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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` n,m,k = map(int,input().split()) l = list(map(int,input().split())) l.sort() x = m//(k+1) a = x*(l[-1]*k+l[-2]) y = m%(k+1) a+=y*l[-1] print(a) ```
instruction
0
71,689
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Yes
output
1
71,689
19
143,379
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` n, m, k=map(int, input().split()) a = [int(x) for x in input().split()] a = sorted(a) mx = a[n-1] mx2 = a[n-2] ans = (m//(k+1)) * mx2 + (m - m // (k+1)) *mx print(ans) ```
instruction
0
71,690
19
143,380
Yes
output
1
71,690
19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` n,m,k=map(int,input().split()) A=list(map(int,input().split())) A.sort() max = A[-1] min = A[-2] if m % (k + 1) == 0: t = m // (k + 1) an = t * k * max + t * min print(an) else: t = m // (k + 1) an = t * k * max + t * min an += (m % (k + 1)) * max print(an) ```
instruction
0
71,691
19
143,382
Yes
output
1
71,691
19
143,383
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` def bin_pow(a, n): if n == 0: return 1 else: if n % 2 == 0: return bin_pow(a, n//2)**2 else: return bin_pow(a, n-1)*a def main(): a = list(map(int, input().split())) b = list(map(int, input().split())) tmp = 1 ans = 0 #print(b) m1 = max(b) #print(m1) b.remove(m1) m2 = max(b) b.append(m1) #print(m2) #print(b) ans = (a[1] / (a[2] + 1)) * (a[2] * m2 + m1) + a[1] % (a[2] + 1) * m2 #print() print(int(ans)) if __name__ == "__main__": main() ```
instruction
0
71,692
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No
output
1
71,692
19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` n,k,m=map(int,input().split()) a=list(map(int,input().split())) a.sort(reverse=True) if m==0: print(0) else: x=k//(m+1) c=0 if k>m: c+=a[0]*m*x+a[1]*(n%(m)) c+=a[1]*x elif k<=m: c+=k*a[0] print(c) ```
instruction
0
71,693
19
143,386
No
output
1
71,693
19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` h = 0 nmk_in = input() nmk = list(map(int, nmk_in.split(' '))) m = nmk[1] k = nmk[2] emotes_in = input() emotes = list(map(int, emotes_in.split(' '))) emotes.sort() emotes.reverse() ##i = 0 ##while m > 0: ## if (i%2==0): ## h += k*emotes[0] ## m -= k ## else: ## h += emotes[1] ## m -= 1 ## i += 1 n1 = m//(k+1) ##print(n1) ##h += (n1-1)*k*emotes[0]+(m-(n1-1)*k)*emotes[1] h += n1*k*emotes[0]+(m-n1*k)*emotes[1] print(h) ```
instruction
0
71,694
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No
output
1
71,694
19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are n emotes in very popular digital collectible card game (the game is pretty famous so we won't say its name). The i-th emote increases the opponent's happiness by a_i units (we all know that emotes in this game are used to make opponents happy). You have time to use some emotes only m times. You are allowed to use any emotion once, more than once, or not use it at all. The only restriction is that you cannot use the same emote more than k times in a row (otherwise the opponent will think that you're trolling him). Note that two emotes i and j (i ≠ j) such that a_i = a_j are considered different. You have to make your opponent as happy as possible. Find the maximum possible opponent's happiness. Input The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ m ≤ 2 ⋅ 10^9) — the number of emotes, the number of times you can use emotes and the maximum number of times you may use the same emote in a row. The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is value of the happiness of the i-th emote. Output Print one integer — the maximum opponent's happiness if you use emotes in a way satisfying the problem statement. Examples Input 6 9 2 1 3 3 7 4 2 Output 54 Input 3 1000000000 1 1000000000 987654321 1000000000 Output 1000000000000000000 Note In the first example you may use emotes in the following sequence: 4, 4, 5, 4, 4, 5, 4, 4, 5. Submitted Solution: ``` t,m,k=map(int,input().split()) l=list(map(int,input().split())) max1=max(l) l.remove(max1) max2=max(l) ans = 0 a =m//(k+1) ans = a*( k*max1 + max2) print(ans) b = m%(k+1) ans += b*max1 print(ans) ```
instruction
0
71,695
19
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No
output
1
71,695
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Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,237
19
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Tags: implementation, probabilities, strings Correct Solution: ``` s=input() n=len(s) pos=[[] for i in range(26)] for i in range(len(s)): pos[ord(s[i])-97].append(s[i:] + s[:i]) ans=0 for i in range(26): max1=0 for j in range(n): b=[0 for i in range(26)] for k in pos[i]: b[ord(k[j])-97]+=1 temp1=0 for k in range(26): if(b[k]==1): temp1+=1 max1=max(temp1,max1) ans+=max1 print(ans/n) ```
output
1
72,237
19
144,475
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,238
19
144,476
Tags: implementation, probabilities, strings Correct Solution: ``` str = input() l = len(str) a = [0] * (2 * l) pos = [[] for i in range(26)] for i, c in enumerate(str): t = ord(c) - ord('a') a[i] = t a[i + l] = t pos[t].append(i) ans = 0 for c in range(26): cur = 0 for k in range(1, l): cnt = [0] * 26 for i in pos[c]: cnt[a[i + k]] += 1 cur = max(cur, len(list(filter(lambda x : x == 1, cnt)))) ans += cur print(ans / l) ```
output
1
72,238
19
144,477
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,239
19
144,478
Tags: implementation, probabilities, strings Correct Solution: ``` str = input() l = len(str) a = [0] * (2 * l) pos = [[] for i in range(26)] for i, c in enumerate(str): t = ord(c) - ord('a') a[i] = t a[i + l] = t pos[t].append(i) ans = 0 for c in range(26): cur = 0 for k in range(1, l): cnt = [0] * 26 for i in pos[c]: cnt[a[i + k]] += 1 cur = max(cur, len([1 for x in cnt if x == 1])) ans += cur print(ans / l) ```
output
1
72,239
19
144,479
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,240
19
144,480
Tags: implementation, probabilities, strings Correct Solution: ``` import sys from collections import defaultdict s = sys.stdin.readline().strip() n = len(s) s_mp = defaultdict(list) for i in range(n): s_mp[s[i]].append(i) result = 0 for let, starts in s_mp.items(): max_p = 0.0 for j in range(1, n): cnter = defaultdict(int) for start in starts: cnter[s[(start + j) % n]] += 1 uniq = 0 for i, v in cnter.items(): if v == 1: uniq += 1 max_p = max(max_p, uniq/len(starts)) total = len(starts) result += max_p * len(starts)/n print('{:.8f}'.format(result)) ```
output
1
72,240
19
144,481
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,241
19
144,482
Tags: implementation, probabilities, strings Correct Solution: ``` str = input() l = len(str) a = [] for c in str: a.append(ord(c) - ord('a')) a *= 2 tot = [[0] * l for i in range(26)] for i in range(1, l): cnt = [[0] * 26 for i in range(26)] for j in range(l): cnt[a[j]][a[j + i]] += 1 for j in range(l): if cnt[a[j]][a[j + i]] == 1: tot[a[j]][i] += 1 ans = 0 for sub in tot: ans += max(sub) print(ans / l) ```
output
1
72,241
19
144,483
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,242
19
144,484
Tags: implementation, probabilities, strings Correct Solution: ``` s = str(input()) n = len(s) t = s+s P = [[[0]*26 for i in range(26)] for j in range(n)] for i in range(n): c1 = ord(t[i])-ord('a') for j in range(1, n): c2 = ord(t[i+j])-ord('a') P[j][c1][c2] += 1 s = set(s) ans = 0 for c1 in s: c1 = ord(c1)-ord('a') M = 0 for j in range(1, n): temp = 0 for c2 in range(26): if P[j][c1][c2] == 1: temp += 1 M = max(M, temp) ans += M print(ans/n) ```
output
1
72,242
19
144,485
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,243
19
144,486
