message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 276 109k | cluster float64 23 23 | __index_level_0__ int64 552 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a rectangle grid. That grid's size is n × m. Let's denote the coordinate system on the grid. So, each point on the grid will have coordinates — a pair of integers (x, y) (0 ≤ x ≤ n, 0 ≤ y ≤ m).
Your task is to find a maximum sub-rectangle on the grid (x1, y1, x2, y2) so that it contains the given point (x, y), and its length-width ratio is exactly (a, b). In other words the following conditions must hold: 0 ≤ x1 ≤ x ≤ x2 ≤ n, 0 ≤ y1 ≤ y ≤ y2 ≤ m, <image>.
The sides of this sub-rectangle should be parallel to the axes. And values x1, y1, x2, y2 should be integers.
<image>
If there are multiple solutions, find the rectangle which is closest to (x, y). Here "closest" means the Euclid distance between (x, y) and the center of the rectangle is as small as possible. If there are still multiple solutions, find the lexicographically minimum one. Here "lexicographically minimum" means that we should consider the sub-rectangle as sequence of integers (x1, y1, x2, y2), so we can choose the lexicographically minimum one.
Input
The first line contains six integers n, m, x, y, a, b (1 ≤ n, m ≤ 109, 0 ≤ x ≤ n, 0 ≤ y ≤ m, 1 ≤ a ≤ n, 1 ≤ b ≤ m).
Output
Print four integers x1, y1, x2, y2, which represent the founded sub-rectangle whose left-bottom point is (x1, y1) and right-up point is (x2, y2).
Examples
Input
9 9 5 5 2 1
Output
1 3 9 7
Input
100 100 52 50 46 56
Output
17 8 86 92
Submitted Solution:
```
import math
n, m, x, y, a, b = map(int, input().split())
gcd = math.gcd(a, b)
a //= gcd
b //= gcd
max_ratio = min(n // a, m // b)
#if (a * max_ratio) % 2 == 1 or (b * max_ratio) % 2 == 1:
# max_ratio -= 1
a *= max_ratio
b *= max_ratio
print(x - a // 2, y - b // 2, x + a // 2, y + b // 2)
``` | instruction | 0 | 76,172 | 23 | 152,344 |
No | output | 1 | 76,172 | 23 | 152,345 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix consisting of digits zero and one, its size is n × m. You are allowed to rearrange its rows. What is the maximum area of the submatrix that only consists of ones and can be obtained in the given problem by the described operations?
Let's assume that the rows of matrix a are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. A matrix cell on the intersection of the i-th row and the j-th column can be represented as (i, j). Formally, a submatrix of matrix a is a group of four integers d, u, l, r (1 ≤ d ≤ u ≤ n; 1 ≤ l ≤ r ≤ m). We will assume that the submatrix contains cells (i, j) (d ≤ i ≤ u; l ≤ j ≤ r). The area of the submatrix is the number of cells it contains.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 5000). Next n lines contain m characters each — matrix a. Matrix a only contains characters: "0" and "1". Note that the elements of the matrix follow without any spaces in the lines.
Output
Print a single integer — the area of the maximum obtained submatrix. If we cannot obtain a matrix of numbers one, print 0.
Examples
Input
1 1
1
Output
1
Input
2 2
10
11
Output
2
Input
4 3
100
011
000
101
Output
2
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Tue Aug 4 08:19:35 2020
@author: Dell
"""
from collections import Counter,defaultdict
n,m=list(map(int,input().split()))
d=defaultdict(list)
for i in range(n):
s=input()
k=0
t=0
for j in range(m-1,-1,-1):
if s[j]=='1' and t==1:
k+=1
d[j].append(k)
elif s[j]=='1' and t==0:
k=1
t=1
d[j].append(k)
elif s[j]=='0' and t==1:
k=0
t=0
#print(k,d)
ma=0
for i in d:
p=Counter(d[i])
for j in p:
ma=max(ma,j*p[j])
print(ma)
``` | instruction | 0 | 76,202 | 23 | 152,404 |
No | output | 1 | 76,202 | 23 | 152,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix consisting of digits zero and one, its size is n × m. You are allowed to rearrange its rows. What is the maximum area of the submatrix that only consists of ones and can be obtained in the given problem by the described operations?
Let's assume that the rows of matrix a are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. A matrix cell on the intersection of the i-th row and the j-th column can be represented as (i, j). Formally, a submatrix of matrix a is a group of four integers d, u, l, r (1 ≤ d ≤ u ≤ n; 1 ≤ l ≤ r ≤ m). We will assume that the submatrix contains cells (i, j) (d ≤ i ≤ u; l ≤ j ≤ r). The area of the submatrix is the number of cells it contains.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 5000). Next n lines contain m characters each — matrix a. Matrix a only contains characters: "0" and "1". Note that the elements of the matrix follow without any spaces in the lines.
