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Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,501
0
197,002
"Correct Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines W = read().rstrip() N = len(W) def Z_algorithm(S): # 共通接頭辞の長さを返す N=len(S) arr = [0]*N arr[0] = N i,j = 1,0 while i<N: while i+j<N and S[j]==S[i+j]: j += 1 arr[i]=j if not j: i += 1 continue k = 1 while i+k<N and k+arr[k]<j: arr[i+k] = arr[k] k += 1 i += k; j -= k return arr def is_periodic_left(W): Z = Z_algorithm(W) is_periodic = [False] * N for p in range(1,N//2 + 1): if is_periodic[p-1]: continue for i in range(p,N,p): if Z[i] >= p: is_periodic[p + i - 1] = True else: break return is_periodic L = is_periodic_left(W) R = is_periodic_left(W[::-1])[::-1] if not L[-1]: answer = (1,1) elif len(set(W)) == 1: answer = (N,1) else: x = sum(not(x or y) for x,y in zip(L,R[1:])) answer = (2,x) print('\n'.join(map(str,answer))) ```
output
1
98,501
0
197,003
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,502
0
197,004
"Correct Solution: ``` w=list(input());n=len(w);t=-1 def Z(s): m=len(s);z=[0]*m;c=0;f=[1]*m; for i in range(1,m): if i+z[i-c]<c+z[c]:z[i]=z[i-c] else: j=max(0,c+z[c]-i) while i+j<n and s[j]==s[i+j]:j=j+1 z[i]=j;c=i for p in range(1,m): for k in range(2,z[p]//p+2):f[k*p-1]=0 return f for j in range(1,n//2+1): if n%j==0 and w[:n-j]==w[j:]:t=j;break; if t==-1:print ('1\n1') elif t==1:print (n);print (1) else: zl=Z(w) w.reverse() zr=Z(w) cnt=0 for i in range(0,n-1): if zl[i] and zr[n-2-i]:cnt=cnt+1 print(2);print(cnt); ```
output
1
98,502
0
197,005
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,503
0
197,006
"Correct Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines W = list(map(int,read().rstrip())) N = len(W) def Z_Algorithm(S): # 共通接頭辞の長さを返す N=len(S) arr = [0]*N arr[0] = N i,j = 1,0 while i<N: while i+j<N and S[j]==S[i+j]: j += 1 arr[i]=j if not j: i += 1 continue k = 1 while i+k<N and k+arr[k]<j: arr[i+k] = arr[k] k += 1 i += k; j -= k return arr def find_good_substr(W): Z = Z_Algorithm(W) is_good = [True]*(N+1) # 長さをインデックス for n in range(1,N//2+1): # n文字での周期をもってくる if not is_good[n]: continue for i in range(n+n,Z[n]+n+1,n): is_good[i] = False return is_good def solve(): G1 = find_good_substr(W) G2 = find_good_substr(W[::-1])[::-1] if G1[-1]: # 自分自身がoptimal return 1,1 if len(set(W)) == 1: return N,1 # 2個にできるはず x = sum(x and y for x,y in zip(G1[1:-1],G2[1:-1])) return 2,x x,y = solve() print(x) print(y) ```
output
1
98,503
0
197,007
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,504
0
197,008
"Correct Solution: ``` import sys readline = sys.stdin.readline class Rollinhash: def __init__(self, S): N = len(S) self.mod = 10**9+9 self.base = 2009 self.has = [0]*(N+1) self.power = [1]*(N+1) for i in range(N): s = S[i] self.has[i+1] = (self.has[i]*self.base + s)%self.mod self.power[i+1] = self.power[i]*self.base%self.mod def rh(self, i, j): return (self.has[j] - self.has[i]*self.power[j-i])%self.mod MOD = 10**9+7 S = list(map(ord, readline().strip())) N = len(S) if len(set(S)) == 1: print(N) print(1) else: Rs = Rollinhash(S) tabler = [True]*(N+1) for d in range(1, 1+N//2): r = Rs.rh(0, d) for i in range(1, N//d): if r != Rs.rh(i*d, (i+1)*d): break tabler[(i+1)*d] = False tablel = [True]*(N+1) for d in range(1, 1+N//2): r = Rs.rh(N-d, N) for i in range(1, N//d): if r != Rs.rh(N-(i+1)*d, N-i*d): break tablel[N-(i+1)*d] = False if tabler[N]: print(1) print(1) else: print(2) ans = 0 for i in range(N+1): if tabler[i] and tablel[i]: ans += 1 assert ans > 0, '' print(ans) ```
output
1
98,504
0
197,009
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,505
0
197,010
"Correct Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines W = read().rstrip() N = len(W) def Z_algorithm(S): # 共通接頭辞の長さを返す N=len(S) arr = [0]*N arr[0] = N i,j = 1,0 while i<N: while i+j<N and S[j]==S[i+j]: j += 1 arr[i]=j if not j: i += 1 continue k = 1 while i+k<N and k+arr[k]<j: arr[i+k] = arr[k] k += 1 i += k; j -= k return arr def is_periodic_left(W): Z = Z_algorithm(W) is_periodic = [False] * N for p in range(1,N//2 + 10): for i in range(p,N,p): if Z[i] >= p: is_periodic[p + i - 1] = True else: break return is_periodic L = is_periodic_left(W) R = is_periodic_left(W[::-1])[::-1] if not L[-1]: answer = (1,1) elif len(set(W)) == 1: answer = (N,1) else: x = sum(not(x or y) for x,y in zip(L,R[1:])) answer = (2,x) print('\n'.join(map(str,answer))) ```
output
1
98,505
0
197,011
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,506
0
197,012
"Correct Solution: ``` from collections import Counter *W, = map(ord, input()) N = len(W) C = Counter(W) if len(C) == 1: print(N) print(1) exit(0) def z_algo(S): A = [0]*N i = 1; j = 0 A[0] = l = len(S) while i < l: while i+j < l and S[j] == S[i+j]: j += 1 A[i] = j if not j: i += 1 continue k = 1 while l-i > k < j - A[k]: A[i+k] = A[k] k += 1 i += k; j -= k return A def calc(W): Z = z_algo(W) G = [0]*N for i in range(N): G[i] = 1 for p in range(1, N): if not G[p-1]: continue for k in range(2, Z[p]//p+2): G[k*p-1] = 0 return G G0 = calc(W) W.reverse() G1 = calc(W) if G0[N-1]: print(1) print(1) exit(0) print(2) print(sum(p and q for p, q in zip(G0[:-1], reversed(G1[:-1])))) ```