Tags: implementation, probabilities, strings Correct Solution: ``` def func(a): b=[0]*26 for i in range(len(a)): b[ord(a[i])-ord("a")]+=1 c=0 for i in b: if i==1: c=c+1 return c s=input() n=len(s) a={} for i in range(n): a[s[i]]=[] for i in range(n): a[s[i]].append(i) c=0 for i in a: if len(a[i])==1: c=c+1 else: e=[] for j in range(n): b=[] d=0 for k in a[i]: b.append((s[(k+j)%n])) d=d+func(b) e.append(d) c=c+max(e) print(c/n) ```
output
1
72,243
19
144,487
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
instruction
0
72,244
19
144,488
Tags: implementation, probabilities, strings Correct Solution: ``` s=input() d=dict() mod=[] mx=[] for k in s: d[k]=[] for i in range(len(s)): d[s[i]].append(i) index=0 for k in d.keys(): mod.append(d[k]) for k in mod: mxct=0 ct=0 x=[] for i in range(len(s)): ct=0 dic=dict() for j in k: elt = s[(j+i)%(len(s))] if elt in dic.keys(): dic[elt]+=1 else: dic[elt]=1 for r in dic.keys(): if dic[r]==1: ct+=1 mxct=max(ct,mxct) mx.append(mxct) sm=0 for k in mx: sm+=k print(sm/len(s)) ```
output
1
72,244
19
144,489
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` str = input() l = len(str) a = [0] * (2 * l) pos = [[] for i in range(26)] for i, c in enumerate(str): t = ord(c) - ord('a') a[i] = t a[i + l] = t pos[t].append(i) ans = 0 for c in range(26): cur = 0 for k in range(1, l): cnt = [0] * 26 for i in pos[c]: cnt[a[i + k]] += 1 tot = 0 for i in cnt: if i == 1: tot += 1 cur = max(cur, tot) ans += cur print(ans / l) ```
instruction
0
72,245
19
144,490
Yes
output
1
72,245
19
144,491
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` #Code by Sounak, IIESTS #------------------------------warmup---------------------------- import os import sys import math from io import BytesIO, IOBase from fractions import Fraction import collections from itertools import permutations from collections import defaultdict BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #-------------------game starts now----------------------------------------------------- s = input() l = len(s) instances = [[] for x in range(26)] s_i = [ord(c) - 97 for c in s] for i in range(l): instances[s_i[i]].append(i) #sum_probability += len * probability #probability = sum_probabilty sum_probability = 0 for c in range(0,26): if not instances[c]: continue if len(instances[c]) == 0: sum_probability += 1 continue max_probability = 0 for guess in range(1, l): num_seen = [0]*26 probability = 0 for index in instances[c]: num_seen[s_i[(index+guess)%l]] += 1 for x in num_seen: if x == 1: probability += 1 max_probability = max(max_probability, probability) sum_probability += max_probability print(sum_probability/l) ```
instruction
0
72,246
19
144,492
Yes
output
1
72,246
19
144,493
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` s = input() l = len(s) instances = [[] for x in range(26)] s_i = [ord(c) - 97 for c in s] for i in range(l): instances[s_i[i]].append(i) #sum_probability += len * probability #probability = sum_probabilty sum_probability = 0 for c in range(0,26): if not instances[c]: continue if len(instances[c]) == 0: sum_probability += 1 continue max_probability = 0 for guess in range(1, l): num_seen = [0]*26 probability = 0 for index in instances[c]: num_seen[s_i[(index+guess)%l]] += 1 for x in num_seen: if x == 1: probability += 1 max_probability = max(max_probability, probability) sum_probability += max_probability print(sum_probability/l) ```
instruction
0
72,247
19
144,494
Yes
output
1
72,247
19
144,495
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` s = input() n = len(s) sett = {} for i in range(n): if s[i] not in sett: sett[s[i]] = [] sett[s[i]].append(s[i + 1:] + s[:i]) ans = 0 # ao fazer sett.items(), é realizado unpack da chave,valor para k,l, respectivamente for k, l in sett.items(): tmp = 0 for j in range(n - 1): seen, sett1 = set(), set() for i in range(len(l)): if l[i][j] in sett1: sett1.remove(l[i][j]) elif l[i][j] not in seen: sett1.add(l[i][j]) seen.add(l[i][j]) tmp = max(tmp, len(sett1)) tmp /= n ans += tmp # precisao 10^6 print('{:.7}'.format(ans)) ```
instruction
0
72,248
19
144,496
Yes
output
1
72,248
19
144,497
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` # https://codeforces.com/problemset/problem/930/B S = input() d = {} is_ok = {} n = len(S) for i, c in enumerate(S): if c not in d: d[c] = [] d[c].append(i) for k in d: is_ok[k] = False for k in range(1, n): for c in d: next_c = [S[(i+k)%n] for i in d[c]] next_c = set(next_c) if len(next_c) == len(d[c]): is_ok[c] = True count = 0 for k in is_ok: if is_ok[k] == True: count += len(d[k]) if count > 0 : print(count / n) else: print(1 / n) ```
instruction
0
72,249
19
144,498
No
output
1
72,249
19
144,499
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` from collections import defaultdict, Counter k_cnt = defaultdict(int) s = input() digs = set(s) n = len(s) for i in range(n): for k in range(1, n-1): k_cnt[(s[i], s[(i+k)%n], k)] += 1 meet_props = Counter(s) # print(meet_props) prop = 0 for b in digs: # print('possible pairs for ', [(b,a,k,' ', k_cnt[(b,a,k)]) for a in digs for k in range(1, n-1) if k_cnt[(b,a,k)]]) min_pairs = min([k_cnt[(b,a,k)] for a in digs for k in range(1, n-1) if k_cnt[(b,a,k)]>0]) # print(b, 'min_pairs = ', min_pairs) if min_pairs == 1: prop += meet_props[b] print(prop/n) ```
instruction
0
72,250
19
144,500
No
output
1
72,250
19
144,501
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. Input The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. Output Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image> Examples Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 Note In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. Submitted Solution: ``` s=input() def uniq(iii): for jj in range(1,len(s)): se=set(s[ii-jj] for ii in iii) if len(se)==len(iii): return 1 aa={} for ii,ss in enumerate(s): aa.setdefault(ss,[]).append(ii) ans=0 for iii in aa.values(): if uniq(iii): ans+=len(iii) print(ans/len(s)) ```
instruction
0
72,251
19
144,502
No
output
1
72,251
19
144,503
Provide tags and a correct Python 3 solution for this coding contest problem. In some country live wizards. They love playing with numbers. The blackboard has two numbers written on it — a and b. The order of the numbers is not important. Let's consider a ≤ b for the sake of definiteness. The players can cast one of the two spells in turns: * Replace b with b - ak. Number k can be chosen by the player, considering the limitations that k > 0 and b - ak ≥ 0. Number k is chosen independently each time an active player casts a spell. * Replace b with b mod a. If a > b, similar moves are possible. If at least one of the numbers equals zero, a player can't make a move, because taking a remainder modulo zero is considered somewhat uncivilized, and it is far too boring to subtract a zero. The player who cannot make a move, loses. To perform well in the magic totalizator, you need to learn to quickly determine which player wins, if both wizards play optimally: the one that moves first or the one that moves second. Input The first line contains a single integer t — the number of input data sets (1 ≤ t ≤ 104). Each of the next t lines contains two integers a, b (0 ≤ a, b ≤ 1018). The numbers are separated by a space. Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator. Output For any of the t input sets print "First" (without the quotes) if the player who moves first wins. Print "Second" (without the quotes) if the player who moves second wins. Print the answers to different data sets on different lines in the order in which they are given in the input. Examples Input 4 10 21 31 10 0 1 10 30 Output First Second Second First Note In the first sample, the first player should go to (11,10). Then, after a single move of the second player to (1,10), he will take 10 modulo 1 and win. In the second sample the first player has two moves to (1,10) and (21,10). After both moves the second player can win. In the third sample, the first player has no moves. In the fourth sample, the first player wins in one move, taking 30 modulo 10.
