message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6 | instruction | 0 | 20,982 | 16 | 41,964 |
"Correct Solution:
```
import re
s = input()
ans = 0
s = s.replace("BC", "D")
L = re.split('[BC]', s)
for i in L:
k = len(i)
temp = 0
for j in range(k):
if i[k-1-j] == "D":
temp += 1
else:
ans += temp
print(ans)
``` | output | 1 | 20,982 | 16 | 41,965 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6 | instruction | 0 | 20,983 | 16 | 41,966 |
"Correct Solution:
```
S = input().replace("BC","D")
ans = 0
cnt = 0
for s in S :
if s == "A" :
cnt += 1
elif s == "D" :
ans += cnt
else :
cnt = 0
print(ans)
``` | output | 1 | 20,983 | 16 | 41,967 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6 | instruction | 0 | 20,984 | 16 | 41,968 |
"Correct Solution:
```
s=input()
s=s.replace('BC','D')
a=0
ans=0
for i in s:
if i=='A':
a+=1
elif i=='D':
ans+=a
else:
a=0
print(ans)
``` | output | 1 | 20,984 | 16 | 41,969 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6 | instruction | 0 | 20,985 | 16 | 41,970 |
"Correct Solution:
```
s = input().replace('BC', 'D')
ans = 0
cnt = 0
for c in s:
if c == 'A':
cnt += 1
elif c == 'D':
ans += cnt
else:
cnt = 0
print(ans)
``` | output | 1 | 20,985 | 16 | 41,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
S = input()
S = S.replace('BC', '>')
ans = 0
a_count = 0
for s in S:
if s == 'A':
a_count += 1
elif s == '>':
ans += a_count
else:
a_count = 0
print(ans)
``` | instruction | 0 | 20,986 | 16 | 41,972 |
Yes | output | 1 | 20,986 | 16 | 41,973 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
s = input()
s = s.replace('BC', 'D')
lst = list(s)
acount = 0
ans = 0
for i in range(len(s)):
if s[i] == 'A':
acount += 1
elif s[i] == 'D':
ans += acount
else:
acount = 0
print(ans)
``` | instruction | 0 | 20,987 | 16 | 41,974 |
Yes | output | 1 | 20,987 | 16 | 41,975 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
s = input()
t = s.replace('BC', 'D')
answer = 0
A = 0
for i in range(len(t)):
if t[i] == 'A':
A+=1
elif t[i] == 'D':
answer+=A
else:
A = 0
print(answer)
``` | instruction | 0 | 20,988 | 16 | 41,976 |
Yes | output | 1 | 20,988 | 16 | 41,977 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
S = input()
S = S.replace("BC", "X")
n = len(S)
ans = 0
cnt_a = 0
for s in S:
if s == "X":
ans += cnt_a
elif s == "A":
cnt_a += 1
else:
cnt_a = 0
print(ans)
``` | instruction | 0 | 20,989 | 16 | 41,978 |
Yes | output | 1 | 20,989 | 16 | 41,979 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
s = input()
ans = 0
while s.count("ABC") != 0:
ans += s.count("ABC")
s = s.replace("ABC", "BCA")
print(ans)
``` | instruction | 0 | 20,990 | 16 | 41,980 |
No | output | 1 | 20,990 | 16 | 41,981 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
def main():
s = input()
s = s.replace('BC', 'D')
a = 0; d = 0
ans = 0
for t in s:
if a > 0:
if t == 'D':
d += 1
elif t != 'D' and d > 0:
ans += a*d
d = 0
elif t == 'A':
pass
else:
a = 0
a += (t == 'A')
if a > 0 and d > 0:
ans += a*d
print(ans)
if __name__ == "__main__":
main()
``` | instruction | 0 | 20,991 | 16 | 41,982 |
No | output | 1 | 20,991 | 16 | 41,983 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
s = input()
c = 0
while(True):
i = s.find("ABC")
if i == -1:
break
else:
s = s[:i] + "BCA" + s[i+3:]
c += 1
print(c)
``` | instruction | 0 | 20,992 | 16 | 41,984 |
No | output | 1 | 20,992 | 16 | 41,985 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string s consisting of `A`, `B` and `C`.
Snuke wants to perform the following operation on s as many times as possible:
* Choose a contiguous substring of s that reads `ABC` and replace it with `BCA`.
Find the maximum possible number of operations.
Constraints
* 1 \leq |s| \leq 200000
* Each character of s is `A`, `B` and `C`.
Input
Input is given from Standard Input in the following format:
s
Output
Find the maximum possible number of operations.
Examples
Input
ABCABC
Output
3
Input
C
Output
0
Input
ABCACCBABCBCAABCB
Output
6
Submitted Solution:
```
s=list(input())
N=len(s)
ans=0
buf=0
for i in range(N-2):
if s[i]=="A":
buf+=1
if s[i]!="A":
if s[i:i+2]!=["B","C"]:
buf=0
if s[i:i+3]==["A","B","C"]:
ans+=buf
s[i+2]="A"
buf=0
print(ans)
``` | instruction | 0 | 20,993 | 16 | 41,986 |
No | output | 1 | 20,993 | 16 | 41,987 |
Provide a correct Python 3 solution for this coding contest problem.