output
1
98,506
0
197,013
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,507
0
197,014
"Correct Solution: ``` w=list(input()) n=len(w) t=-1 def Z(s): m=len(s);z=[0]*m;c=0;f=[1]*m; for i in range(1,m): if i+z[i-c]<c+z[c]:z[i]=z[i-c] else: j=max(0,c+z[c]-i) while i+j<n and s[j]==s[i+j]:j=j+1 z[i]=j;c=i for p in range(1,m): for k in range(2,z[p]//p+2):f[k*p-1]=0 return f for j in range(1,n//2+1): if n%j==0 and w[:n-j]==w[j:]:t=j;break; if t==-1:print ('1\n1') elif t==1:print (n);print (1) else: zl=Z(w) w.reverse() zr=Z(w) cnt=0 for i in range(0,n-1): if zl[i] and zr[n-2-i]:cnt=cnt+1 print(2);print(cnt); ```
output
1
98,507
0
197,015
Provide a correct Python 3 solution for this coding contest problem. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1
instruction
0
98,508
0
197,016
"Correct Solution: ``` def Z_algorithm(S): l=len(S) A=[0]*l A[0]=l i=1; j=0 while i<l: while i+j<l and S[j]==S[i+j]: j+=1 if not j: i+=1 continue A[i]=j k=1 while l-i>k<j-A[k]: A[i+k]=A[k] k+=1 i+=k; j-=k return A def jugde(W): Z=Z_algorithm(W) l=len(W) B=[True]*l for p in range(1,l): if not B[p-1]: continue k=2 while (k-1)*p<=Z[p]: B[k*p-1]=False k+=1 return B def solve(W): n=len(W) if len(set(W))==1: print(n) print(1) return G=jugde(W) W.reverse() G_rev=jugde(W) if G[-1]: print(1) print(1) return print(2) cnt=0 for i in range(n-1): cnt+=G[i] and G_rev[-(i+2)] print(cnt) return solve(list(input())) ```
output
1
98,508
0
197,017
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1 Submitted Solution: ``` import sys readline = sys.stdin.readline class Rollinhash: def __init__(self, S): N = len(S) self.mod = 10**9+9 self.base = 2009 self.has = [0]*(N+1) self.power = [1]*(N+1) for i in range(N): s = S[i] self.has[i+1] = (self.has[i]*self.base + s)%self.mod self.power[i+1] = self.power[i]*self.base%self.mod def rh(self, i, j): return (self.has[j] - self.has[i]*self.power[j-i])%self.mod MOD = 10**9+7 S = list(map(ord, readline().strip())) N = len(S) if len(set(S)) == 1: print(N) print(1) else: Rs = Rollinhash(S) tabler = [True]*(N+1) for d in range(2, 1+N//2): r = Rs.rh(0, d) for i in range(1, N//d): if r != Rs.rh(i*d, (i+1)*d): break tabler[(i+1)*d] = False tablel = [True]*(N+1) for d in range(2, 1+N//2): r = Rs.rh(N-d, N) for i in range(1, N//d): if r != Rs.rh(N-(i+1)*d, N-i*d): break tablel[N-(i+1)*d] = False if tabler[N]: print(1) print(1) else: print(2) ans = 0 for i in range(N+1): if tabler[i] and tablel[i]: ans += 1 assert ans > 0, '' print(ans) ```
instruction
0
98,509
0
197,018
No
output
1
98,509
0
197,019
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1 Submitted Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines W = read().rstrip() N = len(W) def Z_algorithm(S): # 共通接頭辞の長さを返す N=len(S) arr = [0]*N arr[0] = N i,j = 1,0 while i<N: while i+j<N and S[j]==S[i+j]: j += 1 arr[i]=j if not j: i += 1 continue k = 1 while i+k<N and k+arr[k]<j: arr[i+k] = arr[k] k += 1 i += k; j -= k return arr def is_periodic_left(W): Z = Z_algorithm(W) is_periodic = [False] * N for p in range(1,N//2 + 10): for i in range(p,N,p): if Z[i] >= p: is_periodic[p + i - 1] = True else: break return is_periodic L = is_periodic_left(W) R = is_periodic_left(W[::-1])[::-1] if not L[-1]: answer = (1,1) elif len(set(W)) == 1: answer = (N,1) else: x = sum(not(x or y) for x,y in zip(L,R[1:])) answer = (2,x) print('\n'.join(map(str,answer))) ```
instruction
0
98,510
0
197,020
No
output
1
98,510
0
197,021
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1 Submitted Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines W = list(map(int,read().rstrip())) N = len(W) def Z_Algorithm(S): # 共通接頭辞の長さを返す N=len(S) arr = [0]*N arr[0] = N i,j = 1,0 while i<N: while i+j<N and S[j]==S[i+j]: j += 1 arr[i]=j if not j: i += 1 continue k = 1 while i+k<N and k+arr[k]<j: arr[i+k] = arr[k] k += 1 i += k; j -= k return arr def find_good_substr(W): Z = Z_Algorithm(W) is_good = [True]*N for n in range(1,N//2+1): # n文字での周期をもってくる if not is_good[n]: continue for i in range(n+n-1,Z[n]+n,n): is_good[i] = False return is_good def solve(): G1 = find_good_substr(W) G2 = find_good_substr(W[::-1]) if G1[-1]: # 自分自身がoptimal return 1,1 x,y = solve() print(x) print(y) ```
instruction
0
98,511
0
197,022
No
output
1
98,511
0
197,023