instruction
0
72,777
19
145,554
Tags: games, math Correct Solution: ``` def solve(a, b): if a == 0: return False if solve(b % a, a): b //= a return not (b % (a + 1) & 1) return True n = int(input()) for _ in range(n): a, b = [int(x) for x in input().split()] if a > b: a, b = b, a if solve(a, b): print("First") else: print("Second") ```
output
1
72,777
19
145,555
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. In some country live wizards. They love playing with numbers. The blackboard has two numbers written on it — a and b. The order of the numbers is not important. Let's consider a ≤ b for the sake of definiteness. The players can cast one of the two spells in turns: * Replace b with b - ak. Number k can be chosen by the player, considering the limitations that k > 0 and b - ak ≥ 0. Number k is chosen independently each time an active player casts a spell. * Replace b with b mod a. If a > b, similar moves are possible. If at least one of the numbers equals zero, a player can't make a move, because taking a remainder modulo zero is considered somewhat uncivilized, and it is far too boring to subtract a zero. The player who cannot make a move, loses. To perform well in the magic totalizator, you need to learn to quickly determine which player wins, if both wizards play optimally: the one that moves first or the one that moves second. Input The first line contains a single integer t — the number of input data sets (1 ≤ t ≤ 104). Each of the next t lines contains two integers a, b (0 ≤ a, b ≤ 1018). The numbers are separated by a space. Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator. Output For any of the t input sets print "First" (without the quotes) if the player who moves first wins. Print "Second" (without the quotes) if the player who moves second wins. Print the answers to different data sets on different lines in the order in which they are given in the input. Examples Input 4 10 21 31 10 0 1 10 30 Output First Second Second First Note In the first sample, the first player should go to (11,10). Then, after a single move of the second player to (1,10), he will take 10 modulo 1 and win. In the second sample the first player has two moves to (1,10) and (21,10). After both moves the second player can win. In the third sample, the first player has no moves. In the fourth sample, the first player wins in one move, taking 30 modulo 10. Submitted Solution: ``` def gcd(a, b): a, b = min(a, b), max(a, b) if a == 0: return False if not gcd(b % a, a): return True if a % 2 == 1: return 1 - (b // a) % 2 ans1 = True ans2 = False j = a while j <= b: ans1 ^= (b // j) % 2 j *= a j = a while j <= b - a: ans2 ^= ((b - a) // j) % 2 j *= a return ans1 | ans2 t = int(input()) for i in range(t): a, b = map(int, input().split()) if gcd(a, b): print("First") else: print("Second") ```
instruction
0
72,778
19
145,556
No
output
1
72,778
19
145,557
Provide tags and a correct Python 3 solution for this coding contest problem. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing.
instruction
0
72,847
19
145,694
Tags: dp, games Correct Solution: ``` a, b, L = list(map(int, input().split())) import sys import math if a == 1 and 2 ** b >= L: print("Missing") sys.exit() memo = {} memo[(32001, 1)] = 0 memo[(1, 30)] = 0 for i in range(min(int(L ** (1 / b)) + 1, 32000), a - 1, -1): for j in range(29, b - 1, -1): # If it's not a terminal state, we need to compute the mex if i ** j >= L: continue s = set() if (i + 1) ** j < L: s.add(memo[(i + 1, j)]) if i ** (j + 1) < L: s.add(memo[(i, j + 1)]) mex = 0 while mex in s: mex += 1 memo[(i, j)] = mex if memo[(a, b)] > 0: print("Masha") else: print("Stas") ```
output
1
72,847
19
145,695
Provide tags and a correct Python 3 solution for this coding contest problem. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing.
instruction
0
72,848
19
145,696
Tags: dp, games Correct Solution: ``` a, b, L = list(map(int, input().split())) memo = {} #10^9 rougly equals 31700 * 31700 memo[(31701, 1)] = ((L - 31701) + 1)% 2 #2**30 > 10^9 memo[(1, 30)] = -1 for i in range(31700, a - 1, -1): for j in range(29, b - 1, -1): if i**j>=L: continue s = set() if (i + 1) ** j < L: s.add(memo[(i + 1, j)]) if i ** (j + 1) < L: s.add(memo[(i, j + 1)]) if 0 not in s and -1 in s: memo[(i, j)] = -1 else: mex = 0 while mex in s: mex += 1 memo[(i, j)] = mex if memo[(a, b)] > 0: print("Masha") elif memo[(a, b)] == -1: print("Missing") else: print("Stas") ```
output
1
72,848
19
145,697
Provide tags and a correct Python 3 solution for this coding contest problem. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing.