There are infinitely many cards, numbered 1, 2, 3, ... Initially, Cards x_1, x_2, ..., x_N are face up, and the others are face down.
Snuke can perform the following operation repeatedly:
* Select a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.
Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7
Input
Input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
Print the minimum number of operations required to achieve the objective.
Examples
Input
2
4 5
Output
2
Input
9
1 2 3 4 5 6 7 8 9
Output
3
Input
2
1 10000000
Output
4 | instruction | 0 | 21,884 | 16 | 43,768 |
"Correct Solution:
```
import itertools
from math import sqrt
def chunk(a):
i = 0
res = []
while i < len(a):
res.append(a[i])
while i != len(a) - 1 and a[i + 1] == a[i] + 1:
i += 1
res.append(a[i] + 1)
i += 1
return res
def augment(g, src, dest):
o = [None] * len(g)
q = [(src, src)]
while q:
w = q.pop()
if o[w[0]] is None:
o[w[0]] = w[1]
for s in g[w[0]]:
if o[s] is None:
q.append((s, w[0]))
if not o[dest]:
return False
i = dest
while i != src:
g[o[i]].discard(i)
g[i].add(o[i])
i = o[i]
return True
def match(a):
l = {}
c = 0
matches = 0
for i, j in a:
if i not in l:
l[i] = c
c += 1
if j not in l:
l[j] = c
c += 1
L = {v: k for k, v in l.items()}
g = [set() for i in range(len(l) + 2)]
src = len(l)
dest = src + 1
for i, j in a:
g[src].add(l[i])
g[l[i]].add(l[j])
g[l[j]].add(dest)
while augment(g, src, dest):
matches += 1
return matches
def prime(n):
for i in range(2, min(n, int(sqrt(n) + 7))):
if n % i == 0:
return False
return n > 1
def pairs(b):
c = []
for i in b:
for j in b:
if i % 2 == 0 and j % 2 == 1 and prime(abs(i - j)):
c.append((i, j))
return c
n = int(input())
a = list(map(int, input().split()))
b = chunk(a)
r = match(pairs(b))
e = len(list(filter(lambda x: x % 2 == 0, b)))
o = len(b) - e
print(int(r + 2 * ((e - r) // 2 + (o - r) // 2) + 3 * ((e - r) % 2)))
``` | output | 1 | 21,884 | 16 | 43,769 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are infinitely many cards, numbered 1, 2, 3, ... Initially, Cards x_1, x_2, ..., x_N are face up, and the others are face down.
Snuke can perform the following operation repeatedly:
* Select a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.
Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7
Input
Input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
Print the minimum number of operations required to achieve the objective.
Examples
Input
2
4 5
Output
2
Input
9
1 2 3 4 5 6 7 8 9
Output
3
Input
2
1 10000000
Output
4
Submitted Solution:
```
import sys
input = sys.stdin.readline
import itertools
from collections import defaultdict
import numpy as np
N = int(input())
X = set(int(x) for x in input().split())
# 2は素数でないとして扱って
U = 10**7 + 100
is_prime = np.zeros(U,dtype=np.bool)
is_prime[3::2] = 1
for p in range(3,U,2):
if p*p > U:
break
if is_prime[p]:
is_prime[p*p::p+p] = 0
# imosで値を入れないといけない場所
X ^= set(x+1 for x in X)
EV = set(x for x in X if x%2 == 0)
OD = set(x for x in X if x%2 == 1)
# 1手でとれるペアを見つける：最大マッチング
# 奇点から偶点に辺を貼る
source = -1
sink = -2
graph = defaultdict(set)
for x in EV:
graph[x].add(sink)
for x in OD:
graph[source].add(x)
for x,y in itertools.product(OD,EV):
if is_prime[abs(x-y)]:
graph[x].add(y)
def bfs():
level = defaultdict(int)
q = [source]
level[source] = 1
d = 1
while q:
d += 1
if level[sink] != 0:
break
qq = []
for x in q:
for y in graph[x]:
if level[y]!=0:
continue
level[y] = d
qq.append(y)
q = qq
return level
def dfs(v,level,itr):
if v == sink:
return True
for w in itr[v]:
if level[w]!=level[v]+1:
continue
if dfs(w,level,itr):
graph[v].remove(w)
graph[w].add(v)
return True
return False
def max_flow():
flow = 0
while True:
level = bfs()
if level[sink] == 0:
return flow
itr = {v:iter(graph[v]) for v in graph}
while dfs(source,level,itr):
flow += 1
f = max_flow()
od = len(OD); ev = len(EV)
answer = f
od -= f; ev -= f
answer += 2*(od//2); od %= 2
answer += 2*(ev//2); ev %= 2
if od:
answer += 3
print(answer)
``` | instruction | 0 | 21,885 | 16 | 43,770 |
No | output | 1 | 21,885 | 16 | 43,771 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are infinitely many cards, numbered 1, 2, 3, ... Initially, Cards x_1, x_2, ..., x_N are face up, and the others are face down.