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let x be a string of length at least 1. We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x. For example, `a`, `bbc` and `cdcdc` are good strings, while `aa`, `bbbb` and `cdcdcd` are not. Let w be a string of length at least 1. For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements, we will call F a good representation of w, if the following conditions are both satisfied: * For any i \, (1 \leq i \leq m), f_i is a good string. * The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w. For example, when w=`aabb`, there are five good representations of w: * (`aabb`) * (`a`,`abb`) * (`aab`,`b`) * (`a`,`ab`,`b`) * (`a`,`a`,`b`,`b`) Among the good representations of w, the ones with the smallest number of elements are called the best representations of w. For example, there are only one best representation of w=`aabb`: (`aabb`). You are given a string w. Find the following: * the number of elements of a best representation of w * the number of the best representations of w, modulo 1000000007 \, (=10^9+7) (It is guaranteed that a good representation of w always exists.) Constraints * 1 \leq |w| \leq 500000 \, (=5 \times 10^5) * w consists of lowercase letters (`a`-`z`). Input The input is given from Standard Input in the following format: w Output Print 2 lines. * In the first line, print the number of elements of a best representation of w. * In the second line, print the number of the best representations of w, modulo 1000000007. Examples Input aab Output 1 1 Input bcbc Output 2 3 Input ddd Output 3 1 Submitted Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines W = list(map(int,read().rstrip())) N = len(W) def Z_Algorithm(S): # 共通接頭辞の長さを返す N=len(S) arr = [0]*N arr[0] = N i,j = 1,0 while i<N: while i+j<N and S[j]==S[i+j]: j += 1 arr[i]=j if not j: i += 1 continue k = 1 while i+k<N and k+arr[k]<j: arr[i+k] = arr[k] k += 1 i += k; j -= k return arr Z_Algorithm(W) ```
instruction
0
98,512
0
197,024
No
output
1
98,512
0
197,025
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,604
0
197,208
Tags: implementation, strings Correct Solution: ``` from sys import stdin trim = lambda s: s[:-1] if s[-1] == "\n" else s T = int(stdin.readline()) for i in range(0, T): n = int(stdin.readline()) s = trim(stdin.readline()) possible = True for j in range(0, n//2 + 1): if abs(ord(s[j])-ord(s[-(j+1)])) not in [0, 2]: possible = False if possible: print("YES") else: print("NO") ```
output
1
98,604
0
197,209
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,605
0
197,210
Tags: implementation, strings Correct Solution: ``` import sys import os def solve(s): n = len(s) for i in range(n // 2): a = ord(s[i]) b = ord(s[n - 1 - i]) diff = abs(a - b) if diff != 0 and abs(diff) != 2: return 'NO' return 'YES' def main(): t = int(input()) for i in range(t): _ = int(input()) s = input() print(solve(s)) if __name__ == '__main__': main() ```
output
1
98,605
0
197,211
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,606
0
197,212
Tags: implementation, strings Correct Solution: ``` def is_pal(s): for i in range(len(s)//2): dif = abs(ord(s[i]) - ord(s[-i-1])) if dif != 0 and dif != 2 : return False return True t = int(input()) for i in range(t): n = int(input()) s = input() buf = [] print("YES" if is_pal(s) else "NO") ```
output
1
98,606
0
197,213
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,607
0
197,214
Tags: implementation, strings Correct Solution: ``` t = int(input()) while (t): n = int(input()) s = input() ok = 0 for i in range (n): v = abs(ord(s[i]) - ord(s[n-i-1])) if (v != 0 and v != 2): ok = 1 if (ok):print("NO") else: print("YES") t -= 1 ```
output
1
98,607
0
197,215
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,608
0
197,216
Tags: implementation, strings Correct Solution: ``` t = int(input()) alphabet = "abcdefghijklmnopqrstuvwxyz" for i in range(t): n = int(input()) string = input() palindrome = True i = 0 j = len(string) - 1 while(i <= j): if(string[i] != string[j]): esq = alphabet.index(string[i]) dir = alphabet.index(string[j]) if(esq + 1 != dir -1 and esq + 1 != dir + 1 and esq - 1 != dir - 1 and esq -1 != dir + 1): palindrome = False i+= 1 j-= 1 if(palindrome): print("YES") else: print("NO") ```
output
1
98,608
0
197,217
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,609
0
197,218
Tags: implementation, strings Correct Solution: ``` import sys import math from collections import deque def scan(): return list(map(int, sys.stdin.readline().strip().split())) def print_primes_till_n(n): i, j, flag = 0, 0, 0 a = [] c = 0 for i in range(1, n + 1, 1): if i == 1 or i == 0: continue flag = 1 for j in range(2, ((i // 2) + 1), 1): if i % j == 0: flag = 0 break if flag == 1: a.append(i) c += 1 return a, c def is_square(n): b = math.sqrt(n) if n == int(b * b): return True return False def solution(): for _ in range(int(input())): n = int(input()) s = input() s = [i for i in s] c = 0 for i in range(n // 2): if abs(ord(s[n-i-1])-ord(s[i])) == 2 or abs(ord(s[n-i-1])-ord(s[i])) == 0: c += 1 else: c = -1 break if c == n//2: print('YES') else: print('NO') if __name__ == '__main__': solution() ```
output
1
98,609
0
197,219
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,610
0
197,220
Tags: implementation, strings Correct Solution: ``` def can_be_transformed(word): for i in range(len(word)//2): if abs(ord(word[i])-ord(word[-i-1]))>2 or abs(ord(word[i])-ord(word[-i-1])) == 1: return False return True def main(): answers = [] n=int(input()) for i in range(0,n): m=int(input()) s=input() if can_be_transformed(s): answers.append('YES') else: answers.append('NO') for i in range(0,n): print(answers[i]) if __name__ == '__main__': main() ```
output
1
98,610
0
197,221
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm".