instruction
0
72,849
19
145,698
Tags: dp, games Correct Solution: ``` a, b, L = list(map(int, input().split())) import sys import math memo = {} memo[(31701, 1)] = ((L - 31701) + 1)% 2 memo[(1, 30)] = -1 # memo[(a, b)] = 0 if a ** b >= L else 1 # max_a = min(int(L ** (1 / b)) + 1, int(L ** (1 / 2)) + 1) for i in range(31700, a - 1, -1): for j in range(29, b - 1, -1): if i ** j >= L: continue s = set() if (i + 1) ** j < L: s.add(memo[(i + 1, j)]) if i ** (j + 1) < L: s.add(memo[(i, j + 1)]) if 0 not in s and -1 in s: memo[(i, j)] = -1 else: mex = 0 while mex in s: mex += 1 memo[(i, j)] = mex if memo[(a, b)] > 0: print("Masha") elif memo[(a, b)] == -1: print("Missing") else: print("Stas") ```
output
1
72,849
19
145,699
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing. Submitted Solution: ``` from math import log def first_wins(a, b, n): if pow(a + 1, b) >= n and pow(a, b + 1) >= n: return False if pow(a, b + 1) >= n: x = int(log(n, a)) - 1 while pow(a, x) < n: x += 1 return not ((n - pow(a, x - 1)) % 2) return (not first_wins(a + 1, b, n) or not first_wins(a, b + 1, n)) a, b, n = map(int, input().split()) if a == 1 and pow(2, b) >= n: print('Missing') elif first_wins(a, b, n): print('Masha') else: print('Stas') ```
instruction
0
72,850
19
145,700
No
output
1
72,850
19
145,701
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing. Submitted Solution: ``` a, b, L = list(map(int, input().split())) import sys import math # a**b <= L # b <= log(L,a) # if a==1 then b<30 def solve(a, b): memo = {} max_exponent = int(math.log(L, a)) + 1 if a != 1 else int(math.log(L, 2)) + 1 for i in range(int(L ** (1 / b)) + 1, a - 1, -1): for j in range(max_exponent, b - 1, -1): # If it's not a terminal state, we need to compute the mex if i ** j >= L: continue s = set() if (i + 1) ** j < L: s.add(memo[(i + 1, j)]) if i ** (j + 1) < L: s.add(memo[(i, j + 1)]) mex = 0 while mex in s: mex += 1 memo[(i, j)] = mex if memo[(a, b)] > 0: return "Masha" else: return "Stas" if a == 1 and 2 ** b >= L: print("Missing") sys.exit() if a == 1: if solve(2, b) == "Stas": print("Masha") else: print("Stas") else: print(solve(a, b)) ```
instruction
0
72,851
19
145,702
No
output
1
72,851
19
145,703
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing. Submitted Solution: ``` a, b, L = list(map(int, input().split())) import sys import math # a**b <= L # b <= log(L,a) # if a==1 then b<30 def solve(a, b): memo = {} max_exponent = int(math.log(L, a)) + 1 if a != 1 else int(math.log(L, 2)) + 1 for i in range(int(L ** (1 / b)) + 1, a - 1, -1): for j in range(max_exponent, b - 1, -1): # If it's not a terminal state, we need to compute the mex if i ** j >= L: continue s = set() if (i + 1) ** j < L: s.add(memo[(i + 1, j)]) if i ** (j + 1) < L: s.add(memo[(i, j + 1)]) mex = 0 while mex in s: mex += 1 memo[(i, j)] = mex if memo[(a, b)] > 0: return "Masha" else: return "Stas" if a == 1 and 2 ** b >= L: print("Missing") sys.exit() if a == 1: if solve(2, b) == "Stas": print("Mash") else: print("Stas") else: solve(a, b) ```
instruction
0
72,852
19
145,704
No
output
1
72,852
19
145,705
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items. Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty. Who loses if both players play optimally and Stas's turn is first? Input The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n. Output Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing". Examples Input 2 2 10 Output Masha Input 5 5 16808 Output Masha Input 3 1 4 Output Stas Input 1 4 10 Output Missing Note In the second example the initial number of ways is equal to 3125. * If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat. * But if Stas increases the number of items, then any Masha's move will be losing. Submitted Solution: ``` from math import log def first_wins(a, b, n): if pow(a, b) >= n: return True if pow(a, b + 1) >= n: x = log(n, a) - 1 while pow(a, x) < n: x += 1 return not ((n - pow(a, x - 1)) % 2) if not first_wins(a + 1, b, n) or not first_wins(a, b + 1, n): return True return False a, b, n = map(int, input().split()) if a == 1 and pow(2, b) >= n: print('Missing') elif first_wins(a, b, n): print('Masha') else: print('Stas') ```
instruction
0
72,853
19
145,706
No
output
1
72,853
19
145,707
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,966
19
145,932
Tags: brute force, implementation Correct Solution: ``` import sys def finder(arr): if any(map(lambda x: x.find('.xx') > -1 or x.find('xx.') > -1 or x.find('x.x') > -1, arr)): print('YES') sys.exit() field = [input() for _ in range(4)] finder(field) transposed = list(map(lambda x: ''.join(x), zip(*field[::-1]))) finder(transposed) def diags(arr): for y_of in range(2): for x_of in range(2): yield ''.join([arr[y_of + i][x_of + i] for i in range(3)]) yield ''.join([arr[3-(y_of + i)][x_of + i] for i in range(3)]) finder(list(diags(field))) print('NO') ```
output
1
72,966
19
145,933
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,967
19
145,934
Tags: brute force, implementation Correct Solution: ``` def check(AL): for i in AL: if (i[:3].count('x')==2 and '.' in i[:3]) or (i[1:].count('x')==2 and '.' in i[1:]): return True B=[[0,0],[0,1],[1,0],[1,1]] C=[] for a,b in B: l=[] for i in range(3):l.append(AL[a+i][b+i]) C.append(l) for i in C: if i.count('x')==2 and '.'in i:return True return False A=[] for i in range(4):A.append(input()) D=[] for i in range(4): l=[] for j in range(4): l.append(A[j][3-i]) D.append(l) print('YES' if check(A) or check(D) else 'NO') ```
output
1
72,967
19
145,935
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,968
19
145,936
Tags: brute force, implementation Correct Solution: ``` a = [] for i in range(4): s = input() for elem in s: a.append(elem) def c(q, w, e): q -= 1 w -= 1 e -= 1 q = a[q] w = a[w] e = a[e] kr = 0 ps = 0 if (q == 'o') or (w == 'o') or (e == 'o'): return False if (q == 'x'): kr += 1 if (w == 'x'): kr += 1 if (e == 'x'): kr += 1 if (kr == 2): print("YES") exit() return True else: return False c(1, 2, 3) c(2, 3, 4) c(5, 6, 7) c(6, 7, 8) c(9, 10, 11) c(10, 11, 12) c(13, 14, 15) c(14, 15, 16) c(1, 5, 9) c(5, 9, 13) c(2, 6, 10) c(6, 10, 14) c(3, 7, 11) c(7, 11, 15) c(4, 8, 12) c(8, 12, 16) c(1, 6, 11) c(5, 10, 15) c(2, 7, 12) c(6, 11, 16) c(3, 6, 9) c(7, 10, 13) c(4, 7, 10) c(8, 11, 14) print("NO") ```
output
1
72,968
19
145,937
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,969
19
145,938
Tags: brute force, implementation Correct Solution: ``` x=[] for i in range(4): x.append(list(input())) def check(a,b): x[a][b]='x' for i in range(4): for j in range(2): if x[i][j]+x[i][j+1]+x[i][j+2]=='xxx': return('YES') for i in range(2): for j in range(4): if x[i][j]+x[i+1][j]+x[i+2][j]=='xxx': return('YES') if x[2][0]+x[1][1]+x[0][2]=='xxx':return('YES') if x[3][0]+x[2][1]+x[1][2]=='xxx':return('YES') if x[2][1]+x[1][2]+x[0][3]=='xxx':return('YES') if x[3][1]+x[2][2]+x[1][3]=='xxx':return('YES') if x[0][0]+x[1][1]+x[2][2]=='xxx':return('YES') if x[1][0]+x[2][1]+x[3][2]=='xxx':return('YES') if x[0][1]+x[1][2]+x[2][3]=='xxx':return('YES') if x[1][1]+x[2][2]+x[3][3]=='xxx':return('YES') return('NO') for i in range(4): for j in range(4): if x[i][j]=='.': if check(i,j)=='YES': print('YES') quit() x[i][j]='.' else: print('NO') ```
output
1
72,969
19
145,939
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,970
19
145,940
Tags: brute force, implementation Correct Solution: ``` def verify(x): won = 0 for row in x: won += 'xxx' in row xt = ["".join([line[i] for line in x]) for i in range(4)] for col in xt: won += 'xxx' in col for mat in [x, [line[::-1] for line in x]]: won += 'xxx' in mat[0][0] + mat[1][1] + mat[2][2] + mat[3][3] won += 'xxx' in mat[0][1] + mat[1][2] + mat[2][3] won += 'xxx' in mat[1][0] + mat[2][1] + mat[3][2] return won def split_in_rows(x): return [x[i:i+4] for i in range(0, len(x), 4)] if __name__ == '__main__': nlines = 4 lines = list() for _ in range(nlines): lines.append(input()) lines = "".join(lines) won = 0 i = 0 while won == 0 and i < len(lines): if lines[i] == '.': won += verify(split_in_rows(lines[:i]+'x'+lines[i+1:])) i += 1 if won > 0: print("YES") else: print("NO") ```
output
1
72,970
19
145,941
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,971
19
145,942
Tags: brute force, implementation Correct Solution: ``` t = [input() for _ in range(4)] w = ["xx.", ".xx", "x.x"] if any(i in j for i in w for j in t): print("YES") else: for p in range(4): c = "".join([r[p] for r in t]) if any(i in c for i in w): print("YES") break else: d = [t[0][0]+t[1][1]+t[2][2]+t[3][3], t[1][0]+t[2][1]+t[3][2], t[0][1]+t[1][2]+t[2][3], t[3][0]+t[2][1]+t[1][2]+t[0][3], t[2][0]+t[1][1]+t[0][2], t[3][1]+t[2][2]+t[1][3]] if any(i in j for i in w for j in d): print("YES") else: print("NO") ```
output
1
72,971
19
145,943
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,972
19
145,944
Tags: brute force, implementation Correct Solution: ``` A = [] for i in range(4): A.append(input()) answer = False answer_platform = ['xx.', 'x.x', '.xx'] for i in range(4): if A[i][0:3] in answer_platform or A[i][1:] in answer_platform: answer = True if A[0][i] + A[1][i] + A[2][i] in answer_platform or A[1][i] + A[2][i] + A[3][i] in answer_platform : answer = True if A[1][0] + A[2][1] + A[3][2] in answer_platform or A[0][1] + A[1][2] + A[2][3] in answer_platform or A[0][0] + A[1][1] + A[2][2] in answer_platform or A[1][1] + A[2][2]+A[3][3] in answer_platform: answer = True if A[0][2] + A[1][1] + A[2][0] in answer_platform or A[1][3] + A[2][2] + A[3][1] in answer_platform or A[0][3] + A[1][2] + A[2][1] in answer_platform or A[1][2] + A[2][1] + A[3][0] in answer_platform: answer = True if answer: print("YES") else: print("NO") ```
output
1
72,972
19
145,945
Provide tags and a correct Python 3 solution for this coding contest problem. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn.