Snuke can perform the following operation repeatedly:
* Select a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.
Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7
Input
Input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
Print the minimum number of operations required to achieve the objective.
Examples
Input
2
4 5
Output
2
Input
9
1 2 3 4 5 6 7 8 9
Output
3
Input
2
1 10000000
Output
4
Submitted Solution:
```
import sys
input = sys.stdin.readline
import itertools
from collections import defaultdict
import numpy as np
N = int(input())
X = set(int(x) for x in input().split())
# 2は素数でないとして扱って
U = 10**7 + 100
is_prime = np.zeros(U,dtype=np.bool)
is_prime[3::2] = 1
for p in range(3,U,2):
if p*p > U:
break
if is_prime[p]:
is_prime[p*p::p+p] = 0
# imosで値を入れないといけない場所
X ^= set(x+1 for x in X)
EV = set(x for x in X if x%2 == 0)
OD = set(x for x in X if x%2 == 1)
# 1手でとれるペアを見つける：最大マッチング
# 奇点から偶点に辺を貼る
source = -1
sink = -2
graph = defaultdict(set)
for x in EV:
graph[x].add(sink)
for x in OD:
graph[source].add(x)
for x,y in itertools.product(OD,EV):
if is_prime[abs(x-y)]:
graph[x].add(y)
def bfs():
level = defaultdict(int)
q = [source]
level[source] = 1
d = 1
while q:
d += 1
if level[sink] != 0:
break
qq = []
for x in q:
for y in graph[x]:
if level[y]!=0:
continue
level[y] = d
qq.append(y)
q = qq
return level
def dfs(v,level,itr):
if v == sink:
return True
for w in itr[v]:
if level[w]!=level[v]+1:
continue
if w in graph[v] and dfs(w,level,itr):
graph[v].remove(w)
graph[w].add(v)
return True
return False
def max_flow():
flow = 0
while True:
level = bfs()
if level[sink] == 0:
return flow
itr = {v:iter(graph[v]) for v in graph}
while dfs(source,level,itr):
flow += 1
f = max_flow()
od = len(OD); ev = len(EV)
answer = f
od -= f; ev -= f
answer += 2*(od//2); od %= 2
answer += 2*(ev//2); ev %= 2
if od:
answer += 3
print(answer)
``` | instruction | 0 | 21,886 | 16 | 43,772 |
No | output | 1 | 21,886 | 16 | 43,773 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are infinitely many cards, numbered 1, 2, 3, ... Initially, Cards x_1, x_2, ..., x_N are face up, and the others are face down.
Snuke can perform the following operation repeatedly:
* Select a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.
Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7
Input
Input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
Print the minimum number of operations required to achieve the objective.
Examples
Input
2
4 5
Output
2
Input
9
1 2 3 4 5 6 7 8 9
Output
3
Input
2
1 10000000
Output
4
Submitted Solution:
```
import sys
input = sys.stdin.readline
import itertools
from collections import defaultdict
import numpy as np
N = int(input())
X = set(int(x) for x in input().split())
# 2は素数でないとして扱って
U = 10**7 + 100
is_prime = np.zeros(U,dtype=np.bool)
is_prime[3::2] = 1
for p in range(3,U,2):
if p*p > U:
break
if is_prime[p]:
is_prime[p*p::p+p] = 0
# imosで値を入れないといけない場所
X ^= set(x+1 for x in X)
EV = set(x for x in X if x%2 == 0)
OD = set(x for x in X if x%2 == 1)
# 1手でとれるペアを見つける：最大マッチング
# 奇点から偶点に辺を貼る
source = -1
sink = -2
graph = defaultdict(dict)
for x in EV:
graph[x][sink] = 1
graph[sink][x] = 0
for x in OD:
graph[source][x] = 1
graph[x][source] = 0
for x,y in itertools.product(OD,EV):
if is_prime[abs(x-y)]:
graph[x][y] = 1
graph[y][x] = 0
def bfs():
level = defaultdict(int)
q = [source]
level[source] = 1
d = 1
while q:
d += 1
if level[sink] != 0:
break
qq = []
for x in q:
for y,cap in graph[x].items():
if cap==0 or level[y]!=0:
continue
level[y] = d
qq.append(y)
q = qq
return level
def dfs(v,f,level,itr):
if v == sink:
return f
for w,cap in itr[v]:
if cap==0 or level[w]!=level[v]+1:
continue
d = dfs(w,min(f,cap),level,itr)
if d:
graph[v][w] += d
graph[w][v] -= d
return d
return 0
def max_flow():
flow = 0
while True:
level = bfs()
if level[sink] == 0:
return flow
itr = {v:iter(graph[v].items()) for v in graph}
while True:
f = dfs(source,10**9,level,itr)
if f == 0:
break
flow += f
f = max_flow()
od = len(OD); ev = len(EV)
answer = f
od -= f; ev -= f
answer += 2*(od//2); od %= 2
answer += 2*(ev//2); ev %= 2
if od:
answer += 3
print(answer)
``` | instruction | 0 | 21,887 | 16 | 43,774 |
No | output | 1 | 21,887 | 16 | 43,775 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are infinitely many cards, numbered 1, 2, 3, ... Initially, Cards x_1, x_2, ..., x_N are face up, and the others are face down.