instruction
0
98,611
0
197,222
Tags: implementation, strings Correct Solution: ``` def search(s,n): for i in range(n//2): x=abs(ord(s[i])-ord(s[n-i-1])) if x!=0 and x!=2: return(False) return(True) t=int(input()) for _ in range(t): n=int(input()) s=input() if search(s,n): print("YES") else: print("NO") ```
output
1
98,611
0
197,223
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` t = int(input()) def get_str(s): next = '' prev = '' if s == 'a': next = chr(ord(s) + 1) elif s == 'z': prev = chr(ord(s) - 1) else: next = chr(ord(s) + 1) prev = chr(ord(s) - 1) return next + prev def canPalindrome(n, s): options = [] for i in range(n // 2): a = get_str(s[i]) b = get_str(s[(-1 * i) -1]) l = len(options) // 2 options.insert(l,a) options.insert(l + 1 ,b) for i in range(n // 2): if not len(''.join(set(options[i]).intersection(set(options[(-1 * i) - 1])))) > 0: return False return True res = [] for i in range(t): n = int(input()) s = input() res.append(canPalindrome(n, s)) for i in res: if i == True: print('YES') else: print('NO') ```
instruction
0
98,612
0
197,224
Yes
output
1
98,612
0
197,225
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` import math from sys import stdin n_round = int(stdin.readline()) for _ in range(n_round): n_letter = int(stdin.readline()) string = list(stdin.readline().strip()) numbers = [ord(x) for x in string] #a-97 z-122 result = True for _ in range(math.floor(n_letter/2)): if not (numbers[_] == numbers[-(_+1)] or abs(numbers[_]-numbers[-(_+1)])==2): result = False if result == True: print('YES') else: print('NO') ```
instruction
0
98,613
0
197,226
Yes
output
1
98,613
0
197,227
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` def canbe(c, s): for i in range(int(c/2), c): if (abs(ord(s[i]) - ord(s[c-i-1]))>2) or (abs(ord(s[i]) - ord(s[c-i-1]))==1): return False return True t = int(input()) buf = [] for i in range(t): c = int(input()) s = input() if canbe(c, s): buf.append('YES') else: buf.append('NO') for el in buf: print(el) ```
instruction
0
98,614
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197,228
Yes
output
1
98,614
0
197,229
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` n = int(input()) tt = [-2, 0, 2] for jj in range(n): i, inp = input(), input() need = 1 for j in range(len(inp)): if (ord(inp[j]) - ord(inp[len(inp) - j - 1])) not in tt: need = 0 if need: print("YES") else: print("NO") ```
instruction
0
98,615
0
197,230
Yes
output
1
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0
197,231
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` from __future__ import division, print_function from collections import * from math import * from itertools import * from time import time import os import sys from io import BytesIO, IOBase if sys.version_info[0] < 3: from __builtin__ import xrange as range from future_builtins import ascii, filter, hex, map, oct, zip ''' Notes: n = number of balls k = attract power ni = ball's coords ''' def main(): n = int(input()) s = input() if s == s[::-1]: print('YES') return opposite = sorted(s, reverse = True) for i in range(n // 2): first = ord(s[i]) second = ord(opposite[i]) if first - 1 == second or first == second or first + 1 == second: continue else: print('NO') return # region fastio 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") def print(*args, **kwargs): """Prints the values to a stream, or to sys.stdout by default.""" sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout) at_start = True for x in args: if not at_start: file.write(sep) file.write(str(x)) at_start = False file.write(kwargs.pop("end", "\n")) if kwargs.pop("flush", False): file.flush() if sys.version_info[0] < 3: sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout) else: sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # endregion if __name__ == "__main__": t = int(input()) while(t): main() t -= 1 ```
instruction
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98,616
0
197,232
No
output
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98,616
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197,233
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` T=int(input()) for i in range(T): n=int(input()) s=input() l=len(s)-1 for i in range(len(s)): if s[i]==s[l]: l=l-1 if i==(len(s)-1): print ("YES") break continue if abs((ord(s[i])-ord(s[l])))!=2 and (s[i]!='a' or s[i]!='z') and (s[l]!='a' or s[l]!='z'): print ("NO") break if (s[i]=='a' and (s[l] in ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'])): print ("NO") break if (s[l]=='a' and (s[i] in ['c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'])): print ("NO") break if (s[i]=='z' and (s[l] in ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x'])): print ("NO") break if (s[l]=='z' and (s[i] in ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x'])): print ("N0") break else: if i==(len(s)-1): print ("YES") break l=l-1 ```
instruction
0
98,617
0
197,234
No
output
1
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0
197,235
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` i=input t=int(i()) while t: t-=1 i();a=[*map(ord,i())] print("YNEOS"[1-all((x-y)%26in{0,2,24}for x,y in zip(a,a[::-1]))::2]) ```
instruction
0
98,618
0
197,236
No
output
1
98,618
0
197,237
