are known). The weight of the package is the sum of the weights of all n grains in it. Help Nastya understand if this information can be correct. In other words, check whether each grain can have such a mass that the i-th grain weighs some integer number x_i (a - b ≤ x_i ≤ a + b), and in total they weigh from c - d to c + d, inclusive (c - d ≤ ∑_{i=1}^{n}{x_i} ≤ c + d). Input The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. The next t lines contain descriptions of the test cases, each line contains 5 integers: n (1 ≤ n ≤ 1000) — the number of grains that Nastya counted and a, b, c, d (0 ≤ b < a ≤ 1000, 0 ≤ d < c ≤ 1000) — numbers that determine the possible weight of one grain of rice (from a - b to a + b) and the possible total weight of the package (from c - d to c + d). Output For each test case given in the input print "Yes", if the information about the weights is not inconsistent, and print "No" if n grains with masses from a - b to a + b cannot make a package with a total mass from c - d to c + d. Example Input 5 7 20 3 101 18 11 11 10 234 2 8 9 7 250 122 19 41 21 321 10 3 10 8 6 1 Output Yes No Yes No Yes Note In the first test case of the example, we can assume that each grain weighs 17 grams, and a pack 119 grams, then really Nastya could collect the whole pack. In the third test case of the example, we can assume that each grain weighs 16 grams, and a pack 128 grams, then really Nastya could collect the whole pack. In the fifth test case of the example, we can be assumed that 3 grains of rice weigh 2, 2, and 3 grams, and a pack is 7 grams, then really Nastya could collect the whole pack. In the second and fourth test cases of the example, we can prove that it is impossible to determine the correct weight of all grains of rice and the weight of the pack so that the weight of the pack is equal to the total weight of all collected grains. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Shubham has an array a of size n, and wants to select exactly x elements from it, such that their sum is odd. These elements do not have to be consecutive. The elements of the array are not guaranteed to be distinct. Tell him whether he can do so. Input The first line of the input contains a single integer t (1≤ t ≤ 100) — the number of test cases. The description of the test cases follows. The first line of each test case contains two integers n and x (1 ≤ x ≤ n ≤ 1000) — the length of the array and the number of elements you need to choose. The next line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 1000) — elements of the array. Output For each test case, print "Yes" or "No" depending on whether it is possible to choose x elements such that their sum is odd. You may print every letter in any case you want. Example Input 5 1 1 999 1 1 1000 2 1 51 50 2 2 51 50 3 3 101 102 103 Output Yes No Yes Yes No Note For 1st case: We must select element 999, and the sum is odd. For 2nd case: We must select element 1000, so overall sum is not odd. For 3rd case: We can select element 51. For 4th case: We must select both elements 50 and 51 — so overall sum is odd. For 5th case: We must select all elements — but overall sum is not odd. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Every year Santa Claus gives gifts to all children. However, each country has its own traditions, and this process takes place in different ways. For example, in Berland you need to solve the New Year's puzzle. Polycarp got the following problem: given a grid strip of size 2 × n, some cells of it are blocked. You need to check if it is possible to tile all free cells using the 2 × 1 and 1 × 2 tiles (dominoes). For example, if n = 5 and the strip looks like this (black cells are blocked): <image> Then it can be tiled, for example, using two vertical and two horizontal tiles, as in the picture below (different tiles are marked by different colors). <image> And if n = 3 and the strip looks like this: <image> It is impossible to tile free cells. Polycarp easily solved this task and received his New Year's gift. Can you solve it? Input The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow. Each test case is preceded by an empty line. The first line of each test case contains two integers n and m (1 ≤ n ≤ 10^9, 1 ≤ m ≤ 2 ⋅ 10^5) — the length of the strip and the number of blocked cells on it. Each of the next m lines contains two integers r_i, c_i (1 ≤ r_i ≤ 2, 1 ≤ c_i ≤ n) — numbers of rows and columns of blocked cells. It is guaranteed that all blocked cells are different, i.e. (r_i, c_i) ≠ (r_j, c_j), i ≠ j. It is guaranteed that the sum of m over all test cases does not exceed 2 ⋅ 10^5. Output For each test case, print on a separate line: * "YES", if it is possible to tile all unblocked squares with the 2 × 1 and 1 × 2 tiles; * "NO" otherwise. You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive). Example Input 3 5 2 2 2 1 4 3 2 2 1 2 3 6 4 2 1 2 3 2 4 2 6 Output YES NO NO Note The first two test cases are explained in the statement. In the third test case the strip looks like this: <image> It is easy to check that the unblocked squares on it can not be tiled. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You have a board represented as a grid with 2 × n cells. The first k_1 cells on the first row and first k_2 cells on the second row are colored in white. All other cells are colored in black. You have w white dominoes (2 × 1 tiles, both cells are colored in white) and b black dominoes (2 × 1 tiles, both cells are colored in black). You can place a white domino on the board if both board's cells are white and not occupied by any other domino. In the same way, you can place a black domino if both cells are black and not occupied by any other domino. Can you place all w + b dominoes on the board if you can place dominoes both horizontally and vertically? Input The first line contains a single integer t (1 ≤ t ≤ 3000) — the number of test cases. The first line of each test case contains three integers n, k_1 and k_2 (1 ≤ n ≤ 1000; 0 ≤ k_1, k_2 ≤ n). The second line of each test case contains two integers w and b (0 ≤ w, b ≤ n). Output For each test case, print YES if it's possible to place all w + b dominoes on the board and NO, otherwise. You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer). Example Input 5 1 0 1 1 0 1 1 1 0 0 3 0 0 1 3 4 3 1 2 2 5 4 3 3 1 Output NO YES NO YES YES Note In the first test case, n = 1, k_1 = 0 and k_2 = 1. It means that 2 × 1 board has black cell (1, 1) and white cell (2, 1). So, you can't place any white domino, since there is only one white cell. In the second test case, the board of the same size 2 × 1, but both cell are white. Since w = 0 and b = 0, so you can place 0 + 0 = 0 dominoes on the board. In the third test case, board 2 × 3, but fully colored in black (since k_1 = k_2 = 0), so you can't place any white domino. In the fourth test case, cells (1, 1), (1, 2), (1, 3), and (2, 1) are white and other cells are black. You can place 2 white dominoes at positions ((1, 1), (2, 1)) and ((1, 2), (1, 3)) and 2 black dominoes at positions ((1, 4), (2, 4)) ((2, 2), (2, 3)). The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. This is an interactive problem. This is a hard version of the problem. The difference from the easy version is that in the hard version 1 ≤ t ≤ min(n, 10^4) and the total number of queries is limited to 6 ⋅ 10^4. Polycarp is playing a computer game. In this game, an array consisting of zeros and ones is hidden. Polycarp wins if he guesses the position of the k-th zero from the left t times. Polycarp can make no more than 6 ⋅ 10^4 requests totally of the following type: * ? l r — find out the sum of all elements in positions from l to r (1 ≤ l ≤ r ≤ n) inclusive. To make the game more interesting, each guessed zero turns into one and the game continues on the changed array. More formally, if the position of the k-th zero was x, then after Polycarp guesses this position, the x-th element of the array will be replaced from 0 to 1. Help Polycarp win the game. Interaction First, your program must read two integers n and t (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ t ≤ min(n, 10^4)). Then t lines follow, each of which contains one integer k (1 ≤ k ≤ n). It is guaranteed that at the moment of the request the array contains at least k zeros. In order to get the next value of k, you must output the answer for the previous value of k. After that, you can make no more than 6 ⋅ 10^4 requests in total. Use the following format to output the answer (it is not a request, it doesn't count in 6 ⋅ 10^4): * ! x — position of the k-th zero. Positions in the array are numbered from left to right from 1 to n inclusive. After printing t answers, your program should exit immediately. In this task, the interactor is not adaptive. This means that within the same test, the hidden array and the queries do not change. In case of an incorrect query, -1 will be displayed. When this value is received, your program must immediately exit normally (for example, by calling exit(0)), otherwise, the testing system may issue an arbitrary verdict. If the number of requests is exceeded, the verdict wrong answer will be displayed. Your solution may get the verdict Idleness limit exceeded if you don't print anything or forget to flush the output buffer. To flush the output buffer, you need to do the following immediately after the query output and the end-of-line character: * fflush(stdout) or cout.flush() in C ++; * System.out.flush() in Java; * flush(output) in Pascal; * stdout.flush() in Python; * see the documentation for other languages. Hacks Use the following format for hacks: On the first line print the string s (1 ≤ \|s\| ≤ 2 ⋅ 10^5), consisting of zeros and ones, and an integer t (1 ≤ t ≤ min(\|s\|, 10^4)) — hidden array and number of requests, respectively. In the next t lines output the number k (1 ≤ k ≤ \|s\|). The hacked solution will not have direct access to the hidden array. Example Input 6 2 2 2 1 1 0 1 0 Output ? 4 6 ? 1 1 ? 1 2 ? 5 5 ! 5 ? 2 2 ! 