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Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
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108,084
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Tags: combinatorics, dp, math, strings Correct Solution: ``` import sys input=sys.stdin.buffer.readline S=list(input()) T=list(input()) N=len(S)-2 M=len(T)-2 S.append(20) mod=998244353 DP=[[[0]*8 for j in range(M+2)] for i in range(N+2)] for i in range(N): for j in range(M): DP[i][j][0]=1 for i in range(N+1): for j in range(M+1): for k in range(8): if k&4: if S[i-1]!=S[i]: DP[i+1][j][k|1]+=DP[i][j][k] if DP[i+1][j][k|1]>=mod: DP[i+1][j][k|1]-=mod if S[i-1]!=T[j]: DP[i][j+1][(k|2)^4]+=DP[i][j][k] if DP[i][j+1][(k|2)^4]>=mod: DP[i][j+1][(k|2)^4]-=mod else: if T[j-1]!=S[i] or k==0: DP[i+1][j][(k|1)^4]+=DP[i][j][k] if DP[i+1][j][(k|1)^4]>=mod: DP[i+1][j][(k|1)^4]-=mod if T[j-1]!=T[j] or k==0: DP[i][j+1][k|2]+=DP[i][j][k] if DP[i][j+1][k|2]>=mod: DP[i][j+1][k|2]-=mod ANS=0 for i in range(N+1): for j in range(M+1): ANS+=DP[i][j][3]+DP[i][j][7] print(ANS%mod) ```
output
1
108,084
0
216,169
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
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108,085
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216,170
Tags: combinatorics, dp, math, strings Correct Solution: ``` import sys input = sys.stdin.readline mod = 998244353 tot = 0 x = ' ' + input().strip() y = ' ' + input().strip() s = [x,y] dp = [[[[0]*4 for j in range(2)] for k in range(len(y))] for i in range(len(x))] for i in range(1,len(x)): for j in range(1,len(y)): dp[i][j-1][0][2] = 1 dp[i-1][j][1][1] = 1 for i in range(len(x)): for j in range(len(y)): s_idx = [i,j] tot = (tot + dp[i][j][0][3] + dp[i][j][1][3]) % mod for c in range(2): for nex in range(2): for ney in range(2): if i < len(x)-1 and s[c][s_idx[c]] != x[i+1]: dp[i+1][j][0][2+ney] = (dp[i+1][j][0][2+ney] + dp[i][j][c][2*nex+ney]) % mod if j < len(y)-1 and s[c][s_idx[c]] != y[j+1]: dp[i][j+1][1][2*nex+1] = (dp[i][j+1][1][2*nex+1] + dp[i][j][c][2*nex+ney]) % mod print(tot) ```
output
1
108,085
0
216,171
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
0
108,086
0
216,172
Tags: combinatorics, dp, math, strings Correct Solution: ``` import sys from sys import stdin x = stdin.readline()[:-1] xl = len(x) y = stdin.readline()[:-1] yl = len(y) x += "?" y += "!" mod = 998244353 dp = [[[0,0] for i in range(yl+1)] for j in range(xl+1)] dp[-1][-1] = [1,0] for a in range(-1,xl): for b in range(-1,yl): if a == b == -1: for na in range(xl): dp[na][-1][0] += 1 for nb in range(yl): dp[-1][nb][1] += 1 elif a == -1: #put a for na in range(xl): if y[b] != x[na]: dp[na][b][0] += dp[a][b][1] dp[na][b][0] %= mod elif b == -1: #put b for nb in range(yl): if y[nb] != x[a]: dp[a][nb][1] += dp[a][b][0] dp[a][nb][1] %= mod for f in range(2): if a != -1: #put after a if f == 0: if a+1<xl and x[a+1] != x[a]: dp[a+1][b][0] += dp[a][b][f] dp[a+1][b][0] %= mod else: if a+1<xl and x[a+1] != y[b]: dp[a+1][b][0] += dp[a][b][f] dp[a+1][b][0] %= mod if b != -1: #put b if f == 0: if b+1<yl and y[b+1] != x[a]: dp[a][b+1][1] += dp[a][b][f] dp[a][b+1][1] %= mod else: if b+1<yl and y[b+1] != y[b]: dp[a][b+1][1] += dp[a][b][f] dp[a][b+1][1] %= mod #print (dp) ans = 0 for i in range(xl): for j in range(yl): ans += sum(dp[i][j]) print (ans % mod) ```
output
1
108,086
0
216,173
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
0
108,087
0
216,174
Tags: combinatorics, dp, math, strings Correct Solution: ``` import sys;input=sys.stdin.buffer.readline;S=list(input());T=list(input());N=len(S)-2;M=len(T)-2;S.append(20);mod=998244353;DP=[[[0]*8 for j in range(M+2)] for i in range(N+2)] for i in range(N): for j in range(M): DP[i][j][0]=1 for i in range(N+1): for j in range(M+1): for k in range(8): if k&4: if S[i-1]!=S[i]: DP[i+1][j][k|1]+=DP[i][j][k] if DP[i+1][j][k|1]>=mod: DP[i+1][j][k|1]-=mod if S[i-1]!=T[j]: DP[i][j+1][(k|2)^4]+=DP[i][j][k] if DP[i][j+1][(k|2)^4]>=mod: DP[i][j+1][(k|2)^4]-=mod else: if T[j-1]!=S[i] or k==0: DP[i+1][j][(k|1)^4]+=DP[i][j][k] if DP[i+1][j][(k|1)^4]>=mod: DP[i+1][j][(k|1)^4]-=mod if T[j-1]!=T[j] or k==0: DP[i][j+1][k|2]+=DP[i][j][k] if DP[i][j+1][k|2]>=mod: DP[i][j+1][k|2]-=mod print(sum([DP[i][j][3]+DP[i][j][7] for i in range(N+1) for j in range(M+1)])%mod) ```
output
1
108,087
0
216,175
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
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108,088
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Tags: combinatorics, dp, math, strings Correct Solution: ``` def popcount(x): x = x - ((x >> 1) & 0x55555555) x = (x & 0x33333333) + ((x >> 2) & 0x33333333) x = (x + (x >> 4)) & 0x0f0f0f0f x = x + (x >> 8) x = x + (x >> 16) return x & 0x0000007f def eratosthenes(n): res=[0 for i in range(n+1)] prime=set([]) for i in range(2,n+1): if not res[i]: prime.add(i) for j in range(1,n//i+1): res[i*j]=1 return prime def factorization(n): res=[] for p in prime: if n%p==0: while n%p==0: n//=p res.append(p) if n!=1: res.append(n) return res def euler_phi(n): res = n for x in range(2,n+1): if x ** 2 > n: break if n%x==0: res = res//x * (x-1) while n%x==0: n //= x if n!=1: res = res//n * (n-1) return res def ind(b,n): res=0 while n%b==0: res+=1 n//=b return res def isPrimeMR(n): d = n - 1 d = d // (d & -d) L = [2, 3, 5, 7, 11, 13, 17] for a in L: t = d y = pow(a, t, n) if y == 1: continue while y != n - 1: y = (y * y) % n if y == 1 or t == n - 1: return 0 t <<= 1 return 1 def findFactorRho(n): from math import gcd m = 1 << n.bit_length() // 8 for c in range(1, 99): f = lambda x: (x * x + c) % n y, r, q, g = 2, 1, 1, 1 while g == 1: x = y for i in range(r): y = f(y) k = 0 while k < r and g == 1: ys = y for i in range(min(m, r - k)): y = f(y) q = q * abs(x - y) % n g = gcd(q, n) k += m r <<= 1 if g == n: g = 1 while g == 1: ys = f(ys) g = gcd(abs(x - ys), n) if g < n: if isPrimeMR(g): return g elif isPrimeMR(n // g): return n // g return findFactorRho(g) def primeFactor(n): i = 2 ret = {} rhoFlg = 0 while i*i <= n: k = 0 while n % i == 0: n //= i k += 1 if k: ret[i] = k i += 1 + i % 2 if i == 101 and n >= 2 ** 20: while n > 1: if isPrimeMR(n): ret[n], n = 1, 1 else: rhoFlg = 1 j = findFactorRho(n) k = 0 while n % j == 0: n //= j k += 1 ret[j] = k if n > 1: ret[n] = 1 if rhoFlg: ret = {x: ret[x] for x in sorted(ret)} return ret def divisors(n): res = [1] prime = primeFactor(n) for p in prime: newres = [] for d in res: for j in range(prime[p]+1): newres.append(d*p**j) res = newres res.sort() return res def xorfactorial(num):#排他的論理和の階乗 if num==0: return 0 elif num==1: return 1 elif num==2: return 3 elif num==3: return 0 else: x=baseorder(num) return (2**x)*((num-2**x+1)%2)+function(num-2**x) def xorconv(n,X,Y): if n==0: res=[(X[0]*Y[0])%mod] return res x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))] y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))] z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))] w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))] res1=xorconv(n-1,x,y) res2=xorconv(n-1,z,w) former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))] latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))] former=list(map(lambda x:x%mod,former)) latter=list(map(lambda x:x%mod,latter)) return former+latter def merge_sort(A,B): pos_A,pos_B = 0,0 n,m = len(A),len(B) res = [] while pos_A < n and pos_B < m: a,b = A[pos_A],B[pos_B] if a < b: res.append(a) pos_A += 1 else: res.append(b) pos_B += 1 res += A[pos_A:] res += B[pos_B:] return res class UnionFindVerSize(): def __init__(self, N): self._parent = [n for n in range(0, N)] self._size = [1] * N self.group = N def find_root(self, x): if self._parent[x] == x: return x self._parent[x] = self.find_root(self._parent[x]) stack = [x] while self._parent[stack[-1]]!