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a string s consisting of n lowercase Latin letters. n is even. For each position i (1 ≤ i ≤ n) in string s you are required to change the letter on this position either to the previous letter in alphabetic order or to the next one (letters 'a' and 'z' have only one of these options). Letter in every position must be changed exactly once. For example, letter 'p' should be changed either to 'o' or to 'q', letter 'a' should be changed to 'b' and letter 'z' should be changed to 'y'. That way string "codeforces", for example, can be changed to "dpedepqbft" ('c' → 'd', 'o' → 'p', 'd' → 'e', 'e' → 'd', 'f' → 'e', 'o' → 'p', 'r' → 'q', 'c' → 'b', 'e' → 'f', 's' → 't'). String s is called a palindrome if it reads the same from left to right and from right to left. For example, strings "abba" and "zz" are palindromes and strings "abca" and "zy" are not. Your goal is to check if it's possible to make string s a palindrome by applying the aforementioned changes to every position. Print "YES" if string s can be transformed to a palindrome and "NO" otherwise. Each testcase contains several strings, for each of them you are required to solve the problem separately. Input The first line contains a single integer T (1 ≤ T ≤ 50) — the number of strings in a testcase. Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th string. The first line of the pair contains a single integer n (2 ≤ n ≤ 100, n is even) — the length of the corresponding string. The second line of the pair contains a string s, consisting of n lowercase Latin letters. Output Print T lines. The i-th line should contain the answer to the i-th string of the input. Print "YES" if it's possible to make the i-th string a palindrome by applying the aforementioned changes to every position. Print "NO" otherwise. Example Input 5 6 abccba 2 cf 4 adfa 8 abaazaba 2 ml Output YES NO YES NO NO Note The first string of the example can be changed to "bcbbcb", two leftmost letters and two rightmost letters got changed to the next letters, two middle letters got changed to the previous letters. The second string can be changed to "be", "bg", "de", "dg", but none of these resulting strings are palindromes. The third string can be changed to "beeb" which is a palindrome. The fifth string can be changed to "lk", "lm", "nk", "nm", but none of these resulting strings are palindromes. Also note that no letter can remain the same, so you can't obtain strings "ll" or "mm". Submitted Solution: ``` def check(n, s): for i in range(n//2): c1, c2 = ord(s[i]), ord(s[n-i-1]) if abs(c1 - c2) > 2: return False return True T = int(input()) for _ in range(T): n = int(input()) s = input() if check(n, s): print("YES") else: print("NO") ```
instruction
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98,619
0
197,238
No
output
1
98,619
0
197,239
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
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98,661
0
197,322
Tags: constructive algorithms, math, strings Correct Solution: ``` import sys from math import * from fractions import gcd readints=lambda:map(int, input().strip('\n').split()) def hasUnique(s,n,k): freq = {} for i in range(n-k+1): x = s[i:i+k] if x not in freq: freq[x]=0 freq[x]+=1 for k in freq: if freq[k] == 1: return True return False def good(s,n,k): for i in range(1,k): if hasUnique(s,n,i): return False freq={} for i in range(n-k+1): x = s[i:i+k] if x not in freq: freq[x]=0 freq[x]+=1 st = set() for x in freq: if freq[x]==1: if len(st)>0: return False st.add(x) return len(st) == 1 def gen(i,s,n,k): if i==n: if good(s,n,k): print(s) else: gen(i+1,s+'0',n,k) gen(i+1,s+'1',n,k) #gen(0,'',5,3) # for n in range(3,9): # for k in range(1,n+1): # if (n%2 != k%2): # print(n,k,'skip') # print() # continue # print(n,k) # gen(0,'',n,k) # print() n,k = readints() if n == k: print('0' * n) sys.exit(0) s = '' while len(s) < n: r = int((n-k)//2) s = s + (('0'*r) + '1') s = s[:n] print(s) ```
output
1
98,661
0
197,323
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,662
0
197,324
Tags: constructive algorithms, math, strings Correct Solution: ``` n, k = map(int, input().split()) if k == 1: print("1", end = "") for i in range(1, n): print("0", end = "") print() exit() a = (n + k - 2) // 2 ans = "" if (a - k + 2) % 2: for i in range (a - k + 2): ans += chr(i % 2 + 48) else: ans += chr(48) for i in range(1, a - k + 2): ans += chr(49) for i in range(a - k + 2, n): ans += ans[i - a + k - 2] print(ans) ```
output
1
98,662
0
197,325
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,663
0
197,326
Tags: constructive algorithms, math, strings Correct Solution: ``` N, K = map(int, input().split()) if K == 0 or N == K: print("1" * N) elif K == 1: print("0" + "1" * (N - 1)) elif K <= 2//N: if K & 1: print("10" * (K//2+1) + "1" * (N-2-K//2*2)) else: print("0" + "10" * (K//2) + "1" * (N-1-K//2*2)) else: print((("0"+"1"*((N-K)//2))*(N//(((N-K)//2))+1))[:N]) ```
output
1
98,663
0
197,327
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,664
0
197,328
Tags: constructive algorithms, math, strings Correct Solution: ``` n, k = list(map(int,input().split())) chuj_twojej_starej = (n - k) // 2 + 1 i = 1 while True: if i % chuj_twojej_starej == 0: print(0, end = "") else: print(1, end = "") if i == n: break i += 1 ```
output
1
98,664
0
197,329
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,665
0
197,330
Tags: constructive algorithms, math, strings Correct Solution: ``` n,k=map(int,input().split()) d=(n-k)//2 s=0 while s!=n: if (s+1)%(d+1)==0: print("1",end="") else : print("0",end="") s+=1 ```
output
1
98,665
0
197,331
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,666
0
197,332
Tags: constructive algorithms, math, strings Correct Solution: ``` N, K = map(int, input().split()) if N == K: print("0"*N) elif K == 1: print("0"*(N-1) + "1") elif K == 3: print("1" + "0"*(N-4) + "101") else: res = ["0"]*N for i in range(0, N, N//2-K//2+1): res[i] = "1" print(''.join(res)) ```
output
1
98,666
0
197,333
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,667
0
197,334
Tags: constructive algorithms, math, strings Correct Solution: ``` n,k=map(int,input().split()) x=(n-(k-1)+1)//2 STR="0"*(x-1)+"1" ANS=STR*(n//x+1) print(ANS[:n]) ```
output
1
98,667
0
197,335
Provide tags and a correct Python 3 solution for this coding contest problem. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3.