2 Note In the first test, the array [1, 0, 1, 1, 0, 1] is hidden. After answering the query k=2, the array changed to [1, 0, 1, 1, 1, 1]. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The King of Flatland will organize a knights' tournament! The winner will get half the kingdom and the favor of the princess of legendary beauty and wisdom. The final test of the applicants' courage and strength will be a fencing tournament. The tournament is held by the following rules: the participants fight one on one, the winner (or rather, the survivor) transfers to the next round. Before the battle both participants stand at the specified points on the Ox axis with integer coordinates. Then they make moves in turn. The first participant moves first, naturally. During a move, the first participant can transfer from the point x to any integer point of the interval [x + a; x + b]. The second participant can transfer during a move to any integer point of the interval [x - b; x - a]. That is, the options for the players' moves are symmetric (note that the numbers a and b are not required to be positive, and if a ≤ 0 ≤ b, then staying in one place is a correct move). At any time the participants can be located arbitrarily relative to each other, that is, it is allowed to "jump" over the enemy in any direction. A participant wins if he uses his move to transfer to the point where his opponent is. Of course, the princess has already chosen a husband and now she wants to make her sweetheart win the tournament. He has already reached the tournament finals and he is facing the last battle. The princess asks the tournament manager to arrange the tournament finalists in such a way that her sweetheart wins the tournament, considering that both players play optimally. However, the initial location of the participants has already been announced, and we can only pull some strings and determine which participant will be first and which one will be second. But how do we know which participant can secure the victory? Alas, the princess is not learned in the military affairs... Therefore, she asks you to determine how the battle will end considering that both opponents play optimally. Also, if the first player wins, your task is to determine his winning move. Input The first line contains four space-separated integers — x1, x2, a and b (x1 ≠ x2, a ≤ b, - 109 ≤ x1, x2, a, b ≤ 109) — coordinates of the points where the first and the second participant start, and the numbers that determine the players' moves, correspondingly. Output On the first line print the outcome of the battle as "FIRST" (without the quotes), if both players play optimally and the first player wins. Print "SECOND" (without the quotes) if the second player wins and print "DRAW" (without the quotes), if nobody is able to secure the victory. If the first player wins, print on the next line the single integer x — the coordinate of the point where the first player should transfer to win. The indicated move should be valid, that is, it should meet the following condition: x1 + a ≤ x ≤ x1 + b. If there are several winning moves, print any of them. If the first participant can't secure the victory, then you do not have to print anything. Examples Input 0 2 0 4 Output FIRST 2 Input 0 2 1 1 Output SECOND Input 0 2 0 1 Output DRAW Note In the first sample the first player can win in one move. In the second sample the first participant must go to point 1, where the second participant immediately goes and wins. In the third sample changing the position isn't profitable to either participant, so nobody wins. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Let's consider one interesting word game. In this game you should transform one word into another through special operations. Let's say we have word w, let's split this word into two non-empty parts x and y so, that w = xy. A split operation is transforming word w = xy into word u = yx. For example, a split operation can transform word "wordcut" into word "cutword". You are given two words start and end. Count in how many ways we can transform word start into word end, if we apply exactly k split operations consecutively to word start. Two ways are considered different if the sequences of applied operations differ. Two operation sequences are different if exists such number i (1 ≤ i ≤ k), that in the i-th operation of the first sequence the word splits into parts x and y, in the i-th operation of the second sequence the word splits into parts a and b, and additionally x ≠ a holds. Input The first line contains a non-empty word start, the second line contains a non-empty word end. The words consist of lowercase Latin letters. The number of letters in word start equals the number of letters in word end and is at least 2 and doesn't exceed 1000 letters. The third line contains integer k (0 ≤ k ≤ 105) — the required number of operations. Output Print a single number — the answer to the problem. As this number can be rather large, print it modulo 1000000007 (109 + 7). Examples Input ab ab 2 Output 1 Input ababab ababab 1 Output 2 Input ab ba 2 Output 0 Note The sought way in the first sample is: ab → a\|b → ba → b\|a → ab In the second sample the two sought ways are: * ababab → abab\|ab → ababab * ababab → ab\|abab → ababab The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given undirected weighted graph. Find the length of the shortest cycle which starts from the vertex 1 and passes throught all the edges at least once. Graph may contain multiply edges between a pair of vertices and loops (edges from the vertex to itself). Input The first line of the input contains two integers n and m (1 ≤ n ≤ 15, 0 ≤ m ≤ 2000), n is the amount of vertices, and m is the amount of edges. Following m lines contain edges as a triples x, y, w (1 ≤ x, y ≤ n, 1 ≤ w ≤ 10000), x, y are edge endpoints, and w is the edge length. Output Output minimal cycle length or -1 if it doesn't exists. Examples Input 3 3 1 2 1 2 3 1 3 1 1 Output 3 Input 3 2 1 2 3 2 3 4 Output 14 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. One day Ms Swan bought an orange in a shop. The orange consisted of n·k segments, numbered with integers from 1 to n·k. There were k children waiting for Ms Swan at home. The children have recently learned about the orange and they decided to divide it between them. For that each child took a piece of paper and wrote the number of the segment that he would like to get: the i-th (1 ≤ i ≤ k) child wrote the number ai (1 ≤ ai ≤ n·k). All numbers ai accidentally turned out to be different. Now the children wonder, how to divide the orange so as to meet these conditions: * each child gets exactly n orange segments; * the i-th child gets the segment with number ai for sure; * no segment goes to two children simultaneously. Help the children, divide the orange and fulfill the requirements, described above. Input The first line contains two integers n, k (1 ≤ n, k ≤ 30). The second line contains k space-separated integers a1, a2, ..., ak (1 ≤ ai ≤ n·k), where ai is the number of the orange segment that the i-th child would like to get. It is guaranteed that all numbers ai are distinct. Output Print exactly n·k distinct integers. The first n integers represent the indexes of the segments the first child will get, the second n integers represent the indexes of the segments the second child will get, and so on. Separate the printed numbers with whitespaces. You can print a child's segment indexes in any order. It is guaranteed that the answer always exists. If there are multiple correct answers, print any of them. Examples Input 2 2 4 1 Output 2 4 1 3 Input 3 1 2 Output 3 2 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Some large corporation where Polycarpus works has its own short message service center (SMSC). The center's task is to send all sorts of crucial information. Polycarpus decided to check the efficiency of the SMSC. For that, he asked to give him the statistics of the performance of the SMSC for some period of time. In the end, Polycarpus got a list of n tasks that went to the SMSC of the corporation. Each task was described by the time it was received by the SMSC and the number of text messages to send. More formally, the i-th task was described by two integers ti and ci — the receiving time (the second) and the number of the text messages, correspondingly. Polycarpus knows that the SMSC cannot send more than one text message per second. The SMSC uses a queue to organize its work. Consider a time moment x, the SMSC work at that moment as follows: 1. If at the time moment x the queue is not empty, then SMSC sends one message from the queue (SMSC gets the message from the head of the queue). Otherwise it doesn't send messages at the time moment x. 2. If at the time moment x SMSC receives a task, then it adds to the queue all the messages from this task (SMSC adds messages to the tail of the queue). Note, that the messages from the task cannot be send at time moment x. That's because the decision about sending message or not is made at point 1 before adding these messages to the queue. Given the information about all n tasks, Polycarpus wants to count two values: the time when the last text message was sent and the maximum size of the queue at some time. Help him count these two characteristics he needs to evaluate the efficiency of the SMSC. Input The first line contains a single integer n (1 ≤ n ≤ 103) — the number of tasks of the SMSC. Next n lines contain the tasks' descriptions: the i-th line contains two space-separated integers ti and ci (1 ≤ ti, ci ≤ 106) — the time (the second) when the i-th task was received and the number of messages to send, correspondingly. It is guaranteed that all tasks were received at different moments of time. It is guaranteed that the tasks are sorted in the chronological order, that is, ti < ti + 1 for all integer i (1 ≤ i < n). Output In a single line print two space-separated integers — the time when the last text message was sent and the maximum queue size at a certain moment of time. Examples Input 2 1 1 2 1 Output 3 1 Input 1 1000000 10 Output 1000010 10 Input 3 3 3 4 3 5 3 Output 12 7 Note In the first test sample: * second 1: the first message has appeared in the queue, the queue's size is 1; * second 2: the first message is sent, the second message has been received, the queue's size is 1; * second 3: the second message is sent, the queue's size is 0, Thus, the maximum size of the queue is 1, the last message was sent at the second 3. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You know that Japan is the country with almost the largest 'electronic devices per person' ratio. So you might be quite surprised to find out that the primary school in Japan teaches to count using a Soroban — an abacus developed in Japan. This phenomenon has its reasons, of course, but we are not going to speak about them. Let's have a look at the Soroban's construction. <image> Soroban consists of some number of rods, each rod contains five beads. We will assume that the rods are horizontal lines. One bead on each rod (the leftmost one) is divided from the others by a bar (the reckoning bar). This single bead is called go-dama and four others are ichi-damas. Each rod is responsible for representing a single digit from 0 to 9. We can obtain the value of a digit by following simple algorithm: * Set the value of a digit equal to 0. * If the go-dama is shifted to the right, add 5. * Add the number of ichi-damas shifted to the left. Thus, the upper rod on the picture shows digit 0, the middle one shows digit 2 and the lower one shows 7. We will consider the top rod to represent the last decimal digit of a number, so the picture shows number 720. Write the program that prints the way Soroban shows the given number n. Input The first line contains a single integer n (0 ≤ n < 109). Output Print the description of the decimal digits of number n from the last one to the first one (as mentioned on the picture in the statement), one per line. Print the beads as large English letters 'O', rod pieces as character '-' and the reckoning bar as '\|'. Print as many rods, as many digits are in the decimal representation of number n without leading zeroes. We can assume that number 0 has no leading zeroes. Examples Input 2 Output O-\|OO-OO Input 13 Output O-\|OOO-O O-\|O-OOO Input 720 Output O-\|-OOOO O-\|OO-OO -O\|OO-OO The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Piegirl got bored with binary, decimal and other integer based counting systems. Recently she discovered some interesting properties about number <image>, in particular that q2 = q + 1, and she thinks it would make a good base for her new unique system. She called it "golden system". In golden system the number is a non-empty string containing 0's and 1's as digits. The decimal value of expression a0a1...an equals to <image>. Soon Piegirl found out that this system doesn't have same properties that integer base systems do and some operations can not be performed on it. She wasn't able to come up with a fast way of comparing two numbers. She is asking for your help. Given two numbers written in golden system notation, determine which of them has larger decimal value. Input Input consists of two lines — one for each number. Each line contains non-empty string consisting of '0' and '1' characters. The length of each string does not exceed 100000. Output Print ">" if the first number is larger, "<" if it is smaller and "=" if they are equal. Examples Input 1000 111 Output < Input 00100 11 Output = Input 110 101 Output > Note In the first example first number equals to <image>, while second number is approximately 1.6180339882 + 1.618033988 + 1 ≈ 5.236, which is clearly a bigger number. In the second example numbers are equal. Each of them is ≈ 2.618. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Valery is a PE teacher at a school in Berland. Soon the students are going to take a test in long jumps, and Valery has lost his favorite ruler! However, there is no reason for disappointment, as Valery has found another ruler, its length is l centimeters. The ruler already has n marks, with which he can make measurements. We assume that the marks are numbered from 1 to n in the order they appear from the beginning of the ruler to its end. The first point coincides with the beginning of the ruler and represents the origin. The last mark coincides with the end of the ruler, at distance l from the origin. This ruler can be repesented by an increasing sequence a1, a2, ..., an, where ai denotes the distance of the i-th mark from the origin (a1 = 0, an = l). Valery believes that with a ruler he can measure the distance of d centimeters, if there is a pair of integers i and j (1 ≤ i ≤ j ≤ n), such that the distance between the i-th and the j-th mark is exactly equal to d (in other words, aj - ai = d). Under the rules, the girls should be able to jump at least x centimeters, and the boys should be able to jump at least y (x < y) centimeters. To test the children's abilities, Valery needs a ruler to measure each of the distances x and y. Your task is to determine what is the minimum number of additional marks you need to add on the ruler so that they can be used to measure the distances x and y. Valery can add the marks at any integer non-negative distance from the origin not exceeding the length of the ruler. Input The first line contains four positive space-separated integers n, l, x, y (2 ≤ n ≤ 105, 2 ≤ l ≤ 109, 1 ≤ x < y ≤ l) — the number of marks, the length of the ruler and the jump norms for girls and boys, correspondingly. The second line contains a sequence of n integers a1, a2, ..., an (0 = a1 < a2 < ... < an = l), where ai shows the distance from the i-th mark to the origin. Output In the first line print a single non-negative integer v — the minimum number of marks that you need to add on the ruler. In the second line print v space-separated integers p1, p2, ..., pv (0 ≤ pi ≤ l). Number pi means that the i-th mark should be at the distance of pi centimeters from the origin. Print the marks in any order. If there are multiple solutions, print any of them. Examples Input 3 250 185 230 0 185 250 Output 1 230 Input 4 250 185 230 0 20 185 250 Output 0 Input 2 300 185 230 0 300 Output 2 185 230 Note In the first sample it is impossible to initially measure the distance of 230 centimeters. For that it is enough to add a 20 centimeter mark or a 230 centimeter mark. In the second sample you already can use the ruler to measure the distances of 185 and 230 centimeters, so you don't have to add new marks. In the third sample the ruler only contains the initial and the final marks. We will need to add two marks to be able to test the children's skills. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Let's define the sum of two permutations p and q of numbers 0, 1, ..., (n - 1) as permutation <image>, where Perm(x) is the x-th lexicographically permutation of numbers 0, 1, ..., (n - 1) (counting from zero), and Ord(p) is the number of permutation p in the lexicographical order. For example, Perm(0) = (0, 1, ..., n - 2, n - 1), Perm(n! - 1) = (n - 1, n - 2, ..., 1, 0) Misha has two permutations, p and q. Your task is to find their sum. Permutation a = (a0, a1, ..., an - 1) is called to be lexicographically smaller than permutation b = (b0, b1, ..., bn - 1), if for some k following conditions hold: a0 = b0, a1 = b1, ..., ak - 1 = bk - 1, ak < bk. Input The first line contains an integer n (1 ≤ n ≤ 200 000). The second line contains n distinct integers from 0 to n - 1, separated by a space, forming permutation p. The third line contains n distinct integers from 0 to n - 1, separated by spaces, forming permutation q. Output Print n distinct integers from 0 to n - 1, forming the sum of the given permutations. Separate the numbers by spaces. Examples Input 2 0 1 0 1 Output 0 1 Input 2 0 1 1 0 Output 1 0 Input 3 1 2 0 2 1 0 Output 1 0 2 Note Permutations of numbers from 0 to 1 in the lexicographical order: (0, 1), (1, 0). In the first sample Ord(p) = 0 and Ord(q) = 0, so the answer is <image>. In the second sample Ord(p) = 0 and Ord(q) = 1, so the answer is <image>. Permutations of numbers from 0 to 2 in the lexicographical order: (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0). In the third sample Ord(p) = 3 and Ord(q) = 5, so the answer is <image>. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Ford Prefect got a job as a web developer for a small company that makes towels. His current work task is to create a search engine for the website of the company. During the development process, he needs to write a subroutine for comparing strings S and T of equal length to be "similar". After a brief search on the Internet, he learned about the Hamming distance between two strings S and T of the same length, which is defined as the number of positions in which S and T have different characters. For example, the Hamming distance between words "permanent" and "pergament" is two, as these words differ in the fourth and sixth letters. Moreover, as he was searching for information, he also noticed that modern search engines have powerful mechanisms to correct errors in the request to improve the quality of search. Ford doesn't know much about human beings, so he assumed that the most common mistake in a request is swapping two arbitrary letters of the string (not necessarily adjacent). Now he wants to write a function that determines which two letters should be swapped in string S, so that the Hamming distance between a new string S and string T would be as small as possible, or otherwise, determine that such a replacement cannot reduce the distance between the strings. Help him do this! Input The first line contains integer n (1 ≤ n ≤ 200 000) — the length of strings S and T. The second line contains string S. The third line contains string T. Each of the lines only contains lowercase Latin letters. Output In the first line, print number x — the minimum possible Hamming distance between strings S and T if you swap at most one pair of letters in S. In the second line, either print the indexes i and j (1 ≤ i, j ≤ n, i ≠ j), if reaching the minimum possible distance is possible by swapping letters on positions i and j, or print "-1 -1", if it is not necessary to swap characters. If there are multiple possible answers, print any of them. Examples Input 9 pergament permanent Output 1 4 6 Input 6 wookie cookie Output 1 -1 -1 Input 4 petr egor Output 2 1 2 Input 6 double bundle Output 2 4 1 Note In the second test it is acceptable to print i = 2, j = 3. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Vanya is doing his maths homework. He has an expression of form <image>, where x1, x2, ..., xn are digits from 1 to 9, and sign <image> represents either a plus '+' or the multiplication sign ''. Vanya needs to add one pair of brackets in this expression so that to maximize the value of the resulting expression. Input The first line contains expression s (1 ≤ \|s\| ≤ 5001, \|s\| is odd), its odd positions only contain digits from 1 to 9, and even positions only contain signs + and . The number of signs * doesn't exceed 15. Output In the first line print the maximum possible value of an expression. Examples Input 3+57+84 Output 303 Input 2+35 Output 25 Input 345 Output 60 Note Note to the first sample test. 3 + 5 (7 + 8) * 4 = 303. Note to the second sample test. (2 + 3) * 5 = 25. Note to the third sample test. (3 * 4) * 5 = 60 (also many other variants are valid, for instance, (3) * 4 * 5 = 60). The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given a sequence of n integers a1, a2, ..., an. Determine a real number x such that the weakness of the sequence a1 - x, a2 - x, ..., an - x is as small as possible. The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence. The poorness of a segment is defined as the absolute value of sum of the elements of segment. Input The first line contains one integer n (1 ≤ n ≤ 200 000), the length of a sequence. The second line contains n integers a1, a2, ..., an (\|ai\| ≤ 10 000). Output Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., an - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6. Examples Input 3 1 2 3 Output 1.000000000000000 Input 4 1 2 3 4 Output 2.000000000000000 Input 10 1 10 2 9 3 8 4 7 5 6 Output 4.500000000000000 Note For the first case, the optimal value of x is 2 so the sequence becomes - 1, 0, 1 and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case. For the second sample the optimal value of x is 2.5 so the sequence becomes - 1.5, - 0.5, 0.5, 1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to 2 in this case. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given two circles. Find the area of their intersection. Input The first line contains three integers x1, y1, r1 ( - 109 ≤ x1, y1 ≤ 109, 1 ≤ r1 ≤ 109) — the position of the center and the radius of the first circle. The second line contains three integers x2, y2, r2 ( - 109 ≤ x2, y2 ≤ 109, 1 ≤ r2 ≤ 109) — the position of the center and the radius of the second circle. Output Print the area of the intersection of the circles. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6. Examples Input 0 0 4 6 0 4 Output 7.25298806364175601379 Input 0 0 5 11 0 5 Output 0.00000000000000000000 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. One day student Vasya was sitting on a lecture and mentioned a string s1s2... sn, consisting of letters "a", "b" and "c" that was written on his desk. As the lecture was boring, Vasya decided to complete the picture by composing a graph G with the following properties: * G has exactly n vertices, numbered from 1 to n. * For all pairs of vertices i and j, where i ≠ j, there is an edge connecting them if and only if characters si and sj are either equal or neighbouring in the alphabet. That is, letters in pairs "a"-"b" and "b"-"c" are neighbouring, while letters "a"-"c" are not. Vasya painted the resulting graph near the string and then erased the string. Next day Vasya's friend Petya came to a lecture and found some graph at his desk. He had heard of Vasya's adventure and now he wants to find out whether it could be the original graph G, painted by Vasya. In order to verify this, Petya needs to know whether there exists a string s, such that if Vasya used this s he would produce the given graph G. Input The first line of the input contains two integers n and m <image> — the number of vertices and edges in the graph found by Petya, respectively. Each of the next m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the edges of the graph G. It is guaranteed, that there are no multiple edges, that is any pair of vertexes appear in this list no more than once. Output In the first line print "Yes" (without the quotes), if the string s Petya is interested in really exists and "No" (without the quotes) otherwise. If the string s exists, then print it on the second line of the output. The length of s must be exactly n, it must consist of only letters "a", "b" and "c" only, and the graph built using this string must coincide with G. If there are multiple possible answers, you may print any of them. Examples Input 2 1 1 2 Output Yes aa Input 4 3 1 2 1 3 1 4 Output No Note In the first sample you are given a graph made of two vertices with an edge between them. So, these vertices can correspond to both the same and adjacent letters. Any of the following strings "aa", "ab", "ba", "bb", "bc", "cb", "cc" meets the graph's conditions. In the second sample the first vertex is connected to all three other vertices, but these three vertices are not connected with each other. That means that they must correspond to distinct letters that are not adjacent, but that is impossible as there are only two such letters: a and c. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You have recently fallen through a hole and, after several hours of unconsciousness, have realized you are in an underground city. On one of your regular, daily walks through the unknown, you have encountered two unusually looking skeletons called Sanz and P’pairus, who decided to accompany you and give you some puzzles for seemingly unknown reasons. One day, Sanz has created a crossword for you. Not any kind of crossword, but a 1D crossword! You are given m words and a string of length n. You are also given an array p, which designates how much each word is worth — the i-th word is worth pi points. Whenever you find one of the m words in the string, you are given the corresponding number of points. Each position in the crossword can be used at most x times. A certain word can be counted at different places, but you cannot count the same appearance of a word multiple times. If a word is a substring of another word, you can count them both (presuming you haven’t used the positions more than x times). In order to solve the puzzle, you need to tell Sanz what’s the maximum achievable number of points in the crossword. There is no need to cover all postions, just get the maximal score! Crossword and words contain only lowercase English letters. Input The first line of the input contains a single integer n (1 ≤ n ≤ 500) — the length of the crossword. The second line contains the crossword string. The third line contains a single integer m (1 ≤ m ≤ 100) — the number of given words, and next m lines contain description of words: each line will have a string representing a non-empty word (its length doesn't exceed the length of the crossword) and integer pi (0 ≤ pi ≤ 100). Last line of the input will contain x (1 ≤ x ≤ 100) — maximum number of times a position in crossword can be used. Output Output single integer — maximum number of points you can get. Example Input 6 abacba 2 aba 6 ba 3 3 Output 12 Note For example, with the string "abacba", words "aba" (6 points) and "ba" (3 points), and x = 3, you can get at most 12 points - the word "aba" appears once ("abacba"), while "ba" appears two times ("abacba"). Note that for x = 1, you could get at most 9 points, since you wouldn’t be able to count both "aba" and the first appearance of "ba". The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Due to the increase in the number of students of Berland State University it was decided to equip a new computer room. You were given the task of buying mouses, and you have to spend as little as possible. After all, the country is in crisis! The computers bought for the room were different. Some of them had only USB ports, some — only PS/2 ports, and some had both options. You have found a price list of a certain computer shop. In it, for m mouses it is specified the cost and the type of the port that is required to plug the mouse in (USB or PS/2). Each mouse from the list can be bought at most once. You want to buy some set of mouses from the given price list in such a way so that you maximize the number of computers equipped with mouses (it is not guaranteed that you will be able to equip all of the computers), and in case of equality of this value you want to minimize the total cost of mouses you will buy. Input The first line contains three integers a, b and c (0 ≤ a, b, c ≤ 105) — the number of computers that only have USB ports, the number of computers, that only have PS/2 ports, and the number of computers, that have both options, respectively. The next line contains one integer m (0 ≤ m ≤ 3·105) — the number of mouses in the price list. The next m lines each describe another mouse. The i-th line contains first integer vali (1 ≤ vali ≤ 109) — the cost of the i-th mouse, then the type of port (USB or PS/2) that is required to plug the mouse in. Output Output two integers separated by space — the number of equipped computers and the total cost of the mouses you will buy. Example Input 2 1 1 4 5 USB 6 PS/2 3 PS/2 7 PS/2 Output 3 14 Note In the first example you can buy the first three mouses. This way you will equip one of the computers that has only a USB port with a USB mouse, and the two PS/2 mouses you will plug into the computer with PS/2 port and the computer with both ports. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Anton likes to listen to fairy tales, especially when Danik, Anton's best friend, tells them. Right now Danik tells Anton a fairy tale: "Once upon a time, there lived an emperor. He was very rich and had much grain. One day he ordered to build a huge barn to put there all his grain. Best builders were building that barn for three days and three nights. But they overlooked and there remained a little hole in the barn, from which every day sparrows came through. Here flew a sparrow, took a grain and flew away..." More formally, the following takes place in the fairy tale. At the beginning of the first day the barn with the capacity of n grains was full. Then, every day (starting with the first day) the following happens: * m grains are brought to the barn. If m grains doesn't fit to the barn, the barn becomes full and the grains that doesn't fit are brought back (in this problem we can assume that the grains that doesn't fit to the barn are not taken into account). * Sparrows come and eat grain. In the i-th day i sparrows come, that is on the first day one sparrow come, on the second day two sparrows come and so on. Every sparrow eats one grain. If the barn is empty, a sparrow eats nothing. Anton is tired of listening how Danik describes every sparrow that eats grain from the barn. Anton doesn't know when the fairy tale ends, so he asked you to determine, by the end of which day the barn will become empty for the first time. Help Anton and write a program that will determine the number of that day! Input The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018) — the capacity of the barn and the number of grains that are brought every day. Output Output one integer — the number of the day when the barn will become empty for the first time. Days are numbered starting with one. Examples Input 5 2 Output 4 Input 8 1 Output 5 Note In the first sample the capacity of the barn is five grains and two grains are brought every day. The following happens: * At the beginning of the first day grain is brought to the barn. It's full, so nothing happens. * At the end of the first day one sparrow comes and eats one grain, so 5 - 1 = 4 grains remain. * At the beginning of the second day two grains are brought. The barn becomes full and one grain doesn't fit to it. * At the end of the second day two sparrows come. 5 - 2 = 3 grains remain. * At the beginning of the third day two grains are brought. The barn becomes full again. * At the end of the third day three sparrows come and eat grain. 5 - 3 = 2 grains remain. * At the beginning of the fourth day grain is brought again. 2 + 2 = 4 grains remain. * At the end of the fourth day four sparrows come and eat grain. 4 - 4 = 0 grains remain. The barn is empty. So the answer is 4, because by the end of the fourth day the barn becomes empty. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made y submissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y. Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q? Input The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 109; 0 ≤ p ≤ q ≤ 109; y > 0; q > 0). It is guaranteed that p / q is an irreducible fraction. Hacks. For hacks, an additional constraint of t ≤ 5 must be met. Output For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve. Example Input 4 3 10 1 2 7 14 3 8 20 70 2 7 5 6 1 1 Output 4 10 0 -1 Note In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2. In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to 9 / 24, or 3 / 8. In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7. In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. John has just bought a new car and is planning a journey around the country. Country has N cities, some of which are connected by bidirectional roads. There are N - 1 roads and every city is reachable from any other city. Cities are labeled from 1 to N. John first has to select from which city he will start his journey. After that, he spends one day in a city and then travels to a randomly choosen city which is directly connected to his current one and which he has not yet visited. He does this until he can't continue obeying these rules. To select the starting city, he calls his friend Jack for advice. Jack is also starting a big casino business and wants to open casinos in some of the cities (max 1 per city, maybe nowhere). Jack knows John well and he knows that if he visits a city with a casino, he will gamble exactly once before continuing his journey. He also knows that if John enters a casino in a good mood, he will leave it in a bad mood and vice versa. Since he is John's friend, he wants him to be in a good mood at the moment when he finishes his journey. John is in a good mood before starting the journey. In how many ways can Jack select a starting city for John and cities where he will build casinos such that no matter how John travels, he will be in a good mood at the end? Print answer modulo 109 + 7. Input In the first line, a positive integer N (1 ≤ N ≤ 100000), the number of cities. In the next N - 1 lines, two numbers a, b (1 ≤ a, b ≤ N) separated by a single space meaning that cities a and b are connected by a bidirectional road. Output Output one number, the answer to the problem modulo 109 + 7. Examples Input 2 1 2 Output 4 Input 3 1 2 2 3 Output 10 Note Example 1: If Jack selects city 1 as John's starting city, he can either build 0 casinos, so John will be happy all the time, or build a casino in both cities, so John would visit a casino in city 1, become unhappy, then go to city 2, visit a casino there and become happy and his journey ends there because he can't go back to city 1. If Jack selects city 2 for start, everything is symmetrical, so the answer is 4. Example 2: If Jack tells John to start from city 1, he can either build casinos in 0 or 2 cities (total 4 possibilities). If he tells him to start from city 2, then John's journey will either contain cities 2 and 1 or 2 and 3. Therefore, Jack will either have to build no casinos, or build them in all three cities. With other options, he risks John ending his journey unhappy. Starting from 3 is symmetric to starting from 1, so in total we have 4 + 2 + 4 = 10 options. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You have n distinct points on a plane, none of them lie on OY axis. Check that there is a point after removal of which the remaining points are located on one side of the OY axis. Input The first line contains a single positive integer n (2 ≤ n ≤ 105). The following n lines contain coordinates of the points. The i-th of these lines contains two single integers xi and yi (\|xi\|, \|yi\| ≤ 109, xi ≠ 0). No two points coincide. Output Print "Yes" if there is such a point, "No" — otherwise. You can print every letter in any case (upper or lower). Examples Input 3 1 1 -1 -1 2 -1 Output Yes Input 4 1 1 2 2 -1 1 -2 2 Output No Input 3 1 2 2 1 4 60 Output Yes Note In the first example the second point can be removed. In the second example there is no suitable for the condition point. In the third example any point can be removed. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Polycarp likes arithmetic progressions. A sequence [a_1, a_2, ..., a_n] is called an arithmetic progression if for each i (1 ≤ i < n) the value a_{i+1} - a_i is the same. For example, the sequences [42], [5, 5, 5], [2, 11, 20, 29] and [3, 2, 1, 0] are arithmetic progressions, but [1, 0, 1], [1, 3, 9] and [2, 3, 1] are not. It follows from the definition that any sequence of length one or two is an arithmetic progression. Polycarp found some sequence of positive integers [b_1, b_2, ..., b_n]. He agrees to change each element by at most one. In the other words, for each element there are exactly three options: an element can be decreased by 1, an element can be increased by 1, an element can be left unchanged. Determine a minimum possible number of elements in b which can be changed (by exactly one), so that the sequence b becomes an arithmetic progression, or report that it is impossible. It is possible that the resulting sequence contains element equals 0. Input The first line contains a single integer n (1 ≤ n ≤ 100 000) — the number of elements in b. The second line contains a sequence b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^{9}). Output If it is impossible to make an arithmetic progression with described operations, print -1. In the other case, print non-negative integer — the minimum number of elements to change to make the given sequence becomes an arithmetic progression. The only allowed operation is to add/to subtract one from an element (can't use operation twice to the same position). Examples Input 4 24 21 14 10 Output 3 Input 2 500 500 Output 0 Input 3 14 5 1 Output -1 Input 5 1 3 6 9 12 Output 1 Note In the first example Polycarp should increase the first number on 1, decrease the second number on 1, increase the third number on 1, and the fourth number should left unchanged. So, after Polycarp changed three elements by one, his sequence became equals to [25, 20, 15, 10], which is an arithmetic progression. In the second example Polycarp should not change anything, because his sequence is an arithmetic progression. In the third example it is impossible to make an arithmetic progression. In the fourth example Polycarp should change only the first element, he should decrease it on one. After that his sequence will looks like [0, 3, 6, 9, 12], which is an arithmetic progression. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Statement: Sourav and his friends are in kolkata city and they are planning for a city tour. So, they booked a TUBER cab (Stop Giggling). Please help them to find the estimated fare according to the fare evaluator system of TUBER cabs. How to evaluate fare? For first 2 Kilometers, Fare is 50 units (i.e., Base Charge or Minimum Charge). For more than 2 Kilometers, Fare is 12 units/Kilometer (except first 2 Kilometers). Waiting charge is 2 units/min. Maximum distance travelled by cab services is 60 Kilometers. Input: First line of input containts T, i.e., number of test cases, followed by T lines each containing- Total distance, D Waiting time, WT (in minutes) D & WT are space seperated values on each line. Output: T lines each containing estimated fare. If D exceeds maximum distance travel value, print NA. Constraints: 1 ≤ T ≤ 100 \| 1 ≤ D ≤ 60 \| 1 ≤ WT ≤ 250 SAMPLE INPUT 3 5 2 12 0 61 3 SAMPLE OUTPUT 90 170 NA Explanation In the above sample input, For the 1st case, D=5 and WT=2, so estimated fare is 90 units. For the 3rd case, D=61 and WT=3, since TUBER cabs do not travel beyond 60 kilometers, so output is NA. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Mahabir loves matrix and likes to rotate things a lot. Today he is rotating an array in clock-wise direction. He gives you an array of size N X N and an positive integer Q. Each Q number of integers contains an angle A (angle is always multiple of 90 or can be zero). You have to rotate the array ( clock-wise only ) with angle A and have to tell him the resultant matrix after rotating it. Mahabir challenges you to write the code. Input First line contains two positive integers N and Q separated by a space. Next N lines contains N numbers each separated by a space. Next Q lines contains angle A with which you have to rotate the matrix. Output For each query Q print the resultant matrix. Output of each query must be separated by an empty line. Constraints 1=<N ≤ 100 1 ≤ Q ≤ 200 0 ≤ A ≤ 100000 (A will be always multiple of 90) 0 ≤ element of matrix ≤1000 SAMPLE INPUT 3 3 1 4 5 6 7 8 4 0 5 90 180 450 SAMPLE OUTPUT 4 6 1 0 7 4 5 8 5 5 0 4 8 7 6 5 4 1 4 6 1 0 7 4 5 8 5 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Shil got an array of N integers as a present on his birthday. But he didn't liked it. Shil wants to make this array beautiful. Shil considers an array A1,A2,A3 . . . AN beautiful if A1 > AN. Inorder to make it beautiful Shil can swap any two numbers in the array. Also Shil can perform this operation any number of times on any adjacent pairs of integers in the array A.Find the number of ways in which Shil can make this array beautiful.Two ways are considered same if resulting array after making all the swaps have same A1 and AN. Input First line of input contains an integer N denoting the number of elements in an array A. Next line of input contains N space separated integers denoting A1,A2,A3 . . . AN respectively. Output Number of ways in which you can make given array beautiful. Constraints 1 ≤ N ≤ 10^6 1 ≤ Ai ≤ 10^6 Warning Prefer to use fast I/O methods. SAMPLE INPUT 5 1 4 3 2 5 SAMPLE OUTPUT 10 Explanation Total number of ways are (5,1),(4,1),(3,1),(2,1),(5,2),(4,2),(3,2),(5,3),(4,3),(5,4). First number in above pair is A[1] and second number is A[N].Note that two ways are considered same if A[1] and A[N] are same in resulting array after swaps. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. The Hound and his brother the Mountain are engaged in a fight against each other in King's Landing. At the end of the fight, one dies and the other wins. They both are given a decimal number each in the 8 bit binary representation A and B. These numbers will decide their fate in the following manner: If A^B ≤ B^A, then the Hound is declared as the winnner and the Mountain dies. 2.But if A^B >B^A, then the Mountain wins and the Hound dies. Your task is to calculate and print the winner's name as output. Input:: Input the number of testcases T in the first line. Followed by T lines, each line with input A and B. Output: The name of the winner as "The Hound" or "The Mountain". SAMPLE INPUT 7 00111011 01100101 00110011 11001100 01010101 10101010 01011100 10100111 11111100 01011000 00101101 11001011 00101010 10101010 SAMPLE OUTPUT The Mountain The Mountain The Mountain The Mountain The Hound The Mountain The Mountain The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Xsquare loves to play with strings a lot. Today, he has two strings S1 and S2 both consisting of lower case alphabets. Xsquare listed all subsequences of string S1 on a paper and all subsequences of string S2 on a separate paper. Xsquare wants to know whether there exists a string which is listed on both the papers. Xsquare thinks that this task is pretty boring and handed it to you. Please accomplish this task on his behalf. Input First line of input contains a single integer T denoting the number of test cases. Each test case consists of two lines. First line of each test case contains a string denoting string S1. Next line of each test case contains a string denoting string S2. Output For each test case, Print Yes if both papers contain a common string otherwise Print No. Constraints 1 ≤ T ≤ 10^5 1 ≤ \|S1\| ≤ 10^5 1 ≤ \|S2\| ≤ 10^5 Sum of \|S1\| over all test case does not exceed 510^5 Sum of \|S2\| over all test case does not exceed 510^5 SAMPLE INPUT 2 phackerekarthj jhakckerearthp hello buy SAMPLE OUTPUT Yes No Explanation Testcase 1 : There is a common subsequence of letters between S1 and S2. For ex: "hackerearth" is subsequence of S1 and S2 both. Testcase 2 : There is no common subsequence of letters between S1 and S2. The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Given is a positive integer N. Consider repeatedly applying the operation below on N: * First, choose a positive integer z satisfying all of the conditions below: * z can be represented as z=p^e, where p is a prime number and e is a positive integer; * z divides N; * z is different from all integers chosen in previous operations. * Then, replace N with N/z. Find the maximum number of times the operation can be applied. Constraints * All values in input are integers. * 1 \leq N \leq 10^{12} Input Input is given from Standard Input in the following format: N Output Print the maximum number of times the operation can be applied. Examples Input 24 Output 3 Input 1 Output 0 Input 64 Output 3 Input 1000000007 Output 1 Input 997764507000 Output 7 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Takahashi is participating in a programming contest, AXC001. He has just submitted his code to Problem A. The problem has N test cases, all of which must be passed to get an AC verdict. Takahashi's submission has passed M cases out of the N test cases. Determine whether Takahashi's submission gets an AC. Constraints * 1 \leq N \leq 100 * 0 \leq M \leq N * All values in input are integers. Input Input is given from Standard Input in the following format: N M Output If Takahashi's submission gets an AC, print `Yes`; otherwise, print `No`. Examples Input 3 3 Output Yes Input 3 2 Output No Input 1 1 Output Yes The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. There are N gems. The value of the i-th gem is V_i. You will choose some of these gems, possibly all or none, and get them. However, you need to pay a cost of C_i to get the i-th gem. Let X be the sum of the values of the gems obtained, and Y be the sum of the costs paid. Find the maximum possible value of X-Y. Constraints * All values in input are integers. * 1 \leq N \leq 20 * 1 \leq C_i, V_i \leq 50 Input Input is given from Standard Input in the following format: N V_1 V_2 ... V_N C_1 C_2 ... C_N Output Print the maximum possible value of X-Y. Examples Input 3 10 2 5 6 3 4 Output 5 Input 4 13 21 6 19 11 30 6 15 Output 6 Input 1 1 50 Output 0 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Three people, A, B and C, are trying to communicate using transceivers. They are standing along a number line, and the coordinates of A, B and C are a, b and c (in meters), respectively. Two people can directly communicate when the distance between them is at most d meters. Determine if A and C can communicate, either directly or indirectly. Here, A and C can indirectly communicate when A and B can directly communicate and also B and C can directly communicate. Constraints * 1 ≤ a,b,c ≤ 100 * 1 ≤ d ≤ 100 * All values in input are integers. Input Input is given from Standard Input in the following format: a b c d Output If A and C can communicate, print `Yes`; if they cannot, print `No`. Examples Input 4 7 9 3 Output Yes Input 100 10 1 2 Output No Input 10 10 10 1 Output Yes Input 1 100 2 10 Output Yes The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are given two strings s and t consisting of lowercase English letters and an integer L. We will consider generating a string of length L by concatenating one or more copies of s and t. Here, it is allowed to use the same string more than once. For example, when s = `at`, t = `code` and L = 6, the strings `atatat`, `atcode` and `codeat` can be generated. Among the strings that can be generated in this way, find the lexicographically smallest one. In the cases given as input, it is always possible to generate a string of length L. Constraints * 1 ≤ L ≤ 2 × 10^5 * 1 ≤ \|s\|, \|t\| ≤ L * s and t consist of lowercase English letters. * It is possible to generate a string of length L in the way described in Problem Statement. Input Input is given from Standard Input in the following format: N x_1 s_1 x_2 s_2 : x_N s_N Output Print the lexicographically smallest string among the ones that can be generated in the way described in Problem Statement. Examples Input 6 at code Output atatat Input 8 coding festival Output festival Input 8 same same Output samesame Input 10 coin age Output ageagecoin The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. We will call a string that can be obtained by concatenating two equal strings an even string. For example, `xyzxyz` and `aaaaaa` are even, while `ababab` and `xyzxy` are not. You are given an even string S consisting of lowercase English letters. Find the length of the longest even string that can be obtained by deleting one or more characters from the end of S. It is guaranteed that such a non-empty string exists for a given input. Constraints * 2 \leq \|S\| \leq 200 * S is an even string consisting of lowercase English letters. * There exists a non-empty even string that can be obtained by deleting one or more characters from the end of S. Input Input is given from Standard Input in the following format: S Output Print the length of the longest even string that can be obtained. Examples Input abaababaab Output 6 Input xxxx Output 2 Input abcabcabcabc Output 6 Input akasakaakasakasakaakas Output 14 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You have an integer variable x. Initially, x=0. Some person gave you a string S of length N, and using the