instruction
0
72,973
19
145,946
Tags: brute force, implementation Correct Solution: ``` from sys import stdin ,stdout from os import path rd = lambda:stdin.readline().strip() wr = stdout.write if(path.exists('input.txt')): stdin = open("input.txt","r") import time ,math #------------------------------------= mylist= [] for i in range(4): mylist.append(rd()) def validUpOrDown(x,y): if x+2 < 4 : counterX = counterD = 0 for i in range(x,x+3): if mylist[i][y] == 'x': counterX+=1 elif mylist[i][y] == '.': counterD +=1 if counterD == 1 and counterX == 2: return True if x-2 >= 0 : counterX = counterD = 0 for i in range(x,x-3,-1): if mylist[i][y] == 'x': counterX+=1 elif mylist[i][y] == '.': counterD +=1 if counterD == 1 and counterX == 2: return True def validLeftOrRight(x,y): if y+2 < 4 : counterX = counterD = 0 for i in range(y,y+3): if mylist[x][i] == 'x': counterX+=1 elif mylist[x][i] == '.': counterD +=1 if counterD == 1 and counterX == 2: return True if y-2 >= 0 : counterX = counterD = 0 for i in range(y,y-3,-1): if mylist[x][i] == 'x': counterX+=1 elif mylist[x][i] == '.': counterD +=1 if counterD == 1 and counterX == 2: return True def validDiagonal(x,y): if x+2 < 4 and y+2 < 4: counter = counterX = counterD =0 x1,y1 = x,y while counter < 3: if mylist[x1][y1] == 'x': counterX +=1 elif mylist[x1][y1] =='.': counterD+=1 counter+=1 x1+=1 y1+=1 if counterX == 2 and counterD ==1 : return True if x+2 < 4 and y-2 >= 0: counter = counterX = counterD =0 x1,y1 = x,y while counter < 3: if mylist[x1][y1] == 'x': counterX +=1 elif mylist[x1][y1] =='.': counterD+=1 counter+=1 x1+=1 y1-=1 if counterX == 2 and counterD ==1 : return True if x-2 >= 0 and y+2 < 4: counter = counterX = counterD =0 x1,y1 = x,y while counter < 3: if mylist[x1][y1] == 'x': counterX +=1 elif mylist[x1][y1] =='.': counterD+=1 counter+=1 x1-=1 y1+=1 if counterX == 2 and counterD ==1 : return True if x-2 >= 0 and y-2>=0: counter = counterX = counterD =0 x1,y1 = x,y while counter < 3: if mylist[x1][y1] == 'x': counterX +=1 elif mylist[x1][y1] =='.': counterD+=1 counter+=1 x1-=1 y1-=1 if counterX == 2 and counterD ==1 : return True wrong = True for i in range(len(mylist)): for j in range(len(mylist[i])): if mylist[i][j] == 'x': if validLeftOrRight(i,j) == True or validUpOrDown(i,j) == True or validDiagonal(i,j) == True: wrong = False break print("YES" if wrong == False else "NO") ```
output
1
72,973
19
145,947
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` ttt = [] xs = [] mA = [-2, -2, -2, 0, 0, 2, 2, 2] mB = [-2, 0, 2, -2, 2, -2, 0, 2] mA2 = [-1, -1, -1, 0, 0, 1, 1, 1] mB2 = [-1, 0, 1, -1, 1, -1, 0, 1] for a in range(4): red = input() ttt.append(red) for b in range(4): if red[b] == "x": xs.append([a, b]) def isFree(a, b): if a>= 0 and b>= 0 and a <=3 and b<=3: return 1 else: return 0 sol = "NO" for pos in xs: pa = pos[0] pb = pos[1] for mo in range(8): pa1 = pa+mA[mo] pb1 = pb+mB[mo] if isFree(pa1, pb1): pa2 = pa+mA2[mo] pb2 = pb+mB2[mo] if ttt[pa2][pb2] == "." and ttt[pa1][pb1] == "x" or ttt[pa2][pb2] == "x" and ttt[pa1][pb1] == ".": sol = "YES" break if sol == "YES": break print(sol) ```
instruction
0
72,974
19
145,948
Yes
output
1
72,974
19
145,949
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` import sys, copy A = [] def isAllX(a1, a2, b1, b2, c1, c2): global A if A[a1][a2] == "x" and A[b1][b2] == "x" and A[c1][c2] == "x": return True return False for i in range(4): s = input() B = [] for i in s: B.append(i) A.append(B) for i in range(4): for j in range(4): if A[i][j] == ".": C = copy.deepcopy(A) A[i][j] = "x" if isAllX(0, 0, 0, 1, 0, 2) or isAllX(0, 1, 0, 2, 0, 3)\ or isAllX(1, 0, 1, 1, 1, 2)\ or isAllX(1, 1, 1, 2, 1, 3)\ or isAllX(2, 0, 2, 1, 2, 2)\ or isAllX(2, 1, 2, 2, 2, 3)\ or isAllX(3, 0, 3, 1, 3, 2)\ or isAllX(3, 1, 3, 2, 3, 3)\ or isAllX(0, 0, 1, 0, 2, 0)\ or isAllX(1, 0, 2, 0, 3, 0)\ or isAllX(0, 1, 1, 1, 2, 1)\ or isAllX(1, 1, 2, 1, 3, 1)\ or isAllX(0, 2, 1, 2, 2, 2)\ or isAllX(1, 2, 2, 2, 3, 2)\ or isAllX(0, 3, 1, 3, 2, 3)\ or isAllX(1, 3, 2, 3, 3, 3)\ or isAllX(0, 0, 1, 1, 2, 2)\ or isAllX(1, 1, 2, 2, 3, 3)\ or isAllX(1, 0, 2, 1, 3, 2)\ or isAllX(0, 1, 1, 2, 2, 3)\ or isAllX(0, 3, 1, 2, 2, 1)\ or isAllX(1, 2, 2, 1, 3, 0)\ or isAllX(0, 2, 1, 1, 2, 0)\ or isAllX(1, 3, 2, 2, 3, 1): print("YES") sys.exit() A = copy.deepcopy(C) print("NO") ```
instruction
0
72,975
19
145,950
Yes
output
1
72,975
19
145,951
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` def checkwinning(a): for j in range(4): for i in range(2): xc = sum([a[u][j] == "x" for u in range(i,i+3)]) dotc = sum([a[u][j] =="." for u in range(i,i+3)]) if (xc == 2 and dotc ==1): return True for i in range(4): for j in range(2): xc = sum([a[i][u] == "x" for u in range(j,j+3)]) dotc = sum([a[i][u] =="." for u in range(j,j+3)]) if (xc == 2 and dotc ==1): return True for i in range(2): for j in range(2): xc = sum([a[i+k][j+k] == "x" for k in range(3)]) dotc =sum([a[i+k][j+k] == "." for k in range(3)]) if (xc == 2 and dotc ==1): return True for i in range(2): for j in range(2,4): xc = sum([a[i+k][j-k] == "x" for k in range(3)]) dotc =sum([a[i+k][j-k] == "." for k in range(3)]) if (xc == 2 and dotc ==1): return True if __name__ == "__main__": a=[] for i in range(4): a.append((list(input().strip()))) if(checkwinning(a)): print("YES") else: print("NO") ```
instruction
0
72,976
19
145,952
Yes
output
1
72,976
19
145,953