Output
Print a single integer — the area of the maximum obtained submatrix. If we cannot obtain a matrix of numbers one, print 0.
Examples
Input
1 1
1
Output
1
Input
2 2
10
11
Output
2
Input
4 3
100
011
000
101
Output
2
Submitted Solution:
```
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 1/15/20
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def solve(N, M, A):
# t0 = time.time()
# for each index i of each row, we count how many consecutive '1' right at i,
# this is the max width if we include this row into the target submatrix which start from col i
ones = [[0 for _ in range(M)] for _ in range(N)]
for ri in range(N):
count = 0
for ci in range(M-1, -1, -1):
if A[ri][ci] == 0:
count = 0
else:
count += 1
ones[ri][ci] = count
# print(time.time() - t0)
# t0 = time.time()
ans = 0
# we fix the left index of the sub-matrix, and scrub it to right
for left in range(M):
# find out all rows that have '1' after the start index
# and sort it in O(N)
# height = [0 for _ in range(M-left+1)]
# for row in ones:
# height[row[left]] += 1
wc = collections.Counter([row[left] for row in A])
wc = [(w, c) for w, c in wc.items()]
wc.sort(reverse=True)
h = 0
for w, c in wc:
h += c
ans = max(ans, w * h)
# h = 0
# for w in range(M-left, 0, -1):
# if w * N < ans:
# break
# h += height[w]
# ans = max(ans, w * h)
# print(time.time() - t0)
print(ans)
def test():
import random
N, M = 5000, 5000
A = []
for i in range(N):
row = [1 if random.randint(1, 10) > 4 else 0 for _ in range(M)]
A.append(row)
print('starting')
solve(N, M, A)
# test()
N, M = map(int, input().split())
A = []
for i in range(N):
row = [int(x) for x in list(input())]
A.append(row)
solve(N, M, A)
``` | instruction | 0 | 76,203 | 23 | 152,406 |
No | output | 1 | 76,203 | 23 | 152,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix consisting of digits zero and one, its size is n × m. You are allowed to rearrange its rows. What is the maximum area of the submatrix that only consists of ones and can be obtained in the given problem by the described operations?
Let's assume that the rows of matrix a are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. A matrix cell on the intersection of the i-th row and the j-th column can be represented as (i, j). Formally, a submatrix of matrix a is a group of four integers d, u, l, r (1 ≤ d ≤ u ≤ n; 1 ≤ l ≤ r ≤ m). We will assume that the submatrix contains cells (i, j) (d ≤ i ≤ u; l ≤ j ≤ r). The area of the submatrix is the number of cells it contains.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 5000). Next n lines contain m characters each — matrix a. Matrix a only contains characters: "0" and "1". Note that the elements of the matrix follow without any spaces in the lines.
Output
Print a single integer — the area of the maximum obtained submatrix. If we cannot obtain a matrix of numbers one, print 0.
Examples
Input
1 1
1
Output
1
Input
2 2
10
11
Output
2
Input
4 3
100
011
000
101
Output
2
Submitted Solution:
```
'''
Created on Dec 7, 2013
@author: Ismael
'''
def solve():
matCum = [[0 for _ in range(M)] for _ in range(N)]
matCum[0][0] = mat[0][0]
for i in range(1,N):
if(mat[i][0] == 1):
matCum[i][0] = matCum[i-1][0]+1
for j in range(1,M):
if(mat[0][j] == 1):
matCum[0][j] = matCum[0][j-1]+1
for i in range(1,N):
for j in range(1,M):
a = matCum[i][j-1]
b = matCum[i-1][j]
c = matCum[i-1][j-1]
if(mat[i][j] == 1):
matCum[i][j] = a+b+1
if(a > 0 or b > 0):
matCum[i][j] -= c
#print(matCum)
maxArea = 0
for i in range(N):
for j in range(M):
if(matCum[i][j]>maxArea):
maxArea = matCum[i][j]
return maxArea
def main():
global N, M, mat
#global dictRes
#dictRes = dict()
N,M = map(int,input().split())
mat = [[0 for _ in range(M)] for _ in range(N)]
for i in range(N):
line = input()
for j in range(M):
mat[i][j] = int(line[j])
#print(mat)
print(solve())
main()
``` | instruction | 0 | 76,204 | 23 | 152,408 |
No | output | 1 | 76,204 | 23 | 152,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix consisting of digits zero and one, its size is n × m. You are allowed to rearrange its rows. What is the maximum area of the submatrix that only consists of ones and can be obtained in the given problem by the described operations?