instruction
0
98,668
0
197,336
Tags: constructive algorithms, math, strings Correct Solution: ``` #------------------------------warmup---------------------------- import os import sys from io import BytesIO, IOBase 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----------------------------------------------------- import math n,k=map(int,input().split()) a=(n-k)//2 s="" while(len(s)<n): s=s+"0"*(a)+"1" print(s[:n]) ```
output
1
98,668
0
197,337
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` n,k=[int(x) for x in input().split()] a=(n-k)//2 tot='' for i in range(n): if (i+1)%(a+1)==0: tot+='1' else: tot+='0' print(tot) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` from sys import stdin n,m=map(int,stdin.readline().strip().split()) x=n-m x=x//2 s="" y=0 if m==1: print("0"+(n-1)*"1") exit(0) while len(s)<n: if y==1: s+="1"*x else: s+="0" y+=1 y=y%2 print(s[0:n]) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` n, k = map(int, input().split()) # while making the string, k = (n - 2 * length + 2) length = (n - k + 2) // 2 # length of a cycle string = "0" * (length - 1) + "1" # make the cycle answer = string * (n // length + 1) # make the string with length >= n print(answer[ : n]) ```
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197,343
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` n, k = map(int, input().split()) s, v = (n - k) // 2 * '0' + '1', '' while len(v) < n: v += s print(v[:n]) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` n,k=map(int,input().strip().split()) d=n-k//2+1 x=['1' if (i+1)%d==0 else '0' for i in range(n)] print(''.join(x)) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` def solve(n, k): if n // 3 >= k: string1 = ["0"] + ["1"] * (k-2) string2 = ["1"] * (n + 2 - 2*k) answer = (string2 + string1 + string1) return ("".join(answer)) else: key = (n - k) // 2 a, c = key + 1, key - 1 b = n // a string1 = ["1"] * (a-1) + ["0"] string2 = ["1"] * (n - b*a) answer = (string1 * b + string2) return ("".join(answer)) return n, k = map(int, input().split()) print (solve(n, k)) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` def solve(n, k): if n // 2 >= k: string1 = ["0"] + ["1"] * (k-2) string2 = ["1"] * (n + 2 - 2*k) answer = (string2 + string1 + string1) return ("".join(answer)) else: key = (n - k) // 2 a, c = key + 1, key - 1 b = n // a string1 = ["1"] * (a-1) + ["0"] string2 = ["1"] * (n - b*a) answer = (string1 * b + string2) return ("".join(answer)) return n, k = map(int, input().split()) print (solve(n, k)) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let s be some string consisting of symbols "0" or "1". Let's call a string t a substring of string s, if there exists such number 1 ≤ l ≤ |s| - |t| + 1 that t = s_l s_{l+1} … s_{l + |t| - 1}. Let's call a substring t of string s unique, if there exist only one such l. For example, let s = "1010111". A string t = "010" is an unique substring of s, because l = 2 is the only one suitable number. But, for example t = "10" isn't a unique substring of s, because l = 1 and l = 3 are suitable. And for example t ="00" at all isn't a substring of s, because there is no suitable l. Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him. You are given 2 positive integers n and k, such that (n mod 2) = (k mod 2), where (x mod 2) is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols "0" or "1", such that the length of its minimal unique substring is equal to k. Input The first line contains two integers n and k, separated by spaces (1 ≤ k ≤ n ≤ 100 000, (k mod 2) = (n mod 2)). Output Print a string s of length n, consisting of symbols "0" and "1". Minimal length of the unique substring of s should be equal to k. You can find any suitable string. It is guaranteed, that there exists at least one such string. Examples Input 4 4 Output 1111 Input 5 3 Output 01010 Input 7 3 Output 1011011 Note In the first test, it's easy to see, that the only unique substring of string s = "1111" is all string s, which has length 4. In the second test a string s = "01010" has minimal unique substring t ="101", which has length 3. In the third test a string s = "1011011" has minimal unique substring t ="110", which has length 3. Submitted Solution: ``` if __name__ == "__main__": N, K = [int(x) for x in input().split()] if K * 2 <= N: print('0' * K + '1' * (N - K)) elif N == K: print('0' * N) elif N % 2 == 0 and K == N // 2 + 2: print('01' * (N // 2)) elif N % 2 == 1 and K == N // 2 + 1: print('01' * (N // 2) + '0') else: print('orzJumpmelonAKCTS2019') ```
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Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k for some integer k ≥ 0. The string s[1 ... n] is called c-good if at least one of the following three conditions is satisfied: * The length of s is 1, and it consists of the character c (i.e. s_1=c); * The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s_1=s_2=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... s_n) is a (c+1)-good string; * The length of s is greater than 1, the second half of the string consists of only the character c (i.e. s_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{n/2}) is a (c+1)-good string. For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good. In one move, you can choose one index i from 1 to n and replace s_i with any lowercase Latin letter (any character from 'a' to 'z'). Your task is to find the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string for c= 'a'). It is guaranteed that the answer always exists. You have to answer t independent test cases. Another example of an 'a'-good string is as follows. Consider the string s = "cdbbaaaa". It is an 'a'-good string, because: * the second half of the string ("aaaa") consists of only the character 'a'; * the first half of the string ("cdbb") is 'b'-good string, because: * the second half of the string ("bb") consists of only the character 'b'; * the first half of the string ("cd") is 'c'-good string, because: * the first half of the string ("c") consists of only the character 'c'; * the second half of the string ("d") is 'd'-good string. Input The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 131~072) — the length of s. It is guaranteed that n = 2^k for some integer k ≥ 0. The second line of the test case contains the string s consisting of n lowercase Latin letters. It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5). Output For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string with c = 'a'). It is guaranteed that the answer exists. Example Input 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac Output 0 7 4 5 1 1
instruction
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98,808
0
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Tags: bitmasks, brute force, divide and conquer, dp, implementation Correct Solution: ``` def fn(s,a): if len(s)==1: if s==a: return 0 else: return 1 a1=0 a2=0 l=len(s)//2 t=s[:l] p=s[l:] for i in t: if i!=a: a1+=1 for i in p: if i!=a: a2+=1 return min(a1+fn(p,chr(ord(a)+1)),a2+fn(t,chr(ord(a)+1))) for _ in range(int(input())): n=int(input()) a=input() print(fn(a,'a')) ```