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` import sys rows = [input() for i in range(4)] cols = [] for j in range(4): col = [rows[i][j] for i in range(4)] cols.append("".join(col)) diags = [] diags.append("".join([rows[i][i] for i in range(4)])) diags.append("".join([rows[0][1], rows[1][2], rows[2][3]])) diags.append("".join([rows[1][0], rows[2][1], rows[3][2]])) diags.append("".join([rows[i][3-i] for i in range(4)])) diags.append("".join([rows[0][2], rows[1][1], rows[2][0]])) diags.append("".join([rows[1][3], rows[2][2], rows[3][1]])) strs = rows + cols + diags winstrs = ["xx.", "x.x", ".xx"] for winstr in winstrs: for s in strs: if winstr in s: print("YES") sys.exit(0) print("NO") ```
instruction
0
72,977
19
145,954
Yes
output
1
72,977
19
145,955
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` def horizontal(): # xStreak = 0 # pointCounter = 0 for i in range(len(field)): xStreak = 0 pointCounter = 0 borderPointCounter = 0 for j in range(len(field[i])): if (j == 0 and field[i][j] == 'o') or (j == 3 and field[i][j] == 'o'): continue elif (field[i][j] == 'o'): break elif (field[i][j] == 'x'): xStreak += 1 elif (field[i][j] == '.'): pointCounter += 1 if (field[i][j] == '.' and (j == 0 or j == 3)): borderPointCounter += 1 if(pointCounter == 1 and xStreak >= 2): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter == 2 and field[i][0] == '.' and field[i][3] == '.'): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter > 0): print("YES") return True return False def vertical(): # xStreak = 0 # pointCounter = 0 for j in range(len(field)): xStreak = 0 pointCounter = 0 borderPointCounter = 0 for i in range(len(field[j])): if (j == 0 and field[i][j] == 'o') or (j == 3 and field[i][j] == 'o'): continue elif (field[i][j] == 'o'): break elif (field[i][j] == 'x'): xStreak += 1 elif (field[i][j] == '.'): pointCounter += 1 if (field[i][j] == '.' and (i == 0 or i == 3)): borderPointCounter += 1 if (pointCounter == 1 and xStreak >= 2): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter == 2 and field[0][j] == '.' and field[3][j] == '.'): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter > 0): print("YES") return True return False def diagonal1(): if (field[0][1] == 'x' and field[1][2] == 'x' and field[2][3] == '.'): print("YES") return True if (field[0][1] == 'x' and field[1][2] == '.' and field[2][3] == 'x'): print("YES") return True if (field[0][1] == '.' and field[1][2] == 'x' and field[2][3] == 'x'): print("YES") return True if (field[1][0] == 'x' and field[2][1] == 'x' and field[3][2] == '.'): print("YES") return True if (field[1][0] == 'x' and field[2][1] == '.' and field[3][2] == 'x'): print("YES") return True if (field[1][0] == '.' and field[2][1] == 'x' and field[3][2] == 'x'): print("YES") return True if (field[2][0] == 'x' and field[1][1] == 'x' and field[0][2] == '.'): print("YES") return True if (field[2][0] == 'x' and field[1][1] == '.' and field[0][2] == 'x'): print("YES") return True if (field[2][0] == '.' and field[1][1] == 'x' and field[0][2] == 'x'): print("YES") return True if (field[3][1] == 'x' and field[2][2] == 'x' and field[1][3] == '.'): print("YES") return True if (field[3][1] == 'x' and field[2][2] == '.' and field[1][3] == 'x'): print("YES") return True if (field[3][1] == '.' and field[2][2] == 'x' and field[1][3] == 'x'): print("YES") return True return False def diagonal2(): xStreak = 0 pointCounter = 0 borderPointCounter = 0 for i in range(len(field)): if ((i == 0 and field[i][i] == 'o') or (i == 3 and field[i][i] == 'o')): continue elif (field[i][i] == 'o'): return False elif (field[i][i] == 'x'): xStreak += 1 elif (field[i][i] == '.'): pointCounter += 1 if ((i == 0 and field[i][i] == '.') or (i == 3 and field[i][i] == '.')): borderPointCounter += 1 if(pointCounter == 1 and xStreak >= 2): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter == 2 and field[0][0] == '.' and field[3][3] == '.'): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter > 0): print("YES") return True return False def diagonal3(): xStreak = 0 pointCounter = 0 borderPointCounter = 0 for i in range(len(field)): if (field[0][3] == 'o') or (field[3][0] == 'o'): continue elif (field[i][3 - i] == 'o'): return False elif (field[i][3 - i] == 'x'): xStreak += 1 elif (field[i][3 - i] == '.'): pointCounter += 1 if ((i == 0 and field[i][3 - i] == '.') or (i == 3 and field[i][3 - i] == '.')): borderPointCounter += 1 if(pointCounter == 1 and xStreak >= 2): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter == 2 and field[0][3] == '.' and field[3][0] == '.'): print("YES") return True if (pointCounter == 2 and xStreak == 2 and borderPointCounter > 0): print("YES") return True return False field = [] horiz = False vertic = False diag1 = False diag2 = False diag3 = False i = 0 while (i < 4): a = list(input()) field.append(a) i += 1 horiz = horizontal() if (horiz == False): vertic = vertical() if (horiz == False and vertic == False): diag1 = diagonal1() if (horiz == False and vertic == False and diag1 == False): diag2 = diagonal2() if (horiz == False and vertic == False and diag1 == False and diag2 == False): diag3 = diagonal3() if (horiz == False and vertic == False and diag1 == False and diag2 == False and diag3 == False): print("NO") #print(field) ```
instruction
0
72,978
19
145,956
No
output
1
72,978
19
145,957
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` field = [] triggered = False for i in range(4): field.append(input()) for i in field: if ('.xx' in i) or ('x.x' in i) or ('xx.' in i): print('YES') triggered = True if not triggered: new_field = [[],[],[],[]] for i in range(4): for j in range(4): new_field[j].append(field[i][j]) for i in range(4): new_field[i] = "".join(new_field[i]) for i in new_field: if ('.xx' in i) or ('x.x' in i) or ('xx.' in i): print('YES') break else: print('NO') ```
instruction
0
72,979
19
145,958
No
output
1
72,979
19
145,959