Let's assume that the rows of matrix a are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. A matrix cell on the intersection of the i-th row and the j-th column can be represented as (i, j). Formally, a submatrix of matrix a is a group of four integers d, u, l, r (1 ≤ d ≤ u ≤ n; 1 ≤ l ≤ r ≤ m). We will assume that the submatrix contains cells (i, j) (d ≤ i ≤ u; l ≤ j ≤ r). The area of the submatrix is the number of cells it contains.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 5000). Next n lines contain m characters each — matrix a. Matrix a only contains characters: "0" and "1". Note that the elements of the matrix follow without any spaces in the lines.
Output
Print a single integer — the area of the maximum obtained submatrix. If we cannot obtain a matrix of numbers one, print 0.
Examples
Input
1 1
1
Output
1
Input
2 2
10
11
Output
2
Input
4 3
100
011
000
101
Output
2
Submitted Solution:
```
import sys
try:
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
except:
pass
input = sys.stdin.readline
n, m = map(int, input().split())
a = []
dp = [[0]*m for _ in range(n)]
for i in range(n):
a.append(list(input().strip()))
dp[i][0] = int(a[i][0])
for j in range(1, m):
if a[i][j] == "1":
dp[i][j] += dp[i][j-1]
ans = 0
for j in range(m):
temp = []
for i in range(n):
temp.append(dp[i][j])
temp.sort()
for i in range(n):
ans = max(ans, (n-i)*temp[i])
print(ans)
``` | instruction | 0 | 76,205 | 23 | 152,410 |
No | output | 1 | 76,205 | 23 | 152,411 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,521 | 23 | 153,042 |
"Correct Solution:
```
n,m=map(int,input().split())
a=[int(input().replace(" ",""),2) for i in range(n)]
o=998244353
c=0
for j in range(m)[::-1]:
for i in range(c,n):
if a[i]&1<<j:
for k in range(n):
if i!=k and a[k]&1<<j:
a[k]^=a[i]
a[i],a[c]=a[c],a[i]
c+=1
p=lambda x:pow(2,x,o)
print(p(n+m-c-1)*(p(c)-1)%o)
``` | output | 1 | 76,521 | 23 | 153,043 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,522 | 23 | 153,044 |
"Correct Solution:
```
N,M=map(int,input().split());B=[]
for i in[0]*N:
s=int(input().replace(" ",""),2)
for b in B:s=min(s,s^b)
B+=[s]*(s!=0)
N+=M-1;print((2**N-2**(N-len(B)))%998244353)
``` | output | 1 | 76,522 | 23 | 153,045 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,523 | 23 | 153,046 |
"Correct Solution:
```
N,M=map(int,input().split())
A=[[int(i) for i in input().split()] for i in range(N)]
r=0
mod=998244353
for j in range(M):
flag=False
for i in range(r,N):
if not flag:
if A[i][j]:
flag=True
A[i],A[r]=A[r],A[i]
r+=1
else:
if A[i][j]:
for k in range(M):
A[i][k]^=A[r-1][k]
Factorial=[1]*(r+1)
for i in range(1,r+1):
Factorial[i]=Factorial[i-1]*(i)%mod
def power(x,y):
if y==0:
return 1
elif y==1:
return x%mod
elif y%2==0:
return power(x,y//2)**2%mod
else:
return (power(x,y//2)**2)*x%mod
inverseFactorial=[1]*(r+1)
inverseFactorial[r]=power(Factorial[r],mod-2)
for i in range(0,r)[::-1]:
inverseFactorial[i]=(inverseFactorial[i+1]*(i+1))%mod
def comb(x,y):
if x<y or y<0:
return 0
else:
return (Factorial[x]*inverseFactorial[y]*inverseFactorial[x-y])%mod
ans=0
a=1
while a<=r:
ans=(ans+comb(r,a)*power(3,r-a)*power(4,min(N,M)-r)*power(2,max(N,M)-min(N,M)))%mod
a+=2
print(ans)
``` | output | 1 | 76,523 | 23 | 153,047 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,524 | 23 | 153,048 |
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return list(sys.stdin.readline())
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
mod = 1000000007
#A
"""
n,k = LI()
if 2*(k-1) < n:
print("YES")
else:
print("NO")
"""
#B
"""
c = LIR(3)
v = [[] for i in range(4)]
for i in range(3):
c[i][0] -= 1
c[i][1] -= 1
v[c[i][0]].append(c[i][1])
v[c[i][1]].append(c[i][0])