=stack[-1]: stack.append(self._parent[stack[-1]]) for v in stack: self._parent[v] = stack[-1] return self._parent[x] def unite(self, x, y): gx = self.find_root(x) gy = self.find_root(y) if gx == gy: return self.group -= 1 if self._size[gx] < self._size[gy]: self._parent[gx] = gy self._size[gy] += self._size[gx] else: self._parent[gy] = gx self._size[gx] += self._size[gy] def get_size(self, x): return self._size[self.find_root(x)] def is_same_group(self, x, y): return self.find_root(x) == self.find_root(y) class WeightedUnionFind(): def __init__(self,N): self.parent = [i for i in range(N)] self.size = [1 for i in range(N)] self.val = [0 for i in range(N)] self.flag = True self.edge = [[] for i in range(N)] def dfs(self,v,pv): stack = [(v,pv)] new_parent = self.parent[pv] while stack: v,pv = stack.pop() self.parent[v] = new_parent for nv,w in self.edge[v]: if nv!=pv: self.val[nv] = self.val[v] + w stack.append((nv,v)) def unite(self,x,y,w): if not self.flag: return if self.parent[x]==self.parent[y]: self.flag = (self.val[x] - self.val[y] == w) return if self.size[self.parent[x]]>self.size[self.parent[y]]: self.edge[x].append((y,-w)) self.edge[y].append((x,w)) self.size[x] += self.size[y] self.val[y] = self.val[x] - w self.dfs(y,x) else: self.edge[x].append((y,-w)) self.edge[y].append((x,w)) self.size[y] += self.size[x] self.val[x] = self.val[y] + w self.dfs(x,y) class Dijkstra(): class Edge(): def __init__(self, _to, _cost): self.to = _to self.cost = _cost def __init__(self, V): self.G = [[] for i in range(V)] self._E = 0 self._V = V @property def E(self): return self._E @property def V(self): return self._V def add_edge(self, _from, _to, _cost): self.G[_from].append(self.Edge(_to, _cost)) self._E += 1 def shortest_path(self, s): import heapq que = [] d = [10**15] * self.V d[s] = 0 heapq.heappush(que, (0, s)) while len(que) != 0: cost, v = heapq.heappop(que) if d[v] < cost: continue for i in range(len(self.G[v])): e = self.G[v][i] if d[e.to] > d[v] + e.cost: d[e.to] = d[v] + e.cost heapq.heappush(que, (d[e.to], e.to)) return d #Z[i]:length of the longest list starting from S[i] which is also a prefix of S #O(|S|) def Z_algorithm(s): N = len(s) Z_alg = [0]*N Z_alg[0] = N i = 1 j = 0 while i < N: while i+j < N and s[j] == s[i+j]: j += 1 Z_alg[i] = j if j == 0: i += 1 continue k = 1 while i+k < N and k + Z_alg[k]<j: Z_alg[i+k] = Z_alg[k] k += 1 i += k j -= k return Z_alg class BIT(): def __init__(self,n): self.BIT=[0]*(n+1) self.num=n def query(self,idx): res_sum = 0 while idx > 0: res_sum += self.BIT[idx] idx -= idx&(-idx) return res_sum #Ai += x O(logN) def update(self,idx,x): while idx <= self.num: self.BIT[idx] += x idx += idx&(-idx) return class dancinglink(): def __init__(self,n,debug=False): self.n = n self.debug = debug self._left = [i-1 for i in range(n)] self._right = [i+1 for i in range(n)] self.exist = [True for i in range(n)] def pop(self,k): if self.debug: assert self.exist[k] L = self._left[k] R = self._right[k] if L!=-1: if R!=self.n: self._right[L],self._left[R] = R,L else: self._right[L] = self.n elif R!=self.n: self._left[R] = -1 self.exist[k] = False def left(self,idx,k=1): if self.debug: assert self.exist[idx] res = idx while k: res = self._left[res] if res==-1: break k -= 1 return res def right(self,idx,k=1): if self.debug: assert self.exist[idx] res = idx while k: res = self._right[res] if res==self.n: break k -= 1 return res class SparseTable(): def __init__(self,A,merge_func,ide_ele): N=len(A) n=N.bit_length() self.table=[[ide_ele for i in range(n)] for i in range(N)] self.merge_func=merge_func for i in range(N): self.table[i][0]=A[i] for j in range(1,n): for i in range(0,N-2**j+1): f=self.table[i][j-1] s=self.table[i+2**(j-1)][j-1] self.table[i][j]=self.merge_func(f,s) def query(self,s,t): b=t-s+1 m=b.bit_length()-1 return self.merge_func(self.table[s][m],self.table[t-2**m+1][m]) class BinaryTrie: class node: def __init__(self,val): self.left = None self.right = None self.max = val def __init__(self): self.root = self.node(-10**15) def append(self,key,val): pos = self.root for i in range(29,-1,-1): pos.max = max(pos.max,val) if key>>i & 1: if pos.right is None: pos.right = self.node(val) pos = pos.right else: pos = pos.right else: if pos.left is None: pos.left = self.node(val) pos = pos.left else: pos = pos.left pos.max = max(pos.max,val) def search(self,M,xor): res = -10**15 pos = self.root for i in range(29,-1,-1): if pos is None: break if M>>i & 1: if xor>>i & 1: if pos.right: res = max(res,pos.right.max) pos = pos.left else: if pos.left: res = max(res,pos.left.max) pos = pos.right else: if xor>>i & 1: pos = pos.right else: pos = pos.left if pos: res = max(res,pos.max) return res def solveequation(edge,ans,n,m): #edge=[[to,dire,id]...] x=[0]*m used=[False]*n for v in range(n): if used[v]: continue y = dfs(v) if y!=0: return False return x def dfs(v): used[v]=True r=ans[v] for to,dire,id in edge[v]: if used[to]: continue y=dfs(to) if dire==-1: x[id]=y else: x[id]=-y r+=y return r class Matrix(): mod=10**9+7 def set_mod(m): Matrix.mod=m def __init__(self,L): self.row=len(L) self.column=len(L[0]) self._matrix=L for i in range(self.row): for j in range(self.column): self._matrix[i][j]%=Matrix.mod def __getitem__(self,item): if type(item)==int: raise IndexError("you must specific row and column") elif len(item)!=2: raise IndexError("you must specific row and column") i,j=item return self._matrix[i][j] def __setitem__(self,item,val): if type(item)==int: raise IndexError("you must specific row and column") elif len(item)!=2: raise IndexError("you must specific row and column") i,j=item self._matrix[i][j]=val def __add__(self,other): if (self.row,self.column)!=(other.row,other.column): raise SizeError("sizes of matrixes are different") res=[[0 for j in range(self.column)] for i in range(self.row)] for i in range(self.row): for j in range(self.column): res[i][j]=self._matrix[i][j]+other._matrix[i][j] res[i][j]%=Matrix.mod return Matrix(res) def __sub__(self,other): if (self.row,self.column)!=(other.row,other.column): raise SizeError("sizes of matrixes are different") res=[[0 for j in range(self.column)] for i in range(self.row)] for i in range(self.row): for j in range(self.column): res[i][j]=self._matrix[i][j]-other._matrix[i][j] res[i][j]%=Matrix.mod return Matrix(res) def __mul__(self,other): if type(other)!=int: if self.column!=other.row: raise SizeError("sizes of matrixes are different") res=[[0 for j in range(other.column)] for i in range(self.row)] for i in range(self.row): for j in range(other.column): temp=0 for k in range(self.column): temp+=self._matrix[i][k]*other._matrix[k][j] res[i][j]=temp%Matrix.mod return Matrix(res) else: n=other res=[[(n*self._matrix[i][j])%Matrix.mod for j in range(self.column)] for i in range(self.row)] return Matrix(res) def __pow__(self,m): if self.column!