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` board = [] for i in range(4): arr = [str(x) for x in input()] board.append(arr) def check(board): for n in range(4): for nums, item in enumerate(board[n]): if item == '.': board[n][nums] = 'x' if (board[0][0]==board[0][1]==board[0][2]=='x' or board[0][1]==board[0][2]==board[0][3]=='x' or board[1][0]==board[1][1]==board[1][2]=='x' or board[1][1]==board[1][2]==board[1][3]=='x' or board[2][0]==board[2][1]==board[2][2]=='x' or board[2][1]==board[2][2]==board[2][3]=='x' or board[3][0]==board[3][1]==board[3][2]=='x' or board[3][1]==board[3][2]==board[3][3]=='x' or ### Vertical board[0][0]==board[1][0]==board[2][0]=='x' or board[1][0]==board[2][0]==board[3][0]=='x' or board[0][1]==board[1][1]==board[2][1]=='x' or board[1][1]==board[2][1]==board[3][1]=='x' or board[0][2]==board[1][2]==board[2][2]=='x' or board[1][2]==board[2][2]==board[3][2]=='x' or board[0][3]==board[1][3]==board[2][3]=='x' or board[1][3]==board[2][3]==board[3][3]=='x' or ### Dioganal board[0][2]==board[1][1]==board[2][0]=='x' or board[0][3]==board[1][2]==board[2][1]=='x' or board[1][2]==board[2][1]==board[3][0]=='x' or board[1][3]==board[2][2]==board[3][1]=='x' or board[0][1]==board[1][2]==board[2][3]=='x' or board[0][0]==board[1][1]==board[2][2]=='x' or board[1][1]==board[2][2]==board[3][3]=='x' or board[1][0]==board[2][1]==board[3][2]=='x'): return 'YES' board[n][nums] = 'o' return 'NO' check(board) ```
instruction
0
72,980
19
145,960
No
output
1
72,980
19
145,961
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal). Input The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn. Output Print single line: "YES" in case Ilya could have won by making single turn, and "NO" otherwise. Examples Input xx.. .oo. x... oox. Output YES Input x.ox ox.. x.o. oo.x Output NO Input x..x ..oo o... x.xo Output YES Input o.x. o... .x.. ooxx Output NO Note In the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row. In the second example it wasn't possible to win by making single turn. In the third example Ilya could have won by placing X in the last row between two existing Xs. In the fourth example it wasn't possible to win by making single turn. Submitted Solution: ``` def myc(a,b,c,d,e,f): return str(iph[a][b]+iph[c][d]+iph[e][f]) iph=[] for i in range(4): iph.append(str(input())) ipv=[] b=0 for i in range(4): ipv.append(str(iph[0][i]+iph[1][i]+iph[2][i]+iph[3][i])) for i in iph: if 'x.x' in i or 'xx.' in i or '.xx' in i: b=1 if 'ooo' in i: b=2 break if b!=2: for i in ipv: if 'x.x' in i or 'xx.' in i or '.xx' in i: b=1 if 'ooo' in i: b=2 break if b!=2: ipd=[myc(0,0,1,1,2,2),myc(1,1,2,2,3,3),myc(1,0,2,1,3,2),myc(0,1,1,2,2,3), myc(0,2,1,1,2,0),myc(0,3,1,2,2,1),myc(1,2,2,1,3,0),myc(1,3,2,2,3,1)] for i in ipv: if 'x.x' in i or 'xx.' in i or '.xx' in i and b==0: b=1 if 'ooo' in i: b=2 break if b==0 or b==2: print('NO') else: print('YES') ```
instruction
0
72,981
19
145,962
No
output
1
72,981
19
145,963
Provide tags and a correct Python 3 solution for this coding contest problem. Petya and Vasya arranged a game. The game runs by the following rules. Players have a directed graph consisting of n vertices and m edges. One of the vertices contains a chip. Initially the chip is located at vertex s. Players take turns moving the chip along some edge of the graph. Petya goes first. Player who can't move the chip loses. If the game lasts for 106 turns the draw is announced. Vasya was performing big laboratory work in "Spelling and parts of speech" at night before the game, so he fell asleep at the very beginning of the game. Petya decided to take the advantage of this situation and make both Petya's and Vasya's moves. Your task is to help Petya find out if he can win the game or at least draw a tie. Input The first line of input contain two integers n and m — the number of vertices and the number of edges in the graph (2 ≤ n ≤ 105, 0 ≤ m ≤ 2·105). The next n lines contain the information about edges of the graph. i-th line (1 ≤ i ≤ n) contains nonnegative integer ci — number of vertices such that there is an edge from i to these vertices and ci distinct integers ai, j — indices of these vertices (1 ≤ ai, j ≤ n, ai, j ≠ i). It is guaranteed that the total sum of ci equals to m. The next line contains index of vertex s — the initial position of the chip (1 ≤ s ≤ n). Output If Petya can win print «Win» in the first line. In the next line print numbers v1, v2, ..., vk (1 ≤ k ≤ 106) — the sequence of vertices Petya should visit for the winning. Vertex v1 should coincide with s. For i = 1... k - 1 there should be an edge from vi to vi + 1 in the graph. There must be no possible move from vertex vk. The sequence should be such that Petya wins the game. If Petya can't win but can draw a tie, print «Draw» in the only line. Otherwise print «Lose». Examples Input 5 6 2 2 3 2 4 5 1 4 1 5 0 1 Output Win 1 2 4 5 Input 3 2 1 3 1 1 0 2 Output Lose Input 2 2 1 2 1 1 1 Output Draw Note In the first example the graph is the following: <image> Initially the chip is located at vertex 1. In the first move Petya moves the chip to vertex 2, after that he moves it to vertex 4 for Vasya. After that he moves to vertex 5. Now it is Vasya's turn and there is no possible move, so Petya wins. In the second example the graph is the following: <image> Initially the chip is located at vertex 2. The only possible Petya's move is to go to vertex 1. After that he has to go to 3 for Vasya. Now it's Petya's turn but he has no possible move, so Petya loses. In the third example the graph is the following: <image> Petya can't win, but he can move along the cycle, so the players will draw a tie.