Snuke can perform the following operation repeatedly:
* Select a prime p greater than or equal to 3. Then, select p consecutive cards and flip all of them.
Snuke's objective is to have all the cards face down. Find the minimum number of operations required to achieve the objective.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ x_1 < x_2 < ... < x_N ≤ 10^7
Input
Input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
Print the minimum number of operations required to achieve the objective.
Examples
Input
2
4 5
Output
2
Input
9
1 2 3 4 5 6 7 8 9
Output
3
Input
2
1 10000000
Output
4
Submitted Solution:
```
import itertools
from math import sqrt
def chunk(a):
i = 0
res = []
while i < len(a):
res.append(a[i])
while i != len(a) - 1 and a[i + 1] == a[i] + 1:
i += 1
res.append(a[i] + 1)
i += 1
return res
def augment(g, src, dest):
o = [None] * len(g)
q = [(src, src)]
while q:
w = q.pop()
if o[w[0]] is None:
o[w[0]] = w[1]
for s in g[w[0]]:
if o[s] is None:
q.append((s, w[0]))
if not o[dest]:
return False
i = dest
while i != src:
g[o[i]].discard(i)
g[i].add(o[i])
i = o[i]
return True
def match(a):
l = {}
c = 0
matches = 0
for i, j in a:
if i not in l:
l[i] = c
c += 1
if j not in l:
l[j] = c
c += 1
L = {v: k for k, v in l.items()}
g = [set() for i in range(len(l) + 2)]
src = len(l)
dest = src + 1
for i, j in a:
g[src].add(l[i])
g[l[i]].add(l[j])
g[l[j]].add(dest)
while augment(g, src, dest):
matches += 1
return matches
def prime(n):
for i in range(2, min(n, int(sqrt(n) + 7))):
if n % i == 0:
return False
return n > 1
def pairs(b):
c = []
for i in b:
for j in b:
if i % 2 == 0 and j % 2 == 1 and prime(abs(i - j)):
c.append((i, j))
return c
n = int(input())
a = list(map(int, input().split()))
b = chunk(a)
r = match(pairs(b))
e = len(list(filter(lambda x: x % 2 == 0, b)))
o = len(b) - e
print(int(r + 2 * ((e - r) // 2 + (o - r) // 2) + 3 * (e % 2)))
``` | instruction | 0 | 21,888 | 16 | 43,776 |
No | output | 1 | 21,888 | 16 | 43,777 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,889 | 16 | 43,778 |
"Correct Solution:
```
n, m = map(int, input().split())
if 2*n <= m:
print(n+(m-2*n)//4)
else:
print(m//2)
``` | output | 1 | 21,889 | 16 | 43,779 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,890 | 16 | 43,780 |
"Correct Solution:
```
N,M=map(int,input().split())
print((2*min(N,M//2)+M)//4)
``` | output | 1 | 21,890 | 16 | 43,781 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,891 | 16 | 43,782 |
"Correct Solution:
```
N, M = map(int, input().split())
def solve():
ans = min((N*2+M)//4, M//2)
return ans
print(solve())
``` | output | 1 | 21,891 | 16 | 43,783 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,892 | 16 | 43,784 |
"Correct Solution:
```
n, m = map(int, input().split())
c = m - 2*n
if c <= 0:
print(m//2)
else:
print(n + c//4)
``` | output | 1 | 21,892 | 16 | 43,785 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,893 | 16 | 43,786 |
"Correct Solution:
```
n,m = map(int,input().split())
if(2*n >= m):
print(m//2)
else:
m -= 2*n
print(n + (m//4))
``` | output | 1 | 21,893 | 16 | 43,787 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,894 | 16 | 43,788 |
"Correct Solution:
```
n, m = map(int, input().split())
if 2 * n > m:
print(m // 2)
else:
print((m - 2 * n) // 4 + n)
``` | output | 1 | 21,894 | 16 | 43,789 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,895 | 16 | 43,790 |
"Correct Solution:
```
N, M = map(int, input().split())
M = M//2
if N>=M:
print(M)
else:
print((N+M)//2)
``` | output | 1 | 21,895 | 16 | 43,791 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897 | instruction | 0 | 21,896 | 16 | 43,792 |
"Correct Solution:
```
s,c=map(int,input().split())
if s >= c//2 : print(c//2)
else: print(s + (c-2*s)//4)
``` | output | 1 | 21,896 | 16 | 43,793 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
N, M = map(int, input().split())
if N * 2 > M:
print(M // 2)
else:
print(N + (M - 2 * N) // 4)
``` | instruction | 0 | 21,897 | 16 | 43,794 |
Yes | output | 1 | 21,897 | 16 | 43,795 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
S,C=map(int,input().split(' '))
print(min(S,C//2)+(C-min(S,C//2)*2)//4)
``` | instruction | 0 | 21,898 | 16 | 43,796 |
Yes | output | 1 | 21,898 | 16 | 43,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
s,c = map(int,input().split())
ans = 0
t = min(s,c//2)
ans += t
c -= t*2
ans += c//4
print(ans)
``` | instruction | 0 | 21,899 | 16 | 43,798 |
Yes | output | 1 | 21,899 | 16 | 43,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
n,m=map(int,input().split())
if m<=2*n:
print(m//2)
else:
v=m-2*n
print(n+v//4)
``` | instruction | 0 | 21,900 | 16 | 43,800 |
Yes | output | 1 | 21,900 | 16 | 43,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
s,c = map(int,input().split())
if s*2 <= c:
res = s
c -= s*2
s = 0
else:
res += c//2
c = 0
#print(res,s,c)
if c:
res += c//4
print(res)
``` | instruction | 0 | 21,901 | 16 | 43,802 |
No | output | 1 | 21,901 | 16 | 43,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
n, m = map(int, input().split())
m += n * 2
if m <= 3:
print(0)
else:
print(m // 4)
``` | instruction | 0 | 21,902 | 16 | 43,804 |
No | output | 1 | 21,902 | 16 | 43,805 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
#import sys
#import numpy as np
import math
#from fractions import Fraction
import itertools
from collections import deque
from collections import Counter
import heapq
from fractions import gcd
#input=sys.stdin.readline
#import bisect
n,m=map(int,input().split())
if n>=2*m:
print(n)
else:
ans=n+(m-2*n)//4
print(ans)
``` | instruction | 0 | 21,903 | 16 | 43,806 |
No | output | 1 | 21,903 | 16 | 43,807 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves puzzles.
Today, he is working on a puzzle using `S`- and `c`-shaped pieces. In this puzzle, you can combine two `c`-shaped pieces into one `S`-shaped piece, as shown in the figure below:
9b0bd546db9f28b4093d417b8f274124.png
Snuke decided to create as many `Scc` groups as possible by putting together one `S`-shaped piece and two `c`-shaped pieces.
Find the maximum number of `Scc` groups that can be created when Snuke has N `S`-shaped pieces and M `c`-shaped pieces.
Constraints
* 1 ≤ N,M ≤ 10^{12}
Input
The input is given from Standard Input in the following format:
N M
Output
Print the answer.
Examples
Input
1 6
Output
2
Input
12345 678901
Output
175897
Submitted Solution:
```
import sys
from collections import deque, defaultdict
import copy
import bisect
sys.setrecursionlimit(10 ** 9)
import math
import heapq
from itertools import product, permutations,combinations
import fractions
import sys
def input():
return sys.stdin.readline().strip()
N = int(input())
a = list(map(int, input().split()))
top_list = [0]
for i in range(1, N):
if a[i] > a[top_list[-1]]:
top_list.append(i)
num_list = [0]*N
com = []
for i in range(len(top_list)):
bisect.insort(com, a[top_list[i]])
for i in range(N - 1, top_list[-1], -1):
bisect.insort(com, a[i])
stock = 0
#print(com, top_list, num_list)
for top in range(len(top_list) - 2, -1, -1):
for i in range(top_list[top + 1] - 1, top_list[top], -1):
#bisect.insort(com, a[i])
com.append(a[i])
com.sort()
judge = 0
total = stock*(a[top_list[top + 1]] - a[top_list[top]])
#print(total, (a[top_list[top + 1]] - a[top_list[top]])*stock, top)
while judge == 0:
x = com.pop()
if x > a[top_list[top]]:
total += x - a[top_list[top]]
stock += 1
else:
bisect.insort(com, x)
judge = 1
num_list[top_list[top + 1]] = total
#print(com, top_list, num_list, stock)
num_list[top_list[0]] = sum(a) - sum(num_list)
for i in range(N):
print(num_list[i])
``` | instruction | 0 | 21,904 | 16 | 43,808 |
No | output | 1 | 21,904 | 16 | 43,809 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves "paper cutting": he cuts out characters from a newspaper headline and rearranges them to form another string.
He will receive a headline which contains one of the strings S_1,...,S_n tomorrow. He is excited and already thinking of what string he will create. Since he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.
Find the longest string that can be created regardless of which string among S_1,...,S_n the headline contains. If there are multiple such strings, find the lexicographically smallest one among them.
Constraints
* 1 \leq n \leq 50
* 1 \leq |S_i| \leq 50 for every i = 1, ..., n.
* S_i consists of lowercase English letters (`a` - `z`) for every i = 1, ..., n.
Input
Input is given from Standard Input in the following format:
n
S_1
...
S_n
Output
Print the lexicographically smallest string among the longest strings that satisfy the condition. If the answer is an empty string, print an empty line.
Examples
Input
3
cbaa
daacc
acacac
Output
aac
Input
3
a
aa
b
Output
Submitted Solution:
```
n=int(input())
S=[input() for i in range(n)]
s=list(map(chr,range(97,123)))
ans=""
for i in s:
tmp=99
for j in S:
tmp=min(tmp,j.count(i))
ans+=i*tmp
print(ans)
``` | instruction | 0 | 22,727 | 16 | 45,454 |
Yes | output | 1 | 22,727 | 16 | 45,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves "paper cutting": he cuts out characters from a newspaper headline and rearranges them to form another string.