=self.row: raise MatrixPowError("the size of row must be the same as that of column") n=self.row res=Matrix([[int(i==j) for i in range(n)] for j in range(n)]) while m: if m%2==1: res=res*self self=self*self m//=2 return res def __str__(self): res=[] for i in range(self.row): for j in range(self.column): res.append(str(self._matrix[i][j])) res.append(" ") res.append("\n") res=res[:len(res)-1] return "".join(res) class SegmentTree: def __init__(self, init_val, segfunc, ide_ele): n = len(init_val) self.segfunc = segfunc self.ide_ele = ide_ele self.num = 1 << (n - 1).bit_length() self.tree = [ide_ele] * 2 * self.num for i in range(n): self.tree[self.num + i] = init_val[i] for i in range(self.num - 1, 0, -1): self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1]) def update(self, k, x): k += self.num self.tree[k] = x while k > 1: self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1]) k >>= 1 def query(self, l, r): res = self.ide_ele l += self.num r += self.num while l < r: if l & 1: res = self.segfunc(res, self.tree[l]) l += 1 if r & 1: res = self.segfunc(res, self.tree[r - 1]) l >>= 1 r >>= 1 return res def bisect_l(self,l,r,x): l += self.num r += self.num Lmin = -1 Rmin = -1 while l<r: if l & 1: if self.tree[l] <= x and Lmin==-1: Lmin = l l += 1 if r & 1: if self.tree[r-1] <=x: Rmin = r-1 l >>= 1 r >>= 1 if Lmin != -1: pos = Lmin while pos<self.num: if self.tree[2 * pos] <=x: pos = 2 * pos else: pos = 2 * pos +1 return pos-self.num elif Rmin != -1: pos = Rmin while pos<self.num: if self.tree[2 * pos] <=x: pos = 2 * pos else: pos = 2 * pos +1 return pos-self.num else: return -1 import sys,random,bisect from collections import deque,defaultdict from heapq import heapify,heappop,heappush from itertools import permutations from math import log,gcd input = lambda :sys.stdin.readline().rstrip() mi = lambda :map(int,input().split()) li = lambda :list(mi()) mod = 998244353 x = input() n = len(x) y = input() m = len(y) dp_x = [[1 for j in range(m+1)] for i in range(n+1)] dp_y = [[1 for j in range(m+1)] for i in range(n+1)] dp_x[n][m] = 1 dp_y[n][m] = 1 res = 0 for i in range(n,-1,-1): for j in range(m,-1,-1): if i!=n: res += dp_x[i+1][j] res %= mod if j!=m: res += dp_y[i][j+1] res %= mod if i!=0: if i!=n and x[i-1]!=x[i]: dp_x[i][j] += dp_x[i+1][j] dp_x[i][j] %= mod if j!=m and x[i-1]!=y[j]: dp_x[i][j] += dp_y[i][j+1] dp_x[i][j] %= mod if j!=0: if i!=n and y[j-1]!=x[i]: dp_y[i][j] += dp_x[i+1][j] dp_y[i][j] %= mod if j!=m and y[j-1]!=y[j]: dp_y[i][j] += dp_y[i][j+1] dp_y[i][j] %= mod for i in range(n): pre = "" L = 0 for j in range(i,n): if x[j]!=pre: L += 1 pre = x[j] else: break res -= L * (m+1) res %= mod for i in range(m): pre = "" L = 0 for j in range(i,m): if y[j]!=pre: L += 1 pre = y[j] else: break res -= L * (n+1) res %= mod print(res) ```
output
1
108,088
0
216,177
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
0
108,089
0
216,178
Tags: combinatorics, dp, math, strings Correct Solution: ``` mod = 998244353 eps = 10**-9 def main(): import sys input = sys.stdin.readline S = input().rstrip('\n') T = input().rstrip('\n') NS = len(S) NT = len(T) dp_S = [[0] * (NT+1) for _ in range(NS+1)] dp_T = [[0] * (NT+1) for _ in range(NS+1)] for i in range(1, NS+1): dp_S[i][0] = 1 for j in range(1, NT+1): dp_T[0][j] = 1 for i in range(NS+1): for j in range(NT+1): if i == j == 0: continue elif i == 0: if S[0] != T[j-1]: dp_S[1][j] = (dp_S[1][j] + dp_T[0][j])%mod if j+1 <= NT: if T[j-1] != T[j]: dp_T[0][j+1] = (dp_T[0][j+1] + dp_T[0][j])%mod elif j == 0: if T[0] != S[i-1]: dp_T[i][1] = (dp_T[i][1] + dp_S[i][0]) % mod if i + 1 <= NS: if S[i - 1] != S[i]: dp_S[i+1][0] = (dp_S[i+1][0] + dp_S[i][0]) % mod else: if i+1 <= NS: if S[i-1] != S[i]: dp_S[i+1][j] = (dp_S[i+1][j] + dp_S[i][j])%mod if T[j-1] != S[i]: dp_S[i+1][j] = (dp_S[i+1][j] + dp_T[i][j] + dp_T[0][j])%mod if j+1 <= NT: if T[j-1] != T[j]: dp_T[i][j+1] = (dp_T[i][j+1] + dp_T[i][j])%mod if S[i-1] != T[j]: dp_T[i][j+1] = (dp_T[i][j+1] + dp_S[i][j] + dp_S[i][0])%mod ans = 0 for i in range(1, NS+1): for j in range(1, NT+1): ans = (ans + dp_S[i][j] + dp_T[i][j])%mod print(ans) if __name__ == '__main__': main() ```
output
1
108,089
0
216,179
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
0
108,090
0
216,180
Tags: combinatorics, dp, math, strings Correct Solution: ``` from bisect import * from collections import * from math import gcd,ceil,sqrt,floor,inf from heapq import * from itertools import * from operator import add,mul,sub,xor,truediv,floordiv from functools import * #------------------------------------------------------------------------ import os import sys from io import BytesIO, IOBase # 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") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #------------------------------------------------------------------------ def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) def A(n):return [0]*n def AI(n,x): return [x]*n def A2(n,m): return [[0]*m for i in range(n)] def G(n): return [[] for i in range(n)] def GP(it): return [[ch,len(list(g))] for ch,g in groupby(it)] #------------------------------------------------------------------------ from types import GeneratorType def bootstrap(f, stack=[]): def wrappedfunc(*args, **kwargs): if stack: return f(*args, **kwargs) else: to = f(*args, **kwargs) while True: if type(to) is GeneratorType: stack.append(to) to = next(to) else: stack.pop() if not stack: break to = stack[-1].send(to) return to return wrappedfunc mod=10**9+7 farr=[1] ifa=[] def fact(x,mod=0): if mod: while x>=len(farr): farr.append(farr[-1]*len(farr)%mod) else: while x>=len(farr): farr.append(farr[-1]*len(farr)) return farr[x] def ifact(x,mod): global ifa fact(x,mod) ifa.append(pow(farr[-1],mod-2,mod)) for i in range(x,0,-1): ifa.append(ifa[-1]*i%mod) ifa.reverse() def per(i,j,mod=0): if i<j: return 0 if not mod: return fact(i)//fact(i-j) return farr[i]*ifa[i-j]%mod def com(i,j,mod=0): if i<j: return 0 if not mod: return per(i,j)//fact(j) return per(i,j,mod)*ifa[j]%mod def catalan(n): return com(2*n,n)//(n+1) def isprime(n): for i in range(2,int(n**0.5)+1): if n%i==0: return False return True def floorsum(a,b,c,n):#sum((a*i+b)//c for i in range(n+1)) if a==0:return b//c*(n+1) if a>=c or b>=c: return floorsum(a%c,b%c,c,n)+b//c*(n+1)+a//c*n*(n+1)//2 m=(a*n+b)//c return n*m-floorsum(c,c-b-1,a,m-1) def inverse(a,m): a%=m if a<=1: return a return ((1-inverse(m,a)*m)//a)%m def lowbit(n): return n&-n class BIT: def __init__(self,arr): self.arr=arr self.n=len(arr)-1 def update(self,x,v): while x<=self.n: self.arr[x]+=v x+=x&-x def query(self,x): ans=0 while x: ans+=self.arr[x] x&=x-1 return ans class ST: def __init__(self,arr):#n!=0 n=len(arr) mx=n.bit_length()#取不到 self.st=[[0]*mx for i in range(n)] for i in range(n): self.st[i][0]=arr[i] for j in range(1,mx): for i in range(n-(1<<j)+1): self.st[i][j]=max(self.st[i][j-1],self.st[i+(1<<j-1)][j-1]) def query(self,l,r): if l>r:return -inf s=(r+1-l).bit_length()-1 return max(self.st[l][s],self.st[r-(1<<s)+1][s]) ''' class DSU:#容量+路径压缩 def __init__(self,n): self.c=[-1]*n def same(self,x,y): return self.find(x)==self.find(y) def find(self,x): if self.c[x]<0: return x self.c[x]=self.find(self.c[x]) return self.c[x] def union(self,u,v): u,v=self.find(u),self.find(v) if u==v: return False if self.c[u]>self.c[v]: u,v=v,u self.c[u]+=self.c[v] self.c[v]=u return True def size(self,x): return -self.c[self.find(x)]''' class UFS:#秩+路径 def __init__(self,n): self.parent=[i for i in range(n)] self.ranks=[0]*n def find(self,x): if x!=self.parent[x]: self.parent[x]=self.find(self.parent[x]) return self.parent[x] def union(self,u,v): pu,pv=self.find(u),self.find(v) if pu==pv: return False if self.ranks[pu]>=self.ranks[pv]: self.parent[pv]=pu if self.ranks[pv]==self.ranks[pu]: self.ranks[pu]+=1 else: self.parent[pu]=pv def Prime(n): c=0 prime=[] flag=[0]*(n+1) for i in range(2,n+1): if not flag[i]: prime.append(i) c+=1 for j in range(c): if i*prime[j]>n: break flag[i*prime[j]]=prime[j] if i%prime[j]==0: break return flag def dij(s,graph): d={} d[s]=0 heap=[(0,s)] seen=set() while heap: dis,u=heappop(heap) if u in seen: continue seen.add(u) for v,w in graph[u]: if v not in d or d[v]>d[u]+w: d[v]=d[u]+w heappush(heap,(d[v],v)) return d def bell(s,g):#bellman-Ford dis=AI(n,inf) dis[s]=0 for i in range(n-1): for u,v,w in edge: if dis[v]>dis[u]+w: dis[v]=dis[u]+w change=A(n) for i in range(n): for u,v,w in edge: if dis[v]>dis[u]+w: dis[v]=dis[u]+w change[v]=1 return dis def lcm(a,b): return a*b//gcd(a,b) def lis(nums): res=[] for k in nums: i=bisect.bisect_left(res,k) if i==len(res): res.append(k) else: res[i]=k return len(res) def RP(nums):#逆序对 n = len(nums) s=set(nums) d={} for i,k in enumerate(sorted(s),1): d[k]=i bi=BIT([0]*(len(s)+1)) ans=0 for i in range(n-1,-1,-1): ans+=bi.query(d[nums[i]]-1) bi.update(d[nums[i]],1) return ans class DLN: def __init__(self,val): self.val=val self.pre=None self.next=None def nb(i,j,n,m): for ni,nj in [[i+1,j],[i-1,j],[i,j-1],[i,j+1]]: if 0<=ni<n and 0<=nj<m: yield ni,nj def topo(n): q=deque() res=[] for i in range(1,n+1): if ind[i]==0: q.append(i) res.append(i) while q: u=q.popleft() for v in g[u]: ind[v]-=1 if ind[v]==0: q.append(v) res.append(v) return res @bootstrap def gdfs(r,p): if len(g[r])==1 and p!