for i in range(4):
li = [True for i in range(4)]
li[i] = False
q = [i]
c = 0
while q:
x = q.pop(-1)
k = 0
for j in v[x]:
if li[j]:
li[j] = False
q.append(j)
if k == 0:
c += 1
k += 1
if c == 3:
print("YES")
quit()
print("NO")
"""
#C
"""
k,a,b = LI()
if k <= a:
print(k+1)
else:
if b-a < 3:
print(k+1)
else:
ans = a+((k-a+1)//2)*(b-a)+(k-a+1)%2
print(ans)
"""
#D
#E
n,m = LI()
a = LIR(n)
a.sort()
a = a[::-1]
for i in range(n):
for j in range(i+1,n):
s = 0
while a[i][s] == 0 and s < m-1:s+=1
if s < m and a[i][s] != 0:
if a[j][s] > 0:
for k in range(s,m):
a[j][k] -= 1*a[i][k]
a[j][k] = abs(a[j][k])
r = 0
for i in range(n):
if sum(a[i]) > 0:r += 1
print((pow(2,n+m-1)-pow(2,n-r+m-1))%998244353)
#F
#G
#H
#I
#J
#K
#L
#M
#N
#O
#P
#Q
#R
#S
#T
``` | output | 1 | 76,524 | 23 | 153,049 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,525 | 23 | 153,050 |
"Correct Solution:
```
def rankmod2(A):
n,m=len(A),len(A[0])
rank=0
i,j=0,0
while i<n and j<m:
if A[i][j]:
rank+=1
else:
for ii in range(i+1,n):
if A[ii][j]:
A[i],A[ii]=A[ii],A[i]
rank+=1
break
else:
j+=1
continue
for ii in range(i+1,n):
if A[ii][j]:
for jj in range(j,m):
A[ii][jj]=(A[ii][jj]+A[i][jj])% 2
i+=1
j+=1
return rank
n,m=map(int,input().split())
mod=998244353
A=[list(map(int,input().split())) for _ in range(n)]
r=rankmod2(A)
ans=(pow(2,n+m-1,mod)-pow(2,n+m-r-1,mod))%mod
print(ans)
``` | output | 1 | 76,525 | 23 | 153,051 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,526 | 23 | 153,052 |
"Correct Solution:
```
I=input;N,M=map(int,I().split());B=[]
for i in range(N):
s=int(I().replace(" ",""),2)
for b in B:s=min(s,s^b)
if s!=0:B.append(s)
N+=M-1;print((2**N-2**(N-len(B)))%998244353)
``` | output | 1 | 76,526 | 23 | 153,053 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,527 | 23 | 153,054 |
"Correct Solution:
```
# from : https://atcoder.jp/contests/yahoo-procon2019-qual/submissions/4212377
H,W = map(int, input().split())
A = [ [int(j) for j in input().split()] for _ in range(H)]
MOD = 998244353
piv = 0
# Gaussian Elimination to calculate rank of the matrix A
for w in range(W): # fix column,
r = -1
for h in range(piv, H):
if A[h][w] == 1:
r = h
break
if r == -1: # there is no odd cell for all the rows inside intersections.
continue
# You want to set ODD ROW ( A[h][w] == 1 ) into pivot row.
if r != piv: # already, skip.
for j in range(W): # swap rows
A[r][j], A[piv][j] = A[piv][j], A[r][j]
# for h in
for h in range(H):
if h != piv and A[h][w] == 1: # really needed?
# for j in range(W):
for k in range(piv, W):
A[h][k] ^= A[piv][k]
# A[h][j] ^= A[piv][j] # for other rows, erase ...
# Hakidashi method: http://senkei.nomaki.jp/gaussian_elimination.html
# https://ja.wikipedia.org/wiki/%E3%82%AC%E3%82%A6%E3%82%B9%E3%81%AE%E6%B6%88%E5%8E%BB%E6%B3%95 : Gaussian Elimination
piv += 1
# print("----output matrix ----")
# for h in range(H):
# print(A[h])
# exit(0)
# from pprint import pprint; pprint(A)
ret = 1
ret = pow(2, H, MOD)
# for h in range(H):
# ret = ret * 2 % MOD
sub = 1
# for i in range(H-piv):
# sub = sub * 2 % MOD
sub = pow(2, H-piv, MOD)
ret += MOD - sub # ret = 2^N - 2^(N-r)
ret %= MOD
for i in range(W-1): # ret *= 2^(M-1)
ret = ret * 2 % MOD
# from editorial : https://img.atcoder.jp/yahoo-procon2019-qual/editorial.pdf
# rank : r
# 2^(N+M-1) - 2^(N+M-r-1)
print(ret % MOD)
``` | output | 1 | 76,527 | 23 | 153,055 |
Provide a correct Python 3 solution for this coding contest problem.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8 | instruction | 0 | 76,528 | 23 | 153,056 |
"Correct Solution:
```
N,M=map(int,input().split());mod=998244353;base=[]
for i in range(N):
A=input().split();s=sum(int(A[j])*2**j for j in range(M))