He will receive a headline which contains one of the strings S_1,...,S_n tomorrow. He is excited and already thinking of what string he will create. Since he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.
Find the longest string that can be created regardless of which string among S_1,...,S_n the headline contains. If there are multiple such strings, find the lexicographically smallest one among them.
Constraints
* 1 \leq n \leq 50
* 1 \leq |S_i| \leq 50 for every i = 1, ..., n.
* S_i consists of lowercase English letters (`a` - `z`) for every i = 1, ..., n.
Input
Input is given from Standard Input in the following format:
n
S_1
...
S_n
Output
Print the lexicographically smallest string among the longest strings that satisfy the condition. If the answer is an empty string, print an empty line.
Examples
Input
3
cbaa
daacc
acacac
Output
aac
Input
3
a
aa
b
Output
Submitted Solution:
```
from collections import Counter
d = int(input())
l = []
for k in range(d):
r = input()
l.append(Counter(r))
oi = l[0]
for g in range(1,d):
oi = oi & l[g]
print("".join(sorted(oi.elements())))
``` | instruction | 0 | 22,729 | 16 | 45,458 |
Yes | output | 1 | 22,729 | 16 | 45,459 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves "paper cutting": he cuts out characters from a newspaper headline and rearranges them to form another string.
He will receive a headline which contains one of the strings S_1,...,S_n tomorrow. He is excited and already thinking of what string he will create. Since he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.
Find the longest string that can be created regardless of which string among S_1,...,S_n the headline contains. If there are multiple such strings, find the lexicographically smallest one among them.
Constraints
* 1 \leq n \leq 50
* 1 \leq |S_i| \leq 50 for every i = 1, ..., n.
* S_i consists of lowercase English letters (`a` - `z`) for every i = 1, ..., n.
Input
Input is given from Standard Input in the following format:
n
S_1
...
S_n
Output
Print the lexicographically smallest string among the longest strings that satisfy the condition. If the answer is an empty string, print an empty line.
Examples
Input
3
cbaa
daacc
acacac
Output
aac
Input
3
a
aa
b
Output
Submitted Solution:
```
from collections import Counter
n = int(input())
data = [k for k in input()]
ans = Counter(data)
for i in range(n-1):
tmp = Counter([k for k in input()])
for j in set(data):
ans[j] = min(ans[j], tmp[j])
# print(j, ans[j], tmp[j], min(ans[j], tmp[j]))
ans_list = list(ans.elements())
ans_list.sort()
answer = ""
for i in set(ans_list):
answer += i*ans[i]
print(answer)
``` | instruction | 0 | 22,731 | 16 | 45,462 |
No | output | 1 | 22,731 | 16 | 45,463 |
Provide a correct Python 3 solution for this coding contest problem.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722 | instruction | 0 | 22,735 | 16 | 45,470 |
"Correct Solution:
```
n,K=map(int,input().split())
lists=list(map(int,input().split()))
mod=10**9+7
dp=[[["inf" for i in range(256)] for j in range(n+1)] for k in range(n+1)]
#dp[i][j][k]=カードのi番目までからjこまでを取ってxorの値をkにする方法
#dp[i][j]=="inf" (i<jの時)
for i in range(n+1):
dp[i][0][0]=1
for i in range(1,n+1):
num=lists[i-1]
for j in range(1,i+1):
for k in range(256):
if dp[i-1][j-1][k^num]!="inf" or dp[i-1][j][k]!="inf":
s=0
if dp[i-1][j][k]!="inf":
s+=dp[i-1][j][k]
if dp[i-1][j-1][k^num]!="inf":
s+=dp[i-1][j-1][k^num]
dp[i][j][k]=s%mod
else:
pass
ans=0
def find_power(n,mod):
# 0!からn!までのびっくりを出してくれる関数(ただし、modで割った値に対してである）
powlist=[0]*(n+1)
powlist[0]=1
powlist[1]=1
for i in range(2,n+1):
powlist[i]=powlist[i-1]*i%(mod)
return powlist
A=find_power(100,mod)
for i in range(n+1):
if dp[n][i][K]!="inf":
ans+=dp[n][i][K]*A[i]
ans=ans%mod
print(ans)
``` | output | 1 | 22,735 | 16 | 45,471 |
Provide a correct Python 3 solution for this coding contest problem.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722 | instruction | 0 | 22,736 | 16 | 45,472 |
"Correct Solution:
```
n,m = (int(i) for i in input().split())
a = [int(i) for i in input().split()]
dp = [[[0]*(n+1) for i in range(256)] for i in range(n+1)]
dp[1][a[0]][1],x,mod,ans = 1,[0,1],10**9+7,0
for i in range(n+1): dp[i][0][0] = 1
for i in range(2,n+1):
for j in range(256):
for k in range(1,i+1): dp[i][j][k] = dp[i-1][j^a[i-1]][k-1]+dp[i-1][j][k]
for i in range(2,257): x.append((x[-1]*i)%mod)
for i in range(n+1): ans = (ans+dp[-1][m][i]*x[i])%mod
print(ans)
``` | output | 1 | 22,736 | 16 | 45,473 |