=-1: yield None for ch in g[r]: if ch!=p: yield gdfs(ch,r) yield None t=1 for i in range(t): x=input() x=list(x) y=input() y=list(y) x=list(map(lambda ch: ord(ch)-97,x)) y=list(map(lambda ch: ord(ch)-97,y)) ans=0 mod=998244353 m,n=len(x),len(y) v1=[1]*(m+1) v2=[1]*(n+1) for i in range(m-2,-1,-1): if x[i]!=x[i+1]: v1[i]+=v1[i+1] for i in range(n-2,-1,-1): if y[i]!=y[i+1]: v2[i]+=v2[i+1] #print(x,y,v1,v2) dp=[[[0]*27 for j in range(n+1)] for i in range(m+1)] for i in range(m-1,-1,-1): for j in range(n-1,-1,-1): for k in range(27): if x[i]==k: if y[j]!=k: dp[i][j][k]=(dp[i][j+1][y[j]]+v1[i])%mod elif y[j]==k: dp[i][j][k]=(dp[i+1][j][x[i]]+v2[j])%mod else: #print(i,j,k) dp[i][j][k]=(dp[i+1][j][x[i]]+dp[i][j+1][y[j]]+(x[i]!=y[j])*(v2[j]+v1[i]))%mod for i in range(m): for j in range(n): ans=(ans+dp[i][j][26])%mod print(ans) ''' sys.setrecursionlimit(200000) import threading threading.stack_size(10**8) t=threading.Thr ead(target=main) t.start() t.join() ''' ''' sys.setrecursionlimit(200000) import threading threading.stack_size(10**8) t=threading.Thread(target=main) t.start() t.join() ''' ```
output
1
108,090
0
216,181
Provide tags and a correct Python 3 solution for this coding contest problem. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
instruction
0
108,091
0
216,182
Tags: combinatorics, dp, math, strings Correct Solution: ``` # O(16*n^2) import sys input = sys.stdin.readline mod = 998244353 tot = 0 x = ' ' + input().strip() y = ' ' + input().strip() s = [x,y] # the idea is to go from the dp that finds number of chaotic merges of x and y # given that the substrings merged must begin at the start of x and y (are just prefixes) # to the dp where the start of the substrings for the merge can be anything # this is done by adding 1 at dp[i][j-1][0][1][0] and dp[i-1][j][1][0][1] # (the same way we would start the dp normally if i == 1 and j == 1 (prefixes from above)) # dp[i][j][c][nex][ney] = the number of chaotic merges of a substring of x and y such that # either substring of x is empty or ends at i and either substring of y is empty or ends at j # however both substrings cannot be empty # c = 0 -> last character is from x otherwise from y # nex -> 1 if substring from x is not empty else 0 # ney -> 1 if substring from y is not empty else 0 # note that instead of an extra dimension for each nex and ney they are merged to reduce memory (or else MLE) dp = [[[[0]*4 for j in range(2)] for k in range(len(y))] for i in range(len(x))] # base case for i in range(1,len(x)): for j in range(1,len(y)): # to start the dp of chaotic merges of x[i:] and y[j:] dp[i][j-1][0][2] = 1 dp[i-1][j][1][1] = 1 # transitions for i in range(len(x)): for j in range(len(y)): s_idx = [i,j] # add num of chaotic merges of subs that end at i and j to tot tot = (tot + dp[i][j][0][3] + dp[i][j][1][3]) % mod # transition for c in range(2): for nex in range(2): for ney in range(2): # add x[i+1] to the end of the merge and transition if i < len(x)-1 and s[c][s_idx[c]] != x[i+1]: dp[i+1][j][0][2+ney] = (dp[i+1][j][0][2+ney] + dp[i][j][c][2*nex+ney]) % mod # add y[j+1] to the end of the merge and transition if j < len(y)-1 and s[c][s_idx[c]] != y[j+1]: dp[i][j+1][1][2*nex+1] = (dp[i][j+1][1][2*nex+1] + dp[i][j][c][2*nex+ney]) % mod print(tot) ```
output
1
108,091
0
216,183
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s. Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order. A merge z is produced from a sequence a by the following rules: * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i. Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i. Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive. Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered. Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353. Input The first line contains a string x (1 ≤ |x| ≤ 1000). The second line contains a string y (1 ≤ |y| ≤ 1000). Both strings consist only of lowercase Latin letters. Output Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353. Examples Input aaa bb Output 24 Input code forces Output 1574 Input aaaaa aaa Output 0 Input justamassivetesttocheck howwellyouhandlemodulooperations Output 667387032 Note In the first example there are: * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24. Submitted Solution: ``` S=list(input()) T=list(input()) N=len(S)-2 M=len(T)-2 S.append(20) mod=998244353 DP=[[[0]*8 for j in range(M+2)] for i in range(N+2)] for i in range(N): for j in range(M): DP[i][j][0]=1 for i in range(N+1): for j in range(M+1): for k in range(8): if k&4: if S[i-1]!=S[i]: DP[i+1][j][k|1]+=DP[i][j][k] if DP[i+1][j][k|1]>=mod: DP[i+1][j][k|1]-=mod if S[i-1]!=T[j]: DP[i][j+1][(k|2)^4]+=DP[i][j][k] if DP[i][j+1][(k|2)^4]>=mod: DP[i][j+1][(k|2)^4]-=mod else: if T[j-1]!=S[i] or k==0: DP[i+1][j][(k|1)^4]+=DP[i][j][k] if DP[i+1][j][(k|1)^4]>=mod: DP[i+1][j][(k|1)^4]-=mod if T[j-1]!=T[j] or k==0: DP[i][j+1][k|2]+=DP[i][j][k] if DP[i][j+1][k|2]>=mod: DP[i][j+1][k|2]-=mod ANS=0 for i in range(N+1): for j in range(M+1): ANS+=DP[i][j][3]+DP[i][j][7] print(ANS%mod) ```
instruction
0
108,092
0
216,184
No
output
1
108,092
0
216,185
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,130
0
216,260
Tags: greedy, strings Correct Solution: ``` def lms(s): t="" if len(s)==1: return s else: while(len(s)>1): l=0 j=0 for i in range(len(s)): if ord(s[i])>l: l=ord(s[i]) j=i t+= (s.count(s[j]))*s[j] y = len(s) - 1 - s[::-1].index(s[j]) s=s[y+1:] if len(set(map(str,s)))==1: t+=s break return t print(lms(input())) ```
output
1
108,130
0
216,261
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,131
0
216,262
Tags: greedy, strings Correct Solution: ``` a=m='' for x in input()[::-1]: if x>=m: a+=x m=max(m,x) print(a[::-1]) ```
output
1
108,131
0
216,263
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,132
0
216,264
Tags: greedy, strings Correct Solution: ``` from sys import stdin, stdout s = stdin.readline().strip() maximum = [] mx = 'a' for f in s[::-1]: mx = max(f, mx) maximum.append(mx) maximum = maximum[::-1] ans = '' for i in range(len(s)): if s[i] == maximum[i]: ans += s[i] stdout.write(str(ans)) ```
output
1
108,132
0
216,265
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,133
0
216,266
Tags: greedy, strings Correct Solution: ``` A = input() letter_to_index = {} for i, letter in enumerate(A): if letter in letter_to_index: letter_to_index[letter] += [i] else: letter_to_index[letter] = [i] pos = 0 letter = 'z' result = "" while True: if letter in letter_to_index: letter_pos = letter_to_index[letter] for index in letter_pos: if index >= pos: result += letter pos = index if letter == 'a': break letter = chr(ord(letter) - 1) print(result) ```
output
1
108,133
0
216,267
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,134
0
216,268
Tags: greedy, strings Correct Solution: ``` s = input() l = len(s) m = 'a' ans = "" for i in range(l): if s[l-i-1] >= m: ans = s[l-i-1] + ans m = s[l-i-1] print(ans) # Made By Mostafa_Khaled ```
output
1
108,134
0
216,269
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,135
0
216,270
Tags: greedy, strings Correct Solution: ``` s,l=input(),[''] for i in reversed(s): if l[-1]<=i: l.append(i) print(*reversed(l),sep='') ```
output
1
108,135
0
216,271
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,136
0
216,272
Tags: greedy, strings Correct Solution: ``` string = str(input()) listx = [x for x in string] listx.reverse() join = [''.join(listx)] letts = list(set(listx)) letts.sort() letts.reverse() stringx = '' for i in letts: if i in string: for k in range(len(string)): if string[k] == i: indx = k for j in range(indx): if string[j] == i: stringx += i stringx += i string = string[indx+1:] print(stringx) ```