string you performed the following operation N times. In the i-th operation, you incremented the value of x by 1 if S_i=`I`, and decremented the value of x by 1 if S_i=`D`. Find the maximum value taken by x during the operations (including before the first operation, and after the last operation). Constraints * 1≤N≤100 * \|S\|=N * No characters except `I` and `D` occur in S. Input The input is given from Standard Input in the following format: N S Output Print the maximum value taken by x during the operations. Examples Input 5 IIDID Output 2 Input 7 DDIDDII Output 0 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Mr. Takahashi has a string s consisting of lowercase English letters. He repeats the following operation on s exactly K times. * Choose an arbitrary letter on s and change that letter to the next alphabet. Note that the next letter of `z` is `a`. For example, if you perform an operation for the second letter on `aaz`, `aaz` becomes `abz`. If you then perform an operation for the third letter on `abz`, `abz` becomes `aba`. Mr. Takahashi wants to have the lexicographically smallest string after performing exactly K operations on s. Find the such string. Constraints * 1≤\|s\|≤10^5 * All letters in s are lowercase English letters. * 1≤K≤10^9 Input The input is given from Standard Input in the following format: s K Output Print the lexicographically smallest string after performing exactly K operations on s. Examples Input xyz 4 Output aya Input a 25 Output z Input codefestival 100 Output aaaafeaaivap The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. <image> You know the merry-go-round in the amusement park. Vehicles such as horses and carriages are fixed on a large disk, and it is a standard playset that the vehicle swings up and down at the same time as the disk rotates. A merry-go-round in an amusement park has two four-seater carriages, two two-seater cars, four one-seater horses, and a total of eight vehicles in the order shown in Figure 1. .. Customers at the amusement park are waiting somewhere between platforms 0 and 7 shown in Fig. 1. <image> The merry-go-round in this amusement park always stops where the vehicle fits snugly into the landing. And the customers waiting in each of 0 to 7 are supposed to get on the vehicle that stopped in front of them. You cannot hurry to another platform and board from there. In order for customers to enjoy themselves efficiently, we must adjust the stop position of the merry-go-round to minimize the number of passengers who cannot ride. Create a program that reads the number of passengers waiting at platform 0-7 and outputs which vehicle should stop at which position to reduce the number of passengers who cannot get on. input The input consists of multiple datasets. Each dataset is given in the following format: p0 p1 p2 p3 p4 p5 p6 p7 Integers p0, p1, ..., p7 (0 ≤ pi ≤ 10,000) are given on one line, separated by blanks, to represent the number of passengers waiting at platform 0, 1, ..., 7. output Let's assume that the carriage of a merry-go-round vehicle is represented by 4, the car is represented by 2, and the horse is represented by 1. The vehicles that stop at platform 0, 1, ..., 7 are c0, c1, ..., c7, respectively. Prints c0, c1, ..., c7 on a single line, separated by blanks, for each dataset. If there are multiple ways to minimize the number of passengers who cannot ride, c0c1c2c3c4c5c6c7 shall be regarded as an 8-digit integer V, and the method to minimize V shall be selected. The number of datasets does not exceed 100. Example Input 2 3 1 4 0 1 0 1 4 2 3 2 2 2 1 1 Output 1 4 1 4 1 2 1 2 4 1 4 1 2 1 2 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In Square Town, where many people who love squares live, a festival is held to color the town with illuminations that combine square lightning boards. This electric board emits light when electricity is applied, and the plate in contact with the light emitting plate also emits light. Therefore, no matter how many electric boards you use, if all of them are in contact with each other, you only need one power supply. The festival executive committee will solicit designs that combine squares from the townspeople and create a large number of illuminations. For each illumination, the number of power supplies required varies depending on the arrangement of the squares that make up the design, so it takes a lot of time and effort to figure out the number of power supplies required. So you decided to look at the arrangement of the rectangles and write a program to help the executive committee calculate the number of power supplies needed. <image> Create a program that inputs the number of illuminations and the information of the rectangles that make up each illumination, and outputs the number of power supplies required for each illumination. Think of the overlapping and touching rectangles as a group, and count the number of power supplies as one for each group. Input A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format: N M1 xa1 ya1 xb1 yb1 xc1 yc1 xd1 yd1 xa2 ya2 xb2 yb2 xc2 yc2 xd2 yd2 :: xaM1 yaM1 xbM1 ybM1 xcM1 ycM1 xdM1 ydM1 M2 :: :: MN :: :: The number of illuminations N (1 ≤ N ≤ 100) is given on the first line. Then, information on N illuminations is given. As the i-th illumination information, the number of rectangles Mi (1 ≤ Mi ≤ 100) that make up the illumination is given in one line. The following Mi line is given the jth quadrangle vertex xaj, yaj, xbj, ybj, xcj, ycj, xdj, ydj (integer between -1000 and 1000). The coordinates of the vertices of the rectangle entered are entered in a clockwise order. However, all the input data rectangles are convex rectangles. The number of datasets does not exceed 10. Output Outputs the number of power supplies required for each illumination for each input dataset. Follow the order in which each illumination was input for the number of power supplies to be output. Example Input 3 1 0 0 0 1 1 1 1 0 2 0 0 0 1 1 1 1 0 100 100 100 200 200 200 200 100 2 0 0 0 100 100 100 100 0 10 10 10 20 20 20 20 10 2 1 30 40 40 50 40 20 20 10 1 30 40 40 50 40 20 20 10 0 Output 1 2 1 1 1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. In the advanced algorithm class, n2 students sit in n rows and n columns. One day, a professor who teaches this subject comes into the class, asks the shortest student in each row to lift up his left hand, and the tallest student in each column to lift up his right hand. What is the height of the student whose both hands are up ? The student will become a target for professor’s questions. Given the size of the class, and the height of the students in the class, you have to print the height of the student who has both his hands up in the class. Input The input will consist of several cases. the first line of each case will be n(0 < n < 100), the number of rows and columns in the class. It will then be followed by a n-by-n matrix, each row of the matrix appearing on a single line. Note that the elements of the matrix may not be necessarily distinct. The input will be terminated by the case n = 0. Output For each input case, you have to print the height of the student in the class whose both hands are up. If there is no such student, then print 0 for that case. Example Input 3 1 2 3 4 5 6 7 8 9 3 1 2 3 7 8 9 4 5 6 0 Output 7 7 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. <image> The International Clown and Pierrot Competition (ICPC), is one of the most distinguished and also the most popular events on earth in the show business. One of the unique features of this contest is the great number of judges that sometimes counts up to one hundred. The number of judges may differ from one contestant to another, because judges with any relationship whatsoever with a specific contestant are temporarily excluded for scoring his/her performance. Basically, scores given to a contestant's performance by the judges are averaged to decide his/her score. To avoid letting judges with eccentric viewpoints too much influence the score, the highest and the lowest scores are set aside in this calculation. If the same highest score is marked by two or more judges, only one of them is ignored. The same is with the lowest score. The average, which may contain fractions, are truncated down to obtain final score as an integer. You are asked to write a program that computes the scores of performances, given the scores of all the judges, to speed up the event to be suited for a TV program. Input The input consists of a number of datasets, each corresponding to a contestant's performance. There are no more than 20 datasets in the input. A dataset begins with a line with an integer n, the number of judges participated in scoring the performance (3 ≤ n ≤ 100). Each of the n lines following it has an integral score s (0 ≤ s ≤ 1000) marked by a judge. No other characters except for digits to express these numbers are in the input. Judges' names are kept secret. The end of the input is indicated by a line with a single zero in it. Output For each dataset, a line containing a single decimal integer indicating the score for the corresponding performance should be output. No other characters should be on the output line. Example Input 3 1000 342 0 5 2 2 9 11 932 5 300 1000 0 200 400 8 353 242 402 274 283 132 402 523 0 Output 342 7 300 326 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Problem I started a part-time job at the rental DVD shop "NEO". First of all, I decided to study the fee system of this store. There are three types of rental DVDs, old, semi-new, and new, and the rental fee for one DVD is a yen, b yen, and c yen, respectively. The set rental shown below can be applied multiple times at the time of accounting. * Select a few DVDs for which set rental has not yet been applied. * If the number of selected DVDs is d or more, the total price of the selected DVDs exceeds (the number of selected DVDs) * e yen, rent them for (the number of selected DVDs) * e yen. You can. * If the number of selected DVDs is less than d, and the total price of the selected DVDs exceeds d * e yen, you can rent