Provide a correct Python 3 solution for this coding contest problem.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722 | instruction | 0 | 22,737 | 16 | 45,474 |
"Correct Solution:
```
N,K = map(int,input().split())
src = list(map(int,input().split()))
MOD = 10**9+7
dp = [[0 for k in range(256)] for i in range(N+1)]
dp[0][0] = 1
for i,a in enumerate(src):
for j in range(i,-1,-1):
for k in range(256):
if dp[j][k] == 0: continue
dp[j+1][k^a] += dp[j][k]
ans = 0
fact = 1
for i in range(1,N+1):
ans += (dp[i][K] * fact) % MOD
fact = (fact * (i+1)) % MOD
print(ans % MOD)
``` | output | 1 | 22,737 | 16 | 45,475 |
Provide a correct Python 3 solution for this coding contest problem.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722 | instruction | 0 | 22,738 | 16 | 45,476 |
"Correct Solution:
```
n,m = map(int, input().split())
mod = 10**9 + 7
a = list(map(int, input().split()))
dp = [[[0]*256 for _ in range(n+1)]for i in range(n+1)]
dp[0][0][0] = 1
for i in range(n):
x = a[i]
dp[i+1][0] = dp[i][0][:]
for j in range(n):
for k in range(256):
dp[i+1][j+1][k] = (dp[i][j+1][k] + dp[i][j][k^x])%mod
f = 1
ans = 0
for j in range(1,n+1):
f = f*j%mod
ans += dp[n][j][m]*f
ans %= mod
print(ans)
``` | output | 1 | 22,738 | 16 | 45,477 |
Provide a correct Python 3 solution for this coding contest problem.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722 | instruction | 0 | 22,739 | 16 | 45,478 |
"Correct Solution:
```
mod=10**9+7
n,x=map(int,input().split())
a=list(map(int,input().split()))
dp=[[[0]*256 for j in range(n+1)] for k in range(2)]
dp[0][0][0]=1
for i in range(n):
for j in range(n+1):
for k in range(256):
dp[(i+1)&1][j][k]=dp[i&1][j][k]
for j in range(n):
for k in range(256):
dp[(i+1)&1][j+1][k^a[i]]+=dp[i&1][j][k]
if mod<=dp[(i+1)&1][j][k^a[i]]:
dp[(i+1)&1][j][k^a[i]]-=mod
ans=0
fac=[1]*(n+1)
for i in range(1,n+1):
fac[i]=fac[i-1]*i
if mod<=fac[i]:
fac[i]-=mod
for j in range(n+1):
ans+=dp[n&1][j][x]*fac[j]
ans%=mod
print(ans)
``` | output | 1 | 22,739 | 16 | 45,479 |
Provide a correct Python 3 solution for this coding contest problem.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722 | instruction | 0 | 22,740 | 16 | 45,480 |
"Correct Solution:
```
n, k = map(int, input().split())
*A, = map(int, input().split())
MOD = 10**9 + 7
C = {a for a in A}
n = len(C)
m = [[0]*256 for i in range(n+1)]
m[0][0] = 1
for c in C:
for i in range(n-1, -1, -1):
s = m[i]; t = m[i+1]
for j in range(256):
t[c^j] += s[j]
ans = 0
r = 1
for i in range(1, n+1):
r = (r * i) % MOD
ans += r * m[i][k]
ans %= MOD
print(ans)
``` | output | 1 | 22,740 | 16 | 45,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722
Submitted Solution:
```
n, k = map(int, input().split())
*A, = map(int, input().split())
MOD = 10**9 + 7
C = {a for a in A}
n = len(C)
m = [[0]*256 for i in range(n+1)]
m[0][0] = 1
for c in C:
for i in range(n-1, -1, -1):
for j in range(256):
m[i+1][c^j] += m[i][j]
m[i+1][c^j] %= MOD
ans = 0
r = 1
for i in range(1, n+1):
r = (r * i) % MOD
ans += r * m[i][k]
ans %= MOD
print(ans)
``` | instruction | 0 | 22,741 | 16 | 45,482 |
No | output | 1 | 22,741 | 16 | 45,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722
Submitted Solution:
```
n,m = map(int, input().split())
mod = 10**9 + 7
a = list(map(int, input().split()))
dp = [[[0]*256 for _ in range(n+1)]for i in range(n+1)]
dp[0][0][0] = 1
for i in range(n):
x = a[i]
dp[i+1][0] = dp[i][0][:]
for j in range(n):
for k in range(256):
dp[i+1][j+1][k] = (dp[i][j+1][k] + dp[i][j][k^x])%mod
f = 1
ans = 0
for j in range(1,n+1):
f = f*j%mod
ans += dp[n][j][m]*f
ans %= mod
print(ans)
``` | instruction | 0 | 22,742 | 16 | 45,484 |
No | output | 1 | 22,742 | 16 | 45,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722
Submitted Solution:
```
#!/usr/bin/env pypy3
import functools
import itertools
import math
import operator
P = 1000000007
def xors(seq):
return functools.reduce(operator.xor, seq)
def solve(n, k, xs):
l = len(xs)
a = 0
for i in range(1, l + 1):
for ys in itertools.combinations(xs, i):
if xors(ys) == k:
a += math.factorial(i)
a %= P
return a
def main():
n, k = map(int, input().split())
assert n <= 20
xs = [int(x) for x in input().split()]
print(solve(n, k, xs))
if __name__ == '__main__':
main()
``` | instruction | 0 | 22,743 | 16 | 45,486 |
No | output | 1 | 22,743 | 16 | 45,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)
Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.