for b in base:s=min(s,s^b)
if s!=0:base.append(s)
res=N-len(base);print((pow(2,N+M-1,mod)-pow(2,M-1+res,mod))%mod)
``` | output | 1 | 76,528 | 23 | 153,057 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
n,m=map(int,input().split())
a=[int(input().replace(" ",""),2) for i in range(n)]
o=998244353
c=0
for j in range(m)[::-1]:
for i in range(c,n):
if a[i]&1<<j:
for k in range(n):
if i!=k and a[k]&1<<j:a[k]^=a[i]
a[i],a[c]=a[c],a[i];c+=1
p=lambda x:pow(2,x,o)
print(p(n+m-c-1)*(p(c)-1)%o)
``` | instruction | 0 | 76,529 | 23 | 153,058 |
Yes | output | 1 | 76,529 | 23 | 153,059 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
import sys
# この２行は
# a 1 0 1 0
# b 1 1 0 0
# こうしても、作れる集合の内訳が変わらない
# a 1 0 1 0
# b^a 0 1 1 0
# {両方未選択, 上だけ選択, 下だけ選択, 両方選択}: {φ, a, b, a^b} == {φ, a, b^a, b}
# これは列方向に対しても同じことなので、掃き出し法チックなことをして
# 1 0 ... 0 0 0
# 0 1 ... 0 0 0
# : : : : :
# 0 0 ... 1 0 0
# 0 0 ... 0 0 0
# こんな形にできる
# ここで、行の選び方で'1'のある行を1つでも含むような選び方は、
# その'1'の場所の列(どれでもいいので1つ)を選択するかしないかで、
# 全体の和が偶数, 奇数となるパターンがちょうど半分ずつとなる。
# よって、以下が答え
# (行の全体の選び方 - '1'のある行を１つも含めない選び方) * 列の全体の選び方 / 2
n, m = map(int, input().split())
MOD = 998244353
rows = []
for line in sys.stdin:
b = ''.join(line.rstrip().split())
rows.append(int(b, base=2))
independent_row = 0
while rows:
x = max(rows)
if x == 0:
break
independent_row += 1
y = 1 << (x.bit_length() - 1)
rows = [r ^ x if r & y else r for r in rows if r != x]
ans = (pow(2, n + m - 1, MOD) - pow(2, n + m - independent_row - 1, MOD)) % MOD
print(ans)
``` | instruction | 0 | 76,530 | 23 | 153,060 |
Yes | output | 1 | 76,530 | 23 | 153,061 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
N,M=map(int,input().split());mod=998244353;B=[]
for i in range(N):
s=int(input().replace(" ",""),2)
for b in B:s=min(s,s^b)
if s!=0:B.append(s)
print((pow(2,N+M-1,mod)*(1-pow(2,mod-1-len(B),mod)))%mod)
``` | instruction | 0 | 76,531 | 23 | 153,062 |
Yes | output | 1 | 76,531 | 23 | 153,063 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
class GE():
def __init__(self, A, mod):
self.N = len(A)
self.M = len(A[0])
self.A = A[:]
self.mod = mod
self.uptri = None
self.pivot = []
self.R = None
def ut(self):
if self.uptri is not None:
return self.uptri
self.uptri = self.A[:]
c = 0
for i in range(self.N):
if i + c >= self.M:
break
while self.uptri[i][i+c] == 0:
for j in range(i+1, self.N):
if self.uptri[j][i+c]:
self.uptri[i], self.uptri[j] = self.uptri[j], self.uptri[i]
break
else:
c += 1
if i + c == self.M:
return self.uptri
self.pivot.append((i, i+c))
t = pow(self.uptri[i][i+c], self.mod - 2, self.mod)
for j in range(i+1, self.N):
tj = t * self.uptri[j][i+c]
self.uptri[j][i+c:] = [(aj - tj*ai) % self.mod for ai, aj in zip(self.uptri[i][i+c:], self.uptri[j][i+c:])]
for pi, pj in self.pivot[::-1]:
t = pow(self.uptri[pi][pj], self.mod-2, self.mod)
self.uptri[pi][pj:] = [(ai * t) % self.mod for ai in self.uptri[pi][pj:]]
for i in range(pi-1, -1, -1):
ti = self.uptri[i][pj]
self.uptri[i][pj:] = [(ai - api*ti) % self.mod for ai, api in zip(self.uptri[i][pj:], self.uptri[pi][pj:])]
return self.uptri
def rank(self):
if self.R is not None:
return self.R
self.ut()
self.R = len(self.pivot)
return self.R
N, M = map(int, input().split())
A = [list(map(int, input().split())) for _ in range(N)]
mod = 998244353
T = GE(A, 2)
print((pow(2, N+M-1, mod) - pow(2, N+M-T.rank()-1, mod)) % mod)
``` | instruction | 0 | 76,532 | 23 | 153,064 |
Yes | output | 1 | 76,532 | 23 | 153,065 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
import numpy as np
IN=lambda:list(map(int,input().split()))
p=998244353
n,m=IN()
a=np.array([IN() for i in range(n)])
r=np.linalg.matrix_rank(a)
f=n+m-1
d=f-r
print((pow(2,f,p)-pow(2,d,p))%p)