them for d * e yen. * If the above does not apply, the selected DVD will be rented at the regular rate. Here I noticed a problem. The set rental is not applied automatically when you go to the cash register, but is applied manually. This may result in the application of suboptimal set rentals (which can be cheaper). This can lead to complaints. I hate complaints, so I decided to create a program that calculates the price when the set rental is optimally applied. Constraints The input satisfies the following conditions. * All values contained in the input are integers * 0 <a <b <e <c ≤ 1000 * 0 <d ≤ 100000 * 0 ≤ na, nb, nc ≤ 100000 * 0 <na + nb + nc * No more than 100 datasets Input The input consists of multiple datasets. Each dataset is represented below. The first line is given five integers a, b, c, d, e separated by spaces. The number of rentals is given on the second line. The three integers na, nb, nc are given separated by spaces. Represents the number of old, semi-new, and new DVDs, respectively. The end of the input consists of 5 zeros. a b c d e na nb nc Output For each dataset, output the charge when the set rental is optimally applied on one line. Example Input 70 100 340 4 200 1 1 4 70 100 340 4 200 0 1 3 70 100 340 4 200 1 1 2 0 0 0 0 0 Output 970 800 800 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Alice wants to send an email to Miku on her mobile phone. The only buttons that can be used for input on mobile phones are number buttons. Therefore, in order to input characters, the number buttons are pressed several times to input characters. The following characters are assigned to the number buttons of the mobile phone, and the confirmation button is assigned to button 0. With this mobile phone, you are supposed to press the confirm button after you finish entering one character. * 1:.,!? (Space) * 2: a b c * 3: d e f * 4: g h i * 5: j k l * 6: m n o * 7: p q r s * 8: t u v * 9: w x y z * 0: Confirm button For example, if you press button 2, button 2, or button 0, the letter changes from'a'to'b', and the confirm button is pressed here, so the letter b is output. If you enter the same number in succession, the changing characters will loop. That is, if you press button 2 five times and then button 0, the letters change from'a'→' b'→'c' →'a' →'b', and the confirm button is pressed here. 'b' is output. You can press the confirm button when no button is pressed, but in that case no characters are output. Your job is to recreate the message Alice created from a row of buttons pressed by Alice. Input The first line gives the number of test cases. Each test case is then given a string of digits up to 1024 in length in one row. Output Print the string of Alice's message line by line for each test case. However, you can assume that the output is one or more and less than 76 characters. Example Input 5 20 220 222220 44033055505550666011011111090666077705550301110 000555555550000330000444000080000200004440000 Output a b b hello, world! keitai The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. You are a programmer on the development team for new recording media. This recording medium can be randomly accessed for reading and erasing data. On the other hand, when writing data, access is always performed in order from the beginning, and only the first free space found can be written. You have begun to build a file system for this recording medium. In this file system, data is written in order from the first free area due to the limitation of the recording medium. If another data exists in the middle of writing, the remaining data is written from the free area behind it. Data is written in units called sectors. Sectors are assigned numbers starting from 0, which indicate their physical location on the storage medium. The sector numbers are assigned as 0, 1, 2, 3, ... In order from the beginning to the back of the storage medium. There are three commands in the file system: write, delete, and sector reference. Your job is to reproduce the behavior of this file system and then write a program that outputs which files are located in the target sector when the reference command is executed. In the initial state, nothing is written on the recording medium. For example, let's look at the first example of Sample Input. The first instruction writes a file with an identifier of 0 and a size of 2. In the initial state, nothing is written to the recording medium, that is, all sectors are free areas, so writing is performed to the first two sectors, that is, the 0th sector and the 1st sector. Therefore, the storage medium after writing is as follows. 0 0 Sky Sky Sky Sky Sky Sky ... The second instruction writes a file with the identifier 1 to the second and third sectors. The state of the storage medium after this is as follows. 0 0 1 1 Sky Sky Sky Sky ... The third instruction deletes the file with the identifier 0. The state of the storage medium is as follows. Sky Sky 1 1 Sky Sky Sky Sky ... The fourth instruction writes the file with the identifier 2 to the 0th, 1st, 4th, and 5th sectors. 2 2 1 1 2 2 Sky Sky ... The last instruction refers to the third sector. Now that you have a file with the identifier 1 in the third sector, your program should output 1. Input The input consists of multiple datasets. Each dataset is given in the following format. > N > Command1 > Command2 > ... > CommandN N is the number of commands executed (1 ≤ N ≤ 10,000), and Commandi is the i-th command to be executed. Each command consists of a command name and one or two arguments. The command name consists of only one letter and can be either "W", "D", or "R". There is a space between the command and the argument, and between the argument and the argument. "W" represents a write command. Two arguments I (0 ≤ I ≤ 109) and S (1 ≤ S ≤ 109) are given. Each shows the identifier of the file to write and the number of sectors required to store the file. "D" represents the delete command. One argument I (0 ≤ I ≤ 109) is given. Indicates the identifier of the file to be deleted. "R" represents the reference command. One argument P (0 ≤ P ≤ 109) is given. Indicates the number of the sector to be referenced. It can be assumed that sectors with numbers higher than 109 do not need to be accessed. Also, it is guaranteed that a file with the same file identifier will not be written multiple times. The end of the input is indicated by one line containing one 0. Output For each dataset, output the identifier of the file referenced by that command on a single line each time a referenced command appears. If no file has been written to the referenced sector, output -1 instead of the file identifier. Put a blank line after each dataset. Sample Input 6 W 0 2 W 1 2 D 0 W 2 4 R 3 R 1 1 R 1000000000 0 Output for the Sample Input 1 2 -1 Example Input 6 W 0 2 W 1 2 D 0 W 2 4 R 3 R 1 1 R 1000000000 0 Output 1 2 -1 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Example Input 8 -10 0 -10 5 -5 5 -5 0 10 0 10 -5 5 -5 5 0 Output 50 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. I: Ravage Santa Claus was caught in the illuminations of the city and broke it. There are N light bulbs in the illumination, and the $ i $ th light bulb only comes on when the voltage is above $ A_i $ and below $ B_i $. The voltage should be the same everywhere in the illumination. Find out how many light bulbs can be lit at the same time by adjusting the voltage. input The integer $ N $ is given on the first line. Of the following $ N $ lines, $ A_i and B_i $ are given on the $ i $ line, separated by blanks. output Output the maximum number of light bulbs that can be illuminated at the same time. Constraint * $ N $ is an integer greater than or equal to $ 1 $ and less than or equal to $ 100 \ 000 $ * $ A_1, A_2, A_3, \ dots, A_N $ are integers greater than or equal to $ 1 $ and less than or equal to $ 1 \ 000 \ 000 \ 000 $ * $ B_1, B_2, B_3, \ dots, B_N $ are integers greater than or equal to $ 1 $ and less than or equal to $ 1 \ 000 \ 000 \ 000 $ * Satisfy $ A_i \ leq B_i $ for all light bulbs $ i $ Input example 1 Four 14 3 6 2 7 5 8 Output example 1 3 When the voltage is $ 5 $ or $ 3.14 $, there are $ 3 $ bulbs. Input example 2 2 1 2 twenty three Output example 2 2 Example Input 4 1 4 3 6 2 7 5 8 Output 3 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. Write a program which prints the central coordinate ($cx$,$cy$) and the radius $r$ of a incircle of a triangle which is constructed by three points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) on the plane surface. Constraints * $-10000 \leq x_i, y_i \leq 10000$ * The three points are not on the same straight line Input The input is given in the following format $x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ All the input are integers. Output Print $cx$, $cy$ and $r$ separated by a single space in a line. The output values should be in a decimal fraction with an error less than 0.000001. Examples Input 1 -2 3 2 -2 0 Output 0.53907943898209422325 -0.26437392711448356856 1.18845545916395465278 Input 0 3 4 0 0 0 Output 1.00000000000000000000 1.00000000000000000000 1.00000000000000000000 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
Solve the programming task below in a Python markdown code block. For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find the lower bound for a specific value $k$ given as a query. * lower bound: the place pointing to the first element greater than or equal to a specific value, or $n$ if there is no such element. Constraints * $1 \leq n \leq 100,000$ * $1 \leq q \leq 200,000$ * $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$ * $0 \leq k_i \leq 1,000,000,000$ Input The input is given in the following format. $n$ $a_0 \; a_1 \; ,..., \; a_{n-1}$ $q$ $k_1$ $k_2$ : $k_q$ The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries. Output For each query, print the position $i$ ($i = 0, 1, ..., n$) of the lower bound in a line. Example Input 4 1 2 2 4 3 2 3 5 Output 1 3 4 The input will be give Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.

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