instruction
0
73,047
19
146,094
Tags: dfs and similar, dp, games, graphs Correct Solution: ``` n,m = map(int, input().split()) g = [[] for i in range(n)] fs = set() for i in range(n): a = list(map(int , input().split())) c = a[0] if c == 0: fs.add(i) continue for j in range(1,c+1): g[i].append(a[j]-1) s = int(input())-1 prev0 = [None for i in range(n)] prev1=[None for i in range(n)] vis0 = [0 for i in range(n)] vis0[s]=1 vis1 = [0 for i in range(n)] q = [(s, 0)] ans = None draw = False while len(q) > 0: v, c = q[0] del q[0] for u in g[v]: if c == 0: if vis1[u] == 0: vis1[u] =1 q.append((u, 1)) prev1[u] =v if u in fs: ans = u break elif c == 1: if vis0[u] == 0: vis0[u] =1 q.append((u, 0)) prev0[u] =v if ans is not None: break if ans is None: q = [s] vis=[0 for i in range(n)] vis[s]=1 nxt = [0 for i in range(n)] while len(q) > 0: v = q[-1] if nxt[v] < len(g[v]): u = g[v][nxt[v]] if vis[u] == 1: print('Draw') exit() elif vis[u] == 0: vis[u]=1 q.append(u) nxt[v] +=1 else: vis[v] = 2 del q[-1] print('Lose') exit() arn = [] nxt = ans while nxt is not None: arn.append(nxt) if len(arn) % 2 == 1: nxt = prev1[nxt] else: nxt = prev0[nxt] print('Win') arn = list(reversed(arn)) print(' '.join([str(i+1) for i in arn])) ```
output
1
73,047
19
146,095
Provide tags and a correct Python 3 solution for this coding contest problem. Petya and Vasya arranged a game. The game runs by the following rules. Players have a directed graph consisting of n vertices and m edges. One of the vertices contains a chip. Initially the chip is located at vertex s. Players take turns moving the chip along some edge of the graph. Petya goes first. Player who can't move the chip loses. If the game lasts for 106 turns the draw is announced. Vasya was performing big laboratory work in "Spelling and parts of speech" at night before the game, so he fell asleep at the very beginning of the game. Petya decided to take the advantage of this situation and make both Petya's and Vasya's moves. Your task is to help Petya find out if he can win the game or at least draw a tie. Input The first line of input contain two integers n and m — the number of vertices and the number of edges in the graph (2 ≤ n ≤ 105, 0 ≤ m ≤ 2·105). The next n lines contain the information about edges of the graph. i-th line (1 ≤ i ≤ n) contains nonnegative integer ci — number of vertices such that there is an edge from i to these vertices and ci distinct integers ai, j — indices of these vertices (1 ≤ ai, j ≤ n, ai, j ≠ i). It is guaranteed that the total sum of ci equals to m. The next line contains index of vertex s — the initial position of the chip (1 ≤ s ≤ n). Output If Petya can win print «Win» in the first line. In the next line print numbers v1, v2, ..., vk (1 ≤ k ≤ 106) — the sequence of vertices Petya should visit for the winning. Vertex v1 should coincide with s. For i = 1... k - 1 there should be an edge from vi to vi + 1 in the graph. There must be no possible move from vertex vk. The sequence should be such that Petya wins the game. If Petya can't win but can draw a tie, print «Draw» in the only line. Otherwise print «Lose». Examples Input 5 6 2 2 3 2 4 5 1 4 1 5 0 1 Output Win 1 2 4 5 Input 3 2 1 3 1 1 0 2 Output Lose Input 2 2 1 2 1 1 1 Output Draw Note In the first example the graph is the following: <image> Initially the chip is located at vertex 1. In the first move Petya moves the chip to vertex 2, after that he moves it to vertex 4 for Vasya. After that he moves to vertex 5. Now it is Vasya's turn and there is no possible move, so Petya wins. In the second example the graph is the following: <image> Initially the chip is located at vertex 2. The only possible Petya's move is to go to vertex 1. After that he has to go to 3 for Vasya. Now it's Petya's turn but he has no possible move, so Petya loses. In the third example the graph is the following: <image> Petya can't win, but he can move along the cycle, so the players will draw a tie.
instruction
0
73,048
19
146,096
Tags: dfs and similar, dp, games, graphs Correct Solution: ``` import sys data = sys.stdin.readlines() n, m = map(int, data[0].split()) g = {} for i, line in enumerate(data[1:-1], 1): g[i] = list(map(int, line.split()[1:])) mk = {} start = int(data[-1]) queue = [(start, 0, -1, 1)] cycle = False while len(queue) > 0: v, player, prev, color = queue.pop() if color == 2: mk[(v, player)] = (prev, 2) continue if mk.get((v, player), None): if mk[(v, player)][1] == 1: cycle = True continue mk[(v, player)] = (prev, 1) queue.append((v, player, prev, 2)) for w in g[v]: queue.append((w, 1-player, v, 1)) sol = None for v in range(1, n+1): if len(g[v]) == 0 and mk.get((v, 1), None): sol = v break if sol: path = [sol] cur = (sol, 1) while cur != (start, 0): cur = (mk.get(cur)[0], 1-cur[1]) path.append(cur[0]) print('Win') print(*path[::-1]) elif cycle: print('Draw') else: print('Lose') ```
output
1
73,048
19
146,097
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Petya and Vasya arranged a game. The game runs by the following rules. Players have a directed graph consisting of n vertices and m edges. One of the vertices contains a chip. Initially the chip is located at vertex s. Players take turns moving the chip along some edge of the graph. Petya goes first. Player who can't move the chip loses. If the game lasts for 106 turns the draw is announced. Vasya was performing big laboratory work in "Spelling and parts of speech" at night before the game, so he fell asleep at the very beginning of the game. Petya decided to take the advantage of this situation and make both Petya's and Vasya's moves. Your task is to help Petya find out if he can win the game or at least draw a tie. Input The first line of input contain two integers n and m — the number of vertices and the number of edges in the graph (2 ≤ n ≤ 105, 0 ≤ m ≤ 2·105). The next n lines contain the information about edges of the graph. i-th line (1 ≤ i ≤ n) contains nonnegative integer ci — number of vertices such that there is an edge from i to these vertices and ci distinct integers ai, j — indices of these vertices (1 ≤ ai, j ≤ n, ai, j ≠ i). It is guaranteed that the total sum of ci equals to m. The next line contains index of vertex s — the initial position of the chip (1 ≤ s ≤ n). Output If Petya can win print «Win» in the first line. In the next line print numbers v1, v2, ..., vk (1 ≤ k ≤ 106) — the sequence of vertices Petya should visit for the winning. Vertex v1 should coincide with s. For i = 1... k - 1 there should be an edge from vi to vi + 1 in the graph. There must be no possible move from vertex vk. The sequence should be such that Petya wins the game. If Petya can't win but can draw a tie, print «Draw» in the only line. Otherwise print «Lose». Examples Input 5 6 2 2 3 2 4 5 1 4 1 5 0 1 Output Win 1 2 4 5 Input 3 2 1 3 1 1 0 2 Output Lose Input 2 2 1 2 1 1 1 Output Draw Note In the first example the graph is the following: <image> Initially the chip is located at vertex 1. In the first move Petya moves the chip to vertex 2, after that he moves it to vertex 4 for Vasya. After that he moves to vertex 5. Now it is Vasya's turn and there is no possible move, so Petya wins. In the second example the graph is the following: <image> Initially the chip is located at vertex 2. The only possible Petya's move is to go to vertex 1. After that he has to go to 3 for Vasya. Now it's Petya's turn but he has no possible move, so Petya loses. In the third example the graph is the following: <image> Petya can't win, but he can move along the cycle, so the players will draw a tie. Submitted Solution: ``` import sys from collections import deque g = {} data = sys.stdin.readlines() n, m = map(int, data[0].split()) for i, line in enumerate(data[1:-1], 1): g[i] = list(map(int, line.split()[1:])) cycle = False mk = {} start = int(data[-1]) queue = deque() queue.append((start, 0, -1)) while len(queue) > 0: v, player, prev = queue.popleft() if mk.get((v, player), 0): cycle = True continue mk[(v, player)] = prev for w in g[v]: queue.append((w, 1-player, v)) sol = 0 for v in range(1, n+1): if len(g[v]) == 0 and mk.get((v, 1), 0): sol = v break if sol: path = [sol] cur = (sol, 1) while cur != (start, 0): cur = (mk.get(cur), 1-cur[1]) path.append(cur[0]) print('Win') print(*path[::-1]) elif cycle: print('Draw') else: print('Lose') ```
instruction
0
73,049
19
146,098
No
output
1
73,049
19
146,099