``` | instruction | 0 | 76,533 | 23 | 153,066 |
No | output | 1 | 76,533 | 23 | 153,067 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
#!/usr/bin/env python3
import sys, os
try: from typing import Any, Union, List, Tuple, Dict
except ImportError: pass
sys.setrecursionlimit(10**6)
if os.environ.get("USER") == "shun":
def debug(*args): print(*args, file=sys.stderr)
else:
print("NO DEBUG", file=sys.stderr)
def debug(*args): pass
def exit(): sys.exit(0)
l = int(input())
a = []
for _ in range(l):
a.append(int(input()))
init_score = 0
for i in range(l):
if a[i] == 0:
init_score += 2
elif a[i] % 2 == 0:
pass
else:
init_score += 1
left = [0]
for i in range(l):
left.append(left[i])
if a[i] == 0:
left[i+1] -= 2
elif a[i] % 2 == 0:
left[i+1] += a[i]
else:
left[i+1] += a[i] - 1
left_i = 0
left_min = left[0]
for i in range(l+1):
if left[i] < left_min:
left_i = i
left_min = left[i]
debug(left_i, left)
right = [0] * (l+1)
for i in range(l, 0, -1):
right[i-1] = right[i]
if a[i-1] == 0:
right[i-1] -= 2
elif a[i-1] % 2 == 0:
right[i-1] += a[i-1]
else:
right[i-1] += a[i-1] - 1
right_i = 0
right_min = right[0]
for i in range(l+1):
if right[i] < right_min:
right_i = i
right_min = right[i]
debug(right_i, right)
# odd
temp_score = init_score + left_min + right_min
b = a[left_i:right_i]
k = len(b)
for i in range(k):
if b[i] == 0:
temp_score -= 1
elif b[i] % 2 == 0:
temp_score += 1
else:
temp_score -= 1
left = [0]
for i in range(k):
left.append(left[i])
if b[i] == 0:
left[i+1] += 1
elif b[i] % 2 == 0:
left[i+1] -= 1
else:
left[i+1] += 1
left_i = 0
left_min = left[0]
for i in range(k+1):
if left[i] < left_min:
left_i = i
left_min = left[i]
debug(left_i, left)
right = [0] * (k+1)
for i in range(k, 0, -1):
right[i-1] = right[i]
if b[i-1] == 0:
right[i-1] += 1
elif b[i-1] % 2 == 0:
right[i-1] -= 1
else:
right[i-1] += 1
right_i = 0
right_min = right[0]
for i in range(k+1):
if right[i] < right_min:
right_i = i
right_min = right[i]
debug(right_i, right)
score = temp_score + left_min + right_min
print(score)
``` | instruction | 0 | 76,534 | 23 | 153,068 |
No | output | 1 | 76,534 | 23 | 153,069 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
import numpy as np
n,m = map(int,input().split())
a = [list(map(int,input().split())) for i in range(n)]
a_np = np.array(a)
rank = np.linalg.matrix_rank(a_np)
teisu = 998244353
ans = (pow(2,m-1,teisu)*(pow(2,n,teisu)-pow(2,n-rank,teisu)))
print(ans%teisu)
``` | instruction | 0 | 76,535 | 23 | 153,070 |
No | output | 1 | 76,535 | 23 | 153,071 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.
Constraints
* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}
Output
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
Examples
Input
2 2
0 1
1 0
Output
6
Input
2 3
0 0 0
0 1 0
Output
8
Submitted Solution:
```
import numpy as np
n,m = map(int, input().split())
A = np.array([ list(map(int, input().split())) for _ in range(n) ])
r = np.linalg.matrix_rank(A)
print(((2**n - 2**(n-r))*2**(m-1)) % 998244353)
``` | instruction | 0 | 76,536 | 23 | 153,072 |
No | output | 1 | 76,536 | 23 | 153,073 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino has a bar of length N, which has M marks on it. The distance from the left end of the bar to the i-th mark is X_i.
She will place several squares on this bar. Here, the following conditions must be met:
* Only squares with integral length sides can be placed.
* Each square must be placed so that its bottom side touches the bar.
* The bar must be completely covered by squares. That is, no square may stick out of the bar, and no part of the bar may be left uncovered.
* The boundary line of two squares may not be directly above a mark.