output
1
108,136
0
216,273
Provide tags and a correct Python 3 solution for this coding contest problem. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA
instruction
0
108,137
0
216,274
Tags: greedy, strings Correct Solution: ``` from collections import Counter s = input() c = Counter(s) cur_char = 'z' for ch in s: while c[cur_char] == 0: cur_char = chr(ord(cur_char) - 1) if ch == cur_char: print(cur_char, end='') c[ch] -= 1 ```
output
1
108,137
0
216,275
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA Submitted Solution: ``` string = str(input()) listx = [x for x in string] listx.reverse() join = [''.join(listx)] letts = list(set(listx)) letts.sort() letts.reverse() stringx = '' for i in letts: leng = len(string) indx = listx.index(i) for j in range(leng - indx): if string[j] == i: stringx += i string = string[-indx:] print(stringx) ```
instruction
0
108,138
0
216,276
No
output
1
108,138
0
216,277
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA Submitted Solution: ``` string = str(input()) listx = [x for x in string] listx.reverse() join = [''.join(listx)] letts = list(set(listx)) letts.sort() letts.reverse() stringx = '' for i in letts: if i in string: indx = string.index(i) for j in range(indx): if string[j] == i: stringx += i stringx += i string = string[indx+1:] print(stringx) ```
instruction
0
108,139
0
216,278
No
output
1
108,139
0
216,279
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA Submitted Solution: ``` def lms(s): t="" while(len(s)>1): l=0 j=0 for i in range(len(s)): if ord(s[i])>l: l=ord(s[i]) j=i t+= (s.count(s[j]))*s[j] y = len(s) - 1 - s[::-1].index(s[j]) s=s[y+1:] if len(set(map(str,s)))==1: t+=s break return t print(lms(input())) ```
instruction
0
108,140
0
216,280
No
output
1
108,140
0
216,281
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence. We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk(1 ≤ p1 < p2 < ... < pk ≤ |s|) a subsequence of string s = s1s2... s|s|. String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in lines are compared like their ASCII codes. Input The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 105. Output Print the lexicographically maximum subsequence of string s. Examples Input ababba Output bbba Input abbcbccacbbcbaaba Output cccccbba Note Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters). The first sample: aBaBBA The second sample: abbCbCCaCbbCBaaBA Submitted Solution: ``` string = str(input()) listx = [x for x in string] listx.reverse() join = [''.join(listx)] letts = list(set(listx)) letts.sort() letts.reverse() stringx = '' for i in letts: if i in string: leng = len(string) indx = string.index(i) for j in range(leng - indx): if string[j] == i: stringx += i string = string[-indx:] print(stringx) ```
instruction
0
108,141
0
216,282
No
output
1
108,141
0
216,283
Provide tags and a correct Python 3 solution for this coding contest problem. Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is described by a group of three (p, l, r), where p is a string and l and r (l ≤ r) are integers. We’ll say that string t complies with rule (p, l, r), if the number of occurrences of string t in string p lies between l and r, inclusive. For example, string "ab", complies with rules ("ab", 1, 2) and ("aab", 0, 1), but does not comply with rules ("cd", 1, 2) and ("abab", 0, 1). A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (|s| is a length of s) is string slsl + 1... sr. Consider a number of occurrences of string t in string p as a number of pairs of integers l, r (1 ≤ l ≤ r ≤ |p|) such that p[l... r] = t. We’ll say that string t is good if it complies with all n rules. Smart Beaver asks you to help him to write a program that can calculate the number of distinct good substrings of string s. Two substrings s[x... y] and s[z... w] are cosidered to be distinct iff s[x... y] ≠ s[z... w]. Input The first line contains string s. The second line contains integer n. Next n lines contain the rules, one per line. Each of these lines contains a string and two integers pi, li, ri, separated by single spaces (0 ≤ li ≤ ri ≤ |pi|). It is guaranteed that all the given strings are non-empty and only contain lowercase English letters. The input limits for scoring 30 points are (subproblem G1): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 200. The input limits for scoring 70 points are (subproblems G1+G2): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 2000. The input limits for scoring 100 points are (subproblems G1+G2+G3): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 50000. Output Print a single integer — the number of good substrings of string s. Examples Input aaab 2 aa 0 0 aab 1 1 Output 3 Input ltntlnen 3 n 0 0 ttlneenl 1 4 lelllt 1 1 Output 2 Input a 0 Output 1 Note There are three good substrings in the first sample test: «aab», «ab» and «b». In the second test only substrings «e» and «t» are good.
instruction
0
108,158
0
216,316
Tags: hashing, strings Correct Solution: ``` from sys import stdin import re def substrings(s): for i in range(0, len(s)): for l in range(i, len(s)): yield s[i:l+1] test = stdin.readline().rstrip('\n') ruleCount = int(stdin.readline()) rules = [] for i in range(0, ruleCount): ruleStr = stdin.readline() sp = ruleStr.split(' ') m = {} for s in substrings(sp[0]): m[s] = m.get(s, 0) + 1 rules.append((sp[0], int(sp[1]), int(sp[2]), m)) def works(x): for rule in rules: if not rule[1] <= rule[3].get(x, 0) <= rule[2]: return False return True print(len([x for x in set(substrings(test)) if works(x)])) ```
output
1
108,158
0
216,317
Provide tags and a correct Python 3 solution for this coding contest problem. Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is described by a group of three (p, l, r), where p is a string and l and r (l ≤ r) are integers. We’ll say that string t complies with rule (p, l, r), if the number of occurrences of string t in string p lies between l and r, inclusive. For example, string "ab", complies with rules ("ab", 1, 2) and ("aab", 0, 1), but does not comply with rules ("cd", 1, 2) and ("abab", 0, 1). A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (|s| is a length of s) is string slsl + 1... sr. Consider a number of occurrences of string t in string p as a number of pairs of integers l, r (1 ≤ l ≤ r ≤ |p|) such that p[l... r] = t. We’ll say that string t is good if it complies with all n rules. Smart Beaver asks you to help him to write a program that can calculate the number of distinct good substrings of string s. Two substrings s[x... y] and s[z... w] are cosidered to be distinct iff s[x... y] ≠ s[z... w]. Input The first line contains string s. The second line contains integer n. Next n lines contain the rules, one per line. Each of these lines contains a string and two integers pi, li, ri, separated by single spaces (0 ≤ li ≤ ri ≤ |pi|). It is guaranteed that all the given strings are non-empty and only contain lowercase English letters. The input limits for scoring 30 points are (subproblem G1): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 200. The input limits for scoring 70 points are (subproblems G1+G2): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 2000. The input limits for scoring 100 points are (subproblems G1+G2+G3): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 50000. Output Print a single integer — the number of good substrings of string s. Examples Input aaab 2 aa 0 0 aab 1 1 Output 3 Input ltntlnen 3 n 0 0 ttlneenl 1 4 lelllt 1 1 Output 2 Input a 0 Output 1 Note There are three good substrings in the first sample test: «aab», «ab» and «b». In the second test only substrings «e» and «t» are good.