output
1
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197,617
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k for some integer k ≥ 0. The string s[1 ... n] is called c-good if at least one of the following three conditions is satisfied: * The length of s is 1, and it consists of the character c (i.e. s_1=c); * The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s_1=s_2=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... s_n) is a (c+1)-good string; * The length of s is greater than 1, the second half of the string consists of only the character c (i.e. s_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{n/2}) is a (c+1)-good string. For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good. In one move, you can choose one index i from 1 to n and replace s_i with any lowercase Latin letter (any character from 'a' to 'z'). Your task is to find the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string for c= 'a'). It is guaranteed that the answer always exists. You have to answer t independent test cases. Another example of an 'a'-good string is as follows. Consider the string s = "cdbbaaaa". It is an 'a'-good string, because: * the second half of the string ("aaaa") consists of only the character 'a'; * the first half of the string ("cdbb") is 'b'-good string, because: * the second half of the string ("bb") consists of only the character 'b'; * the first half of the string ("cd") is 'c'-good string, because: * the first half of the string ("c") consists of only the character 'c'; * the second half of the string ("d") is 'd'-good string. Input The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 131~072) — the length of s. It is guaranteed that n = 2^k for some integer k ≥ 0. The second line of the test case contains the string s consisting of n lowercase Latin letters. It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5). Output For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string with c = 'a'). It is guaranteed that the answer exists. Example Input 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac Output 0 7 4 5 1 1
instruction
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0
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Tags: bitmasks, brute force, divide and conquer, dp, implementation Correct Solution: ``` LETRAS = "abcdefghijklmnopqrstuvwxyz" def string_boa(indice, string): letras = LETRAS[indice] if len(string) == 1: if string != letras: return 1 else: return 0 direita = 0 esquerda = 0 for l in string[:len(string)//2]: if l != letras: direita += 1 for l in string[len(string)//2:]: if l != letras: esquerda += 1 lado_direito = direita + string_boa(indice + 1, string[len(string)//2:]) lado_esquerdo = esquerda + string_boa(indice + 1, string[:len(string)//2:]) return min(lado_direito , lado_esquerdo) entrada = int(input()) for i in range(entrada): n = int(input()) string = input() print(string_boa(0, string)) ```
output
1
98,809
0
197,619
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k for some integer k ≥ 0. The string s[1 ... n] is called c-good if at least one of the following three conditions is satisfied: * The length of s is 1, and it consists of the character c (i.e. s_1=c); * The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s_1=s_2=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... s_n) is a (c+1)-good string; * The length of s is greater than 1, the second half of the string consists of only the character c (i.e. s_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{n/2}) is a (c+1)-good string. For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good. In one move, you can choose one index i from 1 to n and replace s_i with any lowercase Latin letter (any character from 'a' to 'z'). Your task is to find the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string for c= 'a'). It is guaranteed that the answer always exists. You have to answer t independent test cases. Another example of an 'a'-good string is as follows. Consider the string s = "cdbbaaaa". It is an 'a'-good string, because: * the second half of the string ("aaaa") consists of only the character 'a'; * the first half of the string ("cdbb") is 'b'-good string, because: * the second half of the string ("bb") consists of only the character 'b'; * the first half of the string ("cd") is 'c'-good string, because: * the first half of the string ("c") consists of only the character 'c'; * the second half of the string ("d") is 'd'-good string. Input The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 131~072) — the length of s. It is guaranteed that n = 2^k for some integer k ≥ 0. The second line of the test case contains the string s consisting of n lowercase Latin letters. It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5). Output For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string with c = 'a'). It is guaranteed that the answer exists. Example Input 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac Output 0 7 4 5 1 1
instruction
0
98,810
0
197,620
Tags: bitmasks, brute force, divide and conquer, dp, implementation Correct Solution: ``` """ Author: Q.E.D Time: 2020-07-17 10:11:52 """ def count(s, c): c2 = chr(ord(c) + 1) if len(s) == 1: return 1 - int(s[0] == c) else: n = len(s) h = n // 2 x1 = sum(1 for a in s[:h] if a != c) x2 = sum(1 for a in s[h:] if a != c) y1 = count(s[h:], c2) y2 = count(s[:h], c2) return min(x1 + y1, x2 + y2) T = int(input()) for _ in range(T): n = int(input()) s = input() ans = count(s, 'a') print(ans) ```
output
1
98,810
0
197,621
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k for some integer k ≥ 0. The string s[1 ... n] is called c-good if at least one of the following three conditions is satisfied: * The length of s is 1, and it consists of the character c (i.e. s_1=c); * The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s_1=s_2=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... s_n) is a (c+1)-good string; * The length of s is greater than 1, the second half of the string consists of only the character c (i.e. s_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{n/2}) is a (c+1)-good string. For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good. In one move, you can choose one index i from 1 to n and replace s_i with any lowercase Latin letter (any character from 'a' to 'z'). Your task is to find the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string for c= 'a'). It is guaranteed that the answer always exists. You have to answer t independent test cases. Another example of an 'a'-good string is as follows. Consider the string s = "cdbbaaaa". It is an 'a'-good string, because: * the second half of the string ("aaaa") consists of only the character 'a'; * the first half of the string ("cdbb") is 'b'-good string, because: * the second half of the string ("bb") consists of only the character 'b'; * the first half of the string ("cd") is 'c'-good string, because: * the first half of the string ("c") consists of only the character 'c'; * the second half of the string ("d") is 'd'-good string. Input The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 131~072) — the length of s. It is guaranteed that n = 2^k for some integer k ≥ 0. The second line of the test case contains the string s consisting of n lowercase Latin letters. It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5). Output For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string with c = 'a'). It is guaranteed that the answer exists. Example Input 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac Output 0 7 4 5 1 1