<image>
Examples of arrangements that satisfy/violate the conditions
The beauty of an arrangement of squares is defined as the product of the areas of all the squares placed. Joisino is interested in the sum of the beauty over all possible arrangements that satisfy the conditions. Write a program to find it. Since it can be extremely large, print the sum modulo 10^9+7.
Constraints
* All input values are integers.
* 1 \leq N \leq 10^9
* 0 \leq M \leq 10^5
* 1 \leq X_1 < X_2 < ... < X_{M-1} < X_M \leq N-1
Input
Input is given from Standard Input in the following format:
N M
X_1 X_2 ... X_{M-1} X_M
Output
Print the sum of the beauty over all possible arrangements that satisfy the conditions, modulo 10^9+7.
Examples
Input
3 1
2
Output
13
Input
5 2
2 3
Output
66
Input
10 9
1 2 3 4 5 6 7 8 9
Output
100
Input
1000000000 0
Output
693316425 | instruction | 0 | 76,575 | 23 | 153,150 |
"Correct Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
N,M,*X = map(int,read().split())
MOD = 10 ** 9 + 7
def mult(a,b,c,d,e,f):
# (a+bx+cx^2)(d+ex+fx^2) modulo 1-4x+2x^2-x^3
a,b,c,d,e = a*d,a*e+b*d,a*f+b*e+c*d,b*f+c*e,c*f
b += e; c -= 4*e; d += 2*e; e = 0
a += d; b -= 4*d; c += 2*d; d = 0
a %= MOD; b %= MOD; c %= MOD
return a,b,c
# (1/x)^i modulo (1-4x+2x^2-x^3)
M = 10 ** 5
A1 = [0] * (M+1)
a,b,c = 1,0,0
for i in range(M+1):
A1[i] = (a,b,c)
a,b,c = b+4*a,c-2*a,a
a %= MOD; b %= MOD; c %= MOD
# (1/x)^Mi modulo (1-4x+2x^2-x^3)
A2 = [0] * (M+1)
a,b,c = 1,0,0
d,e,f = A1[M]
for i in range(M+1):
A2[i] = (a,b,c)
a,b,c = mult(a,b,c,d,e,f)
def power(n):
# (1/x)^n modulo (1-4x+2x^2-x^3)
q,r = divmod(n,M)
a,b,c = A1[r]
d,e,f = A2[q]
return mult(a,b,c,d,e,f)
X.append(N)
a,b,c = 0,1,1
prev_x = 0
for x in X:
a,b,c = mult(a,b,c,*power(x - prev_x))
b -= a; c -= a
prev_x = x
answer = a
print(answer)
``` | output | 1 | 76,575 | 23 | 153,151 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino has a bar of length N, which has M marks on it. The distance from the left end of the bar to the i-th mark is X_i.
She will place several squares on this bar. Here, the following conditions must be met:
* Only squares with integral length sides can be placed.
* Each square must be placed so that its bottom side touches the bar.
* The bar must be completely covered by squares. That is, no square may stick out of the bar, and no part of the bar may be left uncovered.
* The boundary line of two squares may not be directly above a mark.
<image>
Examples of arrangements that satisfy/violate the conditions
The beauty of an arrangement of squares is defined as the product of the areas of all the squares placed. Joisino is interested in the sum of the beauty over all possible arrangements that satisfy the conditions. Write a program to find it. Since it can be extremely large, print the sum modulo 10^9+7.
Constraints
* All input values are integers.
* 1 \leq N \leq 10^9
* 0 \leq M \leq 10^5
* 1 \leq X_1 < X_2 < ... < X_{M-1} < X_M \leq N-1
Input
Input is given from Standard Input in the following format:
N M
X_1 X_2 ... X_{M-1} X_M
Output
Print the sum of the beauty over all possible arrangements that satisfy the conditions, modulo 10^9+7.