instruction
0
108,159
0
216,318
Tags: hashing, strings Correct Solution: ``` def count(p, s): start = 0 c = 0 while True: try: pos = s.index(p, start) c += 1 start = pos + 1 except ValueError: return c s = input() n = int(input()) pravs = [] for i in range(n): p, l, r = input().split() l = int(l); r = int(r) pravs.append((p, l, r)) var = set() for l in range(len(s)): for r in range(l+1, len(s)+1): pods = s[l:r] for prav in pravs: if not prav[1] <= count(pods, prav[0]) <= prav[2]: break else: var.add(pods) print(len(var)) ```
output
1
108,159
0
216,319
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is described by a group of three (p, l, r), where p is a string and l and r (l ≤ r) are integers. We’ll say that string t complies with rule (p, l, r), if the number of occurrences of string t in string p lies between l and r, inclusive. For example, string "ab", complies with rules ("ab", 1, 2) and ("aab", 0, 1), but does not comply with rules ("cd", 1, 2) and ("abab", 0, 1). A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (|s| is a length of s) is string slsl + 1... sr. Consider a number of occurrences of string t in string p as a number of pairs of integers l, r (1 ≤ l ≤ r ≤ |p|) such that p[l... r] = t. We’ll say that string t is good if it complies with all n rules. Smart Beaver asks you to help him to write a program that can calculate the number of distinct good substrings of string s. Two substrings s[x... y] and s[z... w] are cosidered to be distinct iff s[x... y] ≠ s[z... w]. Input The first line contains string s. The second line contains integer n. Next n lines contain the rules, one per line. Each of these lines contains a string and two integers pi, li, ri, separated by single spaces (0 ≤ li ≤ ri ≤ |pi|). It is guaranteed that all the given strings are non-empty and only contain lowercase English letters. The input limits for scoring 30 points are (subproblem G1): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 200. The input limits for scoring 70 points are (subproblems G1+G2): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 2000. The input limits for scoring 100 points are (subproblems G1+G2+G3): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 50000. Output Print a single integer — the number of good substrings of string s. Examples Input aaab 2 aa 0 0 aab 1 1 Output 3 Input ltntlnen 3 n 0 0 ttlneenl 1 4 lelllt 1 1 Output 2 Input a 0 Output 1 Note There are three good substrings in the first sample test: «aab», «ab» and «b». In the second test only substrings «e» and «t» are good. Submitted Solution: ``` s = input() n = int(input()) rules = [] for i in range(n): rules.append(input().split()) rules[-1][1]=int(rules[-1][1]) rules[-1][2]=int(rules[-1][2]) used = set() ans=0 def check(rules,s): for ru in rules: if ru[1]<=ru[0].count(s)<=ru[2]:continue else: return False return True for i in range(len(s)): for j in range(len(s)): sk=s[i:j+1] if(sk not in used): if check(rules,sk): ans+=1 used.add(sk) print(ans) ```
instruction
0
108,160
0
216,320
No
output
1
108,160
0
216,321
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is described by a group of three (p, l, r), where p is a string and l and r (l ≤ r) are integers. We’ll say that string t complies with rule (p, l, r), if the number of occurrences of string t in string p lies between l and r, inclusive. For example, string "ab", complies with rules ("ab", 1, 2) and ("aab", 0, 1), but does not comply with rules ("cd", 1, 2) and ("abab", 0, 1). A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (|s| is a length of s) is string slsl + 1... sr. Consider a number of occurrences of string t in string p as a number of pairs of integers l, r (1 ≤ l ≤ r ≤ |p|) such that p[l... r] = t. We’ll say that string t is good if it complies with all n rules. Smart Beaver asks you to help him to write a program that can calculate the number of distinct good substrings of string s. Two substrings s[x... y] and s[z... w] are cosidered to be distinct iff s[x... y] ≠ s[z... w]. Input The first line contains string s. The second line contains integer n. Next n lines contain the rules, one per line. Each of these lines contains a string and two integers pi, li, ri, separated by single spaces (0 ≤ li ≤ ri ≤ |pi|). It is guaranteed that all the given strings are non-empty and only contain lowercase English letters. The input limits for scoring 30 points are (subproblem G1): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 200. The input limits for scoring 70 points are (subproblems G1+G2): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 2000. The input limits for scoring 100 points are (subproblems G1+G2+G3): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 50000. Output Print a single integer — the number of good substrings of string s. Examples Input aaab 2 aa 0 0 aab 1 1 Output 3 Input ltntlnen 3 n 0 0 ttlneenl 1 4 lelllt 1 1 Output 2 Input a 0 Output 1 Note There are three good substrings in the first sample test: «aab», «ab» and «b». In the second test only substrings «e» and «t» are good. Submitted Solution: ``` s = input() n = int(input()) rules = [] for i in range(n): rules.append(input().split()) rules[i][1]=int(rules[i][1]) rules[i][2]=int(rules[i][2]) used = set() ans=0 def check(rules,s): for ru in rules: if ru[1]<=ru[0].count(s)<=ru[2]:continue else: return False return True for i in range(len(s)): sk = '' for j in range(i,len(s)): sk+=s[j] if(sk not in used): if check(rules,sk): ans+=1 used.add(sk) print(ans) ```
instruction
0
108,161
0
216,322
No
output
1
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0
216,323
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is described by a group of three (p, l, r), where p is a string and l and r (l ≤ r) are integers. We’ll say that string t complies with rule (p, l, r), if the number of occurrences of string t in string p lies between l and r, inclusive. For example, string "ab", complies with rules ("ab", 1, 2) and ("aab", 0, 1), but does not comply with rules ("cd", 1, 2) and ("abab", 0, 1). A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (|s| is a length of s) is string slsl + 1... sr. Consider a number of occurrences of string t in string p as a number of pairs of integers l, r (1 ≤ l ≤ r ≤ |p|) such that p[l... r] = t. We’ll say that string t is good if it complies with all n rules. Smart Beaver asks you to help him to write a program that can calculate the number of distinct good substrings of string s. Two substrings s[x... y] and s[z... w] are cosidered to be distinct iff s[x... y] ≠ s[z... w]. Input The first line contains string s. The second line contains integer n. Next n lines contain the rules, one per line. Each of these lines contains a string and two integers pi, li, ri, separated by single spaces (0 ≤ li ≤ ri ≤ |pi|). It is guaranteed that all the given strings are non-empty and only contain lowercase English letters. The input limits for scoring 30 points are (subproblem G1): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 200. The input limits for scoring 70 points are (subproblems G1+G2): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 2000. The input limits for scoring 100 points are (subproblems G1+G2+G3): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 50000. Output Print a single integer — the number of good substrings of string s. Examples Input aaab 2 aa 0 0 aab 1 1 Output 3 Input ltntlnen 3 n 0 0 ttlneenl 1 4 lelllt 1 1 Output 2 Input a 0 Output 1 Note There are three good substrings in the first sample test: «aab», «ab» and «b». In the second test only substrings «e» and «t» are good. Submitted Solution: ``` s = input() n = int(input()) rules = [] def count(a,b): ans = 0 for i in range(len(a)-len(b)): if a[i:i+len(b)]==b: ans+=1 return ans for i in range(n): rules.append(input().split()) rules[-1][1]=int(rules[-1][1]) rules[-1][2]=int(rules[-1][2]) used = set() ans=0 def check(rules,s): for ru in rules: if ru[1]<=count(ru[0],s)<=ru[2]:continue else: return False return True for i in range(len(s)): for j in range(i,len(s)): sk=s[i:j+1] if(sk not in used): if check(rules,sk): ans+=1 used.add(sk) print(ans) ```
instruction
0
108,162
0
216,324
No
output
1
108,162
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216,325