He made a sequence $b$, but actually, he is not remembered it.
However, he is remembered a few things about sequence $b$.
* All elements in $b$ are distinct.
* All elements in $b$ is in $a$.
* $b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]
For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.
He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it. Please calculate the ways to make $b$ and help him.
Since the answer can be large, print the answer modulo $1,000,000,007$.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Output
* Print the number of ways to make sequence $b$.
* Print the answer modulo $1,000,000,007$.
Constraints
* $1 \le n \le 100$
* $1 \le a_i, k \le 255$
* $i \neq j \Rightarrow a_i \neq a_j$
Subtasks
Subtask 1 [ $50$ points ]
* $1 \le n \le 4$
Subtask 2 [ $170$ points ]
* $1 \le n \le 20$
Subtask 3 [ $180$ points ]
* There are no additional constraints.
Input
The input is given from Standard Input in the following format:
> $n \ k$ $a_1 \ a_2 \ \cdots \ a_n$
Examples
Input
3 1
1 2 3
Output
3
Input
3 10
8 7 5
Output
6
Input
25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125
Output
235924722
Submitted Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
"""
・項数、和 -> 通り数 を持ってdp
"""
import numpy as np
N,K,*A = map(int,read().split())
MOD = 10**9 + 7
dp = np.zeros((N+1,256),np.int64)
dp[0,0] = 1
for x in A:
dp[1:,np.arange(256)^x] += dp[:-1]
fact = np.ones(N+1,np.int64)
for n in range(1,N+1):
fact[n] = fact[n-1] * n % MOD
answer = (fact * dp[:,K] % MOD).sum() % MOD
print(answer)
``` | instruction | 0 | 22,744 | 16 | 45,488 |
No | output | 1 | 22,744 | 16 | 45,489 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,667 | 16 | 47,334 |
"Correct Solution:
```
mod = 10**9 + 7
n = int(input())
s1 = input(); s2 = input()
s = ""
i = 0
while i < n:
if s1[i] == s2[i]:
s += "A"
i += 1
else:
s += "B"
i += 2
answer = 3 if s[0] == "A" else 6
for i in range(len(s) - 1):
if s[i] + s[i + 1] == "AA":
answer *= 2
elif s[i] + s[i + 1] == "AB":
answer *= 2
elif s[i] + s[i + 1] == "BA":
answer *= 1
else:
answer *= 3
answer %= mod
print(answer)
``` | output | 1 | 23,667 | 16 | 47,335 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,668 | 16 | 47,336 |
"Correct Solution:
```
# 横か縦か。各時点でn-2 or n-1C2
# str1だけ見ればよい
N = int(input())
txt = input()
pattern = []
j = 0
while j < N:
if j == N-1 or txt[j] != txt[j+1]:
pattern.append(1)
j += 1
else:
pattern.append(2)
j += 2
MOD = 10**9 + 7
ans = 3 if pattern[0] == 1 else 6
for j in range(1,len(pattern)):
a,b = pattern[j-1:j+1]
if (a,b) == (1,1):
ans *= 2
elif (a,b) == (1,2):
ans *= 2
elif (a,b) == (2,1):
ans *= 1
else:
ans *= 3
ans %= MOD
print(ans)
``` | output | 1 | 23,668 | 16 | 47,337 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,669 | 16 | 47,338 |
"Correct Solution:
```
MOD = 10**9 + 7
N = input()
S1 = list(input())
S2 = list(input())
res = 1
right_used_color = 0
while len(S1) > 0:
if S1[len(S1)-1] == S2[len(S1)-1]:
res = res * (3 - right_used_color) % MOD
right_used_color = 1
elif right_used_color == 2:
res = res * 3 % MOD
S1.pop()
S2.pop()
else:
res = res * (3 - right_used_color) * (2 - right_used_color) % MOD
right_used_color = 2
S1.pop()
S2.pop()
S1.pop()
S2.pop()
print(res)
``` | output | 1 | 23,669 | 16 | 47,339 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,670 | 16 | 47,340 |
"Correct Solution:
```
mod=1000000007
n=int(input())
a=input()
d=[0]
for i in range(1,n):
if a[i-1]==a[i]:
d[-1]+=1
else:
d.append(0)
ans=[3,6][d[0]]
for i in range(1,len(d)):
if d[i-1]==d[i]==1:
t=3
elif d[i-1]==1 and d[i]==0:
t=1
else:
t=2
ans=(ans*t)%mod
print(ans)
``` | output | 1 | 23,670 | 16 | 47,341 |
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