instruction
0
98,811
0
197,622
Tags: bitmasks, brute force, divide and conquer, dp, implementation Correct Solution: ``` import sys from math import log def num(l, r, d): mid = (l+r)//2 if d>=k: return 0 if list_s[l] == n2a[d] else 1 count_l = len([0 for i in range(l, mid+1) if list_s[i] != n2a[d]]) count_r = len([0 for i in range(mid+1, r+1) if list_s[i] != n2a[d]]) return min(num(l, mid, d+1)+count_r, num(mid+1, r, d+1)+count_l) a2n = {chr(97+i):i for i in range(26)} n2a = {i:chr(97+i) for i in range(26)} T=int(sys.stdin.readline()) for _ in range(T): n = int(sys.stdin.readline()) # 0<=k<=17 list_s = sys.stdin.readline().strip() k = int(log(n, 2)) print(num(0, n-1, 0)) ```
output
1
98,811
0
197,623
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k for some integer k ≥ 0. The string s[1 ... n] is called c-good if at least one of the following three conditions is satisfied: * The length of s is 1, and it consists of the character c (i.e. s_1=c); * The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s_1=s_2=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... s_n) is a (c+1)-good string; * The length of s is greater than 1, the second half of the string consists of only the character c (i.e. s_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{n/2}) is a (c+1)-good string. For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good. In one move, you can choose one index i from 1 to n and replace s_i with any lowercase Latin letter (any character from 'a' to 'z'). Your task is to find the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string for c= 'a'). It is guaranteed that the answer always exists. You have to answer t independent test cases. Another example of an 'a'-good string is as follows. Consider the string s = "cdbbaaaa". It is an 'a'-good string, because: * the second half of the string ("aaaa") consists of only the character 'a'; * the first half of the string ("cdbb") is 'b'-good string, because: * the second half of the string ("bb") consists of only the character 'b'; * the first half of the string ("cd") is 'c'-good string, because: * the first half of the string ("c") consists of only the character 'c'; * the second half of the string ("d") is 'd'-good string. Input The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 131~072) — the length of s. It is guaranteed that n = 2^k for some integer k ≥ 0. The second line of the test case contains the string s consisting of n lowercase Latin letters. It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5). Output For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string with c = 'a'). It is guaranteed that the answer exists. Example Input 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac Output 0 7 4 5 1 1
instruction
0
98,812
0
197,624
Tags: bitmasks, brute force, divide and conquer, dp, implementation Correct Solution: ``` import sys def rs(): return sys.stdin.readline().rstrip() def ri(): return int(sys.stdin.readline()) def ria(): return list(map(int, sys.stdin.readline().split())) def ws(s): sys.stdout.write(s); sys.stdout.write('\n') def wi(n): sys.stdout.write(str(n)); sys.stdout.write('\n') def wia(a, sep=' '): sys.stdout.write(sep.join([str(x) for x in a])); sys.stdout.write('\n') def solve(n, s, c): if n == 1: return 0 if s[0] == c else 1 mid = n // 2 c1 = s[:mid].count(c) c2 = s[mid:].count(c) return min(mid - c1 + solve(mid, s[mid:], chr(ord(c) + 1)), mid - c2 + solve(mid, s[:mid], chr(ord(c) + 1))) def main(): for _ in range(ri()): n = ri() s = rs() wi(solve(n, s, 'a')) if __name__ == '__main__': main() ```
output
1
98,812
0
197,625
Provide tags and a correct Python 3 solution for this coding contest problem. You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k for some integer k ≥ 0. The string s[1 ... n] is called c-good if at least one of the following three conditions is satisfied: * The length of s is 1, and it consists of the character c (i.e. s_1=c); * The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s_1=s_2=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... s_n) is a (c+1)-good string; * The length of s is greater than 1, the second half of the string consists of only the character c (i.e. s_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{n/2}) is a (c+1)-good string. For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good. In one move, you can choose one index i from 1 to n and replace s_i with any lowercase Latin letter (any character from 'a' to 'z'). Your task is to find the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string for c= 'a'). It is guaranteed that the answer always exists. You have to answer t independent test cases. Another example of an 'a'-good string is as follows. Consider the string s = "cdbbaaaa". It is an 'a'-good string, because: * the second half of the string ("aaaa") consists of only the character 'a'; * the first half of the string ("cdbb") is 'b'-good string, because: * the second half of the string ("bb") consists of only the character 'b'; * the first half of the string ("cd") is 'c'-good string, because: * the first half of the string ("c") consists of only the character 'c'; * the second half of the string ("d") is 'd'-good string. Input The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. The first line of the test case contains one integer n (1 ≤ n ≤ 131~072) — the length of s. It is guaranteed that n = 2^k for some integer k ≥ 0. The second line of the test case contains the string s consisting of n lowercase Latin letters. It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5). Output For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from s (i.e. c-good string with c = 'a'). It is guaranteed that the answer exists. Example Input 6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac Output 0 7 4 5 1 1
instruction
0
98,813
0
197,626
Tags: bitmasks, brute force, divide and conquer, dp, implementation Correct Solution: ``` import sys, threading sys.setrecursionlimit(10**8) threading.stack_size(10**8) # new thread will get stack of such size def main(): def findMinCost(s,targetChar): if len(s)==1: return int(s[0]!=targetChar) mid=len(s)//2 leftCost=sum(c!=targetChar for c in s[:mid])+findMinCost(s[mid:],chr(ord(targetChar)+1)) rightCost=sum(c!=targetChar for c in s[mid:])+findMinCost(s[:mid],chr(ord(targetChar)+1)) return min(leftCost,rightCost) t=int(input()) for _ in range(t): _,s=int(input()),input() print(findMinCost(s,"a")) threading.Thread(target=main).start() ```
output
1
98,813
0
197,627