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Smart Beaver recently got interested in a new word game. The point is as follows: count the number of distinct good substrings of some string s. To determine if a string is good or not the game uses rules. Overall there are n rules. Each rule is described by a group of three (p, l, r), where p is a string and l and r (l ≤ r) are integers. We’ll say that string t complies with rule (p, l, r), if the number of occurrences of string t in string p lies between l and r, inclusive. For example, string "ab", complies with rules ("ab", 1, 2) and ("aab", 0, 1), but does not comply with rules ("cd", 1, 2) and ("abab", 0, 1). A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (|s| is a length of s) is string slsl + 1... sr. Consider a number of occurrences of string t in string p as a number of pairs of integers l, r (1 ≤ l ≤ r ≤ |p|) such that p[l... r] = t. We’ll say that string t is good if it complies with all n rules. Smart Beaver asks you to help him to write a program that can calculate the number of distinct good substrings of string s. Two substrings s[x... y] and s[z... w] are cosidered to be distinct iff s[x... y] ≠ s[z... w]. Input The first line contains string s. The second line contains integer n. Next n lines contain the rules, one per line. Each of these lines contains a string and two integers pi, li, ri, separated by single spaces (0 ≤ li ≤ ri ≤ |pi|). It is guaranteed that all the given strings are non-empty and only contain lowercase English letters. The input limits for scoring 30 points are (subproblem G1): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 200. The input limits for scoring 70 points are (subproblems G1+G2): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 2000. The input limits for scoring 100 points are (subproblems G1+G2+G3): * 0 ≤ n ≤ 10. * The length of string s and the maximum length of string p is ≤ 50000. Output Print a single integer — the number of good substrings of string s. Examples Input aaab 2 aa 0 0 aab 1 1 Output 3 Input ltntlnen 3 n 0 0 ttlneenl 1 4 lelllt 1 1 Output 2 Input a 0 Output 1 Note There are three good substrings in the first sample test: «aab», «ab» and «b». In the second test only substrings «e» and «t» are good. Submitted Solution: ``` s = input() n = int(input()) sp = [] l = [] r = [] for i in range(n): tmp = input() tsp, tl, tr = tmp.split() sp += [tsp] l += [int(tl)] r += [int(tr)] was = {} for i in range(len(s)): for j in range(len(s)): if (i <= j): c = s[i:j + 1] #print(c) good = True for q in range(n): if (sp[q].count(c) < l[q]) or (sp[q].count(c) > r[q]): #print(c) #print(q + 1) good = False break if (good) and not (c in was): was[c] = 1 #print(c) print(len(was.keys())) ```
instruction
0
108,163
0
216,326
No
output
1
108,163
0
216,327
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,271
0
216,542
Tags: constructive algorithms, implementation, strings Correct Solution: ``` n = int(input()) s = input() if n > 26: print(-1) else: az = [0 for i in range(26)] cnt = 0 for i in s: ind = ord(i)-97 az[ind] += 1 if az[ind] > 1: cnt += 1 print(cnt) ```
output
1
108,271
0
216,543
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,272
0
216,544
Tags: constructive algorithms, implementation, strings Correct Solution: ``` def different_is_good(mystr): if len(mystr) > 26: print(-1) return hash_, diff = [0] * 128, 0 for char in mystr: if hash_[ord(char)] == 1: diff += 1 else: hash_[ord(char)] = 1 print(diff) _ = int(input()) different_is_good(str(input())) ```
output
1
108,272
0
216,545
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,273
0
216,546
Tags: constructive algorithms, implementation, strings Correct Solution: ``` n=int(input()) string=input() if(n>26): print(-1) else: char_dict={} for i in string: if i in char_dict.keys(): char_dict[i]=char_dict[i]+1 else: char_dict[i]=1 characters_to_change=0 for key,value in char_dict.items(): characters_to_change=characters_to_change+value-1 print(characters_to_change) ```
output
1
108,273
0
216,547
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,274
0
216,548
Tags: constructive algorithms, implementation, strings Correct Solution: ``` n = int(input()) s = input() if n == 1: print(0) exit(0) visited = set() visited.add(s[0]) ans = 0 d = {} d[s[0]] = 1 for i in range(1, n): if s[i] in visited: d[s[i]] += 1 else: visited.add(s[i]) d[s[i]] = 1 x = len(visited) for i in d: x += d[i] - 1 ans += d[i] - 1 if x > 26: print(-1) else: print(ans) ```
output
1
108,274
0
216,549
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,275
0
216,550
Tags: constructive algorithms, implementation, strings Correct Solution: ``` def check(s1): if len(s1)==len(set(s1)): return False else: return True n=int(input()) s=input() s1=list(s) res=[] c=0 if(n>26): print(-1) elif(check(s1)==True): for i in s1: if i not in res: res.append(i) else: c+=1 print(c) else: print(0) ```
output
1
108,275
0
216,551
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,276
0
216,552
Tags: constructive algorithms, implementation, strings Correct Solution: ``` n=int(input()) k=len(set(input())) if n<=26: print(n-k) else: print(-1) ```
output
1
108,276
0
216,553
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,277
0
216,554
Tags: constructive algorithms, implementation, strings Correct Solution: ``` n = int(input()) word = input() newWord = "" LETTERS = "abcdefghijklmnopqrstuvwxyz" usedChars = {} moves = 0 if n > 26: print("-1") else: for c in word: if c not in usedChars: usedChars[c] = 0 for c in word: if usedChars[c] > 0: for l in LETTERS: if l not in usedChars: usedChars[l] = 0 newWord = newWord + str(l) moves = moves + 1 break else: usedChars[c] += 1 print(moves) ```
output
1
108,277
0
216,555
Provide tags and a correct Python 3 solution for this coding contest problem. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko".
instruction
0
108,278
0
216,556
Tags: constructive algorithms, implementation, strings Correct Solution: ``` from collections import Counter n = int(input().strip()) s = input().strip() def solve(s): freq = Counter(s) l = len(freq.keys()) c = 0 for i in freq.values(): if i > 1: l += i-1 c += i-1 if l > 26: return -1 return c print(solve(s)) ```
output
1
108,278
0
216,557
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` num = int(input()) arr = list(input()) if num > 26: print(-1) else: print(num - len(set(arr))) ```
instruction
0
108,279
0
216,558
Yes
output
1
108,279
0
216,559
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` p=int(input()) s=input() z=set(s) if(p>26): print('-1') else: print(p-len(z)) ```
instruction
0
108,280
0
216,560
Yes
output
1
108,280
0
216,561
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` n = int(input()) st = input() if(n > 26): print(-1) else: li = [0] * 26 for i in range(n): ch = ord(st[i]) - 97 li[ch] = li[ch] + 1 total = 0 count = 0 for i in range(26): if(li[i] == 0): count = count + 1 else: total = total + (li[i] - 1) if(total <= count): print(total) else: print(-1) ```
instruction
0
108,281
0
216,562
Yes
output
1
108,281
0
216,563
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` from sys import stdin n = int(input()) str = stdin.readline() alphabet = "abcdefghijklmnopqrstuvwxyz" count = [0] * 26 res = 0 if(n > 26): print("-1") else: for ch in range(n): for i in range(26): if(str[ch] == alphabet[i]): if(count[i] == 0): count[i] = 1 else: res += 1 print (res) ```
instruction
0
108,282
0
216,564
Yes
output
1
108,282
0
216,565
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` a=int(input()) t=input() print(a-len(set(t))) ```
instruction
0
108,283
0
216,566
No
output
1
108,283
0
216,567
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` # https://codeforces.com/problemset/problem/672/B n = input() s = input() l = [] l.extend(s) print(len(l) - len(set(l))) ```
instruction
0
108,284
0
216,568
No
output
1
108,284
0
216,569
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` def check(s1): if len(s1)==len(set(s1)): return False else: return True n=int(input()) s=input() s1=list(s) res=[] c=0 if(check(s1)==True): for i in s1: if i not in res: res.append(i) c+=1 else: print(0) print(c) ```
instruction
0
108,285
0
216,570
No
output
1
108,285
0
216,571
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A wise man told Kerem "Different is good" once, so Kerem wants all things in his life to be different. Kerem recently got a string s consisting of lowercase English letters. Since Kerem likes it when things are different, he wants all substrings of his string s to be distinct. Substring is a string formed by some number of consecutive characters of the string. For example, string "aba" has substrings "" (empty substring), "a", "b", "a", "ab", "ba", "aba". If string s has at least two equal substrings then Kerem will change characters at some positions to some other lowercase English letters. Changing characters is a very tiring job, so Kerem want to perform as few changes as possible. Your task is to find the minimum number of changes needed to make all the substrings of the given string distinct, or determine that it is impossible. Input The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the length of the string s. The second line contains the string s of length n consisting of only lowercase English letters. Output If it's impossible to change the string s such that all its substring are distinct print -1. Otherwise print the minimum required number of changes. Examples Input 2 aa Output 1 Input 4 koko Output 2 Input 5 murat Output 0 Note In the first sample one of the possible solutions is to change the first character to 'b'. In the second sample, one may change the first character to 'a' and second character to 'b', so the string becomes "abko". Submitted Solution: ``` n=int(input("")) str=input("") cnt=0 for i in range(n-1): if str[i] in str[i+1:]: cnt+=1 if cnt==0: print(-1) else: print(cnt) ```
instruction
0
108,286
0
216,572
No
output
1
108,286
0
216,573
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences.
instruction
0
108,361
0
216,722
Tags: data structures, dp, strings Correct Solution: ``` n = int(input()); s = input(); m = int(input()) a = [0]*(n+2); b = [0]*(n+2); q = [0]*(n+1); dp = [(0, 0)]*(n+2) for i in range(0, n): b[i] = b[i-2]+(s[i] == 'b') a[i] = a[i-2]+(s[i] == 'a') q[i] = q[i-1]+(s[i] == '?') for i in range(n-1, -1, -1): if i+m-1 >= n: continue dp[i] = dp[i+1] i_b = 1 if m%2 == 1 else 2 i_a = 1 if m%2 == 0 else 2 if not (b[i+m-i_b]-b[i-2] or a[i+m-i_a]-a[i-1]): t, r = dp[i+m] dp[i] = min((t-1, r+q[i+m-1]-q[i-1]), dp[i]) print(dp[0][1]) ```
output
1
108,361
0
216,723
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences.
instruction
0
108,362
0
216,724
Tags: data structures, dp, strings Correct Solution: ``` n = int(input()); s = input(); m = int(input()) a = [0]*(n+2); b = [0]*(n+2); q = [0]*(n+1); dp = [(0, 0)]*(n+2) for i in range(0, n): b[i] = b[i-2]+(s[i] == 'b') a[i] = a[i-2]+(s[i] == 'a') q[i] = q[i-1]+(s[i] == '?') for i in range(n-m, -1, -1): dp[i] = dp[i+1] i_b = 1 if m%2 == 1 else 2 i_a = 1 if m%2 == 0 else 2 if not (b[i+m-i_b]-b[i-2] or a[i+m-i_a]-a[i-1]): t, r = dp[i+m] dp[i] = min((t-1, r+q[i+m-1]-q[i-1]), dp[i]) print(dp[0][1]) ```
output
1
108,362
0
216,725
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences.
instruction
0
108,363
0
216,726
Tags: data structures, dp, strings Correct Solution: ``` match = 0; nonmatch = 0; count = 0 def calc_match(s, t, p): global match global nonmatch global count if p == len(s)-len(t): return if p+len(t) < len(s): if s[p+len(t)] == '?': count -= 1 elif s[p+len(t)] == t[-1]: match -= 1 else: nonmatch -= 1 match, nonmatch = nonmatch, match if p+len(t) < len(s): if s[p] == '?': count += 1 elif s[p] == 'a': match += 1 else: nonmatch += 1 def init_match(s, t): global match global nonmatch global count p = len(s)-len(t) for i in range(len(t)): if s[p+i] == '?': count += 1 elif s[p+i] == t[i]: match += 1 else: nonmatch += 1 n = int(input()) s = input() m = int(input()) t = "" for i in range(m): if i%2==0: t = t + 'a' else: t = t + 'b' init_match(s,t) dp = [] for i in range(n+3): dp.append((0, 0)) p = n-m while p >= 0: calc_match(s, t, p) if nonmatch == 0: if dp[p+1][0] == dp[p+m][0]+1: dp[p] = (dp[p+1][0], min(dp[p+1][1], dp[p+m][1]+count)) elif dp[p+1][0] > dp[p+m][0]+1: dp[p] = dp[p+1] else: dp[p] = (dp[p+m][0]+1, dp[p+m][1]+count) else: dp[p] = dp[p+1] p -= 1 print(dp[0][1]) ```
output
1
108,363
0
216,727
Provide tags and a correct Python 3 solution for this coding contest problem. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences.
instruction
0
108,364
0
216,728
Tags: data structures, dp, strings Correct Solution: ``` match = 0 nonmatch = 0 count = 0 def calc_match(s, t, p): global match global nonmatch global count if p == len(s)-len(t): return if p+len(t) < len(s): if s[p+len(t)] == '?': count -= 1 elif s[p+len(t)] == t[-1]: match -= 1 else: nonmatch -= 1 match, nonmatch = nonmatch, match if p+len(t) < len(s): if s[p] == '?': count += 1 elif s[p] == 'a': match += 1 else: nonmatch += 1 def init_match(s, t): global match global nonmatch global count p = len(s)-len(t) for i in range(len(t)): if s[p+i] == '?': count += 1 elif s[p+i] == t[i]: match += 1 else: nonmatch += 1 n = int(input()) s = input() m = int(input()) t = "" for i in range(m): if i%2==0: t = t + 'a' else: t = t + 'b' init_match(s,t) dp = [] for i in range(n+3): dp.append((0, 0)) p = n-m while p >= 0: calc_match(s, t, p) if nonmatch == 0: if dp[p+1][0] == dp[p+m][0]+1: dp[p] = (dp[p+1][0], min(dp[p+1][1], dp[p+m][1]+count)) elif dp[p+1][0] > dp[p+m][0]+1: dp[p] = dp[p+1] else: dp[p] = (dp[p+m][0]+1, dp[p+m][1]+count) else: dp[p] = dp[p+1] p -= 1 print(dp[0][1]) ```
output
1
108,364
0
216,729
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences. Submitted Solution: ``` n = int(input()) s = list(input()) t = int(input()) re = s.copy() kras = 'ab' kras *= t kras = kras[:t] col = s.count('?') c = 0 v = 0 q = 0 h = 0 for i in range(2 ** col): shable = bin(i)[2:] priv = '0' * (col - len(shable)) priv += shable shable = priv for el in range(n): if s[el] == '?': if shable[q] == '1': if el % 2 == 0: s[el] = 'a' else: s[el] = 'b' q += 1 new = ''.join(s).count(kras) if new > c: v = shable.count('1') c = new s = re.copy() q = 0 h = 0 for i in range(2 ** col): shable = bin(i)[2:] priv = '0' * (col - len(shable)) priv += shable shable = priv for el in range(n): if s[el] == '?': if shable[q] == '1': if el % 2 == 0: s[el] = 'b' else: s[el] = 'a' q += 1 new = ''.join(s).count(kras) if new > c: v = shable.count('1') c = new s = re.copy() q = 0 h = 0 print(v) ```
instruction
0
108,365
0
216,730
No
output
1
108,365
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216,731
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences. Submitted Solution: ``` match = 0 nonmatch = 0 count = 0 def calc_match(s, t, p): global match global nonmatch global count if p+len(t) < len(s): if s[p+len(t)] == '?': count -= 1 elif s[p+len(t)] == t[-1]: match -= 1 else: nonmatch -= 1 match, nonmatch = nonmatch, match if p+len(t) < len(s): if s[p] == '?': count += 1 elif s[p] == 'a': match += 1 else: nonmatch += 1 def init_match(s, t): global match global nonmatch global count p = len(s)-len(t) for i in range(len(t)): if s[p+i] == '?': count += 1 elif s[p+i] == t[i]: match += 1 else: nonmatch += 1 n = int(input()) s = input() m = int(input()) t = "" for i in range(m): if i%2==0: t = t + 'a' else: t = t + 'b' init_match(s,t) dp = [] for i in range(n+3): dp.append((0, 0)) p = n-m while p >= 0: calc_match(s, t, p) if nonmatch == 0: if dp[p+1][0] == dp[p+m][0]+1: dp[p] = (dp[p+1][0], min(dp[p+1][1], dp[p+m][1]+count)) elif dp[p+1][0] > dp[p+m][0]+1: dp[p] = dp[p+1] else: dp[p] = (dp[p+m][0]+1, dp[p+m][1]+count) else: dp[p] = dp[p+1] p -= 1 print(dp[0][1]) ```
instruction
0
108,366
0
216,732
No
output
1
108,366
0
216,733
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Vasya wrote down two strings s of length n and t of length m consisting of small English letters 'a' and 'b'. What is more, he knows that string t has a form "abab...", namely there are letters 'a' on odd positions and letters 'b' on even positions. Suddenly in the morning, Vasya found that somebody spoiled his string. Some letters of the string s were replaced by character '?'. Let's call a sequence of positions i, i + 1, ..., i + m - 1 as occurrence of string t in s, if 1 ≤ i ≤ n - m + 1 and t1 = si, t2 = si + 1, ..., tm = si + m - 1. The boy defines the beauty of the string s as maximum number of disjoint occurrences of string t in s. Vasya can replace some letters '?' with 'a' or 'b' (letters on different positions can be replaced with different letter). Vasya wants to make some replacements in such a way that beauty of string s is maximum possible. From all such options, he wants to choose one with the minimum number of replacements. Find the number of replacements he should make. Input The first line contains a single integer n (1 ≤ n ≤ 105) — the length of s. The second line contains the string s of length n. It contains small English letters 'a', 'b' and characters '?' only. The third line contains a single integer m (1 ≤ m ≤ 105) — the length of t. The string t contains letters 'a' on odd positions and 'b' on even positions. Output Print the only integer — the minimum number of replacements Vasya has to perform to make the beauty of string s the maximum possible. Examples Input 5 bb?a? 1 Output 2 Input 9 ab??ab??? 3 Output 2 Note In the first sample string t has a form 'a'. The only optimal option is to replace all characters '?' by 'a'. In the second sample using two replacements we can make string equal to "aba?aba??". It is impossible to get more than two occurrences. Submitted Solution: ``` n = int(input()) s = list(input()) t = int(input()) re = s.copy() kras = 'ab' kras *= t kras = kras[:t] col = s.count('?') c = 0 v = 0 q = 0 h = 0 for i in range(2 ** col): shable = bin(i)[2:] priv = '0' * (col - len(shable)) priv += shable shable = priv for el in range(n): if s[el] == '?': if shable[q] == '1': h += 1 if el % 2 == 0: s[el] = 'a' else: s[el] = 'b' q += 1 new = ''.join(s).count(kras) if new > c: v = h c = new s = re.copy() q = 0 h = 0 print(v) ```
instruction
0
108,367
0
216,734
No
output
1
108,367
0
216,735