Examples
Input
3 1
2
Output
13
Input
5 2
2 3
Output
66
Input
10 9
1 2 3 4 5 6 7 8 9
Output
100
Input
1000000000 0
Output
693316425 | instruction | 0 | 76,576 | 23 | 153,152 |
"Correct Solution:
```
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 __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)
N,M=map(int,input().split())
X=list(map(int,input().split()))+[N]
dp=[0]*(M+2)
dp[0]=1
A=Matrix([[4,-2,1],[1,0,0],[0,1,0]])
DP=Matrix([[0],[0],[0]])
first=0
base=Matrix([[5],[1],[0]])
for i in range(1,M+2):
DP=(A**(X[i-1]-first))*(DP+base*(-dp[i-1]))
dp[i]=DP[2,0]
first=X[i-1]
print((-dp[-1])%(10**9+7))
``` | output | 1 | 76,576 | 23 | 153,153 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,752 | 23 | 153,504 |
"Correct Solution:
```
for id in range(21, 51):
print(((min(id, 25) + id) % (2 + id % 3)) > 0 and 1 or 0)
``` | output | 1 | 76,752 | 23 | 153,505 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,753 | 23 | 153,506 |
"Correct Solution:
```
for id in range(21,51):
print(int(((min(id,25)+id)%(2+id%3))>0))
``` | output | 1 | 76,753 | 23 | 153,507 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,754 | 23 | 153,508 |
"Correct Solution:
```
for i in range(21,51):
print(1 if (((min(i,25)+i)%(2+i%3))>0) else 0)
``` | output | 1 | 76,754 | 23 | 153,509 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,755 | 23 | 153,510 |
"Correct Solution:
```
for i in range(21,51):
if(((min(i, 25) + i) % (2 + i % 3))>0):
print(1)
else:
print(0)
``` | output | 1 | 76,755 | 23 | 153,511 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,756 | 23 | 153,512 |
"Correct Solution:
```
for i in range(21,51):
if (min(i,25)+i)%(2+i%3)>0:print(1)
else:print(0)
``` | output | 1 | 76,756 | 23 | 153,513 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,757 | 23 | 153,514 |
"Correct Solution:
```
print(*[int((min(i, 25) + i) % (2 + i % 3) > 0) for i in range(21, 51)], sep='\n')
``` | output | 1 | 76,757 | 23 | 153,515 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,758 | 23 | 153,516 |
"Correct Solution:
```
def main():
for i in range(21, 51):
print('1' if ((min(i, 25) + i) % (2 + i % 3)) > 0 else '0')
if __name__ == '__main__':
main()
``` | output | 1 | 76,758 | 23 | 153,517 |
Provide a correct Python 3 solution for this coding contest problem.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png. | instruction | 0 | 76,759 | 23 | 153,518 |
"Correct Solution:
```
print(0)
print(1)
print(1)
print(0)
print(1)
print(1)
print(0)
print(1)
print(1)
print(1)
print(1)
print(1)
print(0)
print(1)
print(0)
print(1)
print(1)
print(1)
print(0)
print(1)
print(1)
print(1)
print(1)
print(1)
print(0)
print(1)
print(0)
print(1)
print(1)
print(1)
``` | output | 1 | 76,759 | 23 | 153,519 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
for id in range(21, 51):
if ((min(id, 25) + id) % (2 + id % 3)) > 0:
print('1')
else:
print('0')
``` | instruction | 0 | 76,760 | 23 | 153,520 |
Yes | output | 1 | 76,760 | 23 | 153,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
for i in (0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1):
print(i)
``` | instruction | 0 | 76,761 | 23 | 153,522 |
Yes | output | 1 | 76,761 | 23 | 153,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
for id in range(21,51):
print(1 if ((min(id,25)+id)%(2+id%3))>0 else 0)
``` | instruction | 0 | 76,762 | 23 | 153,524 |
Yes | output | 1 | 76,762 | 23 | 153,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
# coding: utf-8
for i in range(21, 51):
print(int(((min(i, 25) + i) % (2 + i % 3)) > 0))
``` | instruction | 0 | 76,763 | 23 | 153,526 |
Yes | output | 1 | 76,763 | 23 | 153,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
mask = [1, 0, 0, 1, 1, 0]
for i in range(20, 50):
print(mask[i%6])
``` | instruction | 0 | 76,764 | 23 | 153,528 |
No | output | 1 | 76,764 | 23 | 153,529 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
``` | instruction | 0 | 76,765 | 23 | 153,530 |
No | output | 1 | 76,765 | 23 | 153,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
print("""0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
""")
``` | instruction | 0 | 76,766 | 23 | 153,532 |
No | output | 1 | 76,766 | 23 | 153,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
Submitted Solution:
```
# text = input()
#
# nums = list(map(lambda x: ord(x) - ord('A'), list(text)))
# print(nums)
# print(sum(nums))
print(0)
print(1)
print(1)
print(0)
print(1)
print(0)
print(0)
print(1)
print(1)
print(0)
print(1)
print(0)
print(0)
print(1)
print(1)
print(0)
print(1)
print(0)
print(0)
print(1)
print(1)
print(0)
print(1)
print(0)
print(0)
print(1)
print(1)
print(0)
print(1)
print(0)
``` | instruction | 0 | 76,767 | 23 | 153,534 |
No | output | 1 | 76,767 | 23 | 153,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
n, m = map(int, input().split())
x = [list(map(int, input().split())) for i in range(n)]
a, b = map(int, input().split())
def solve(n, m, x):
y = [[0]*(m+1) for i in range(n+1)]
for i in range(n):
for j in range(m):
y[i+1][j+1]=y[i+1][j]+x[i][j]
for j in range(m):
y[i+1][j+1]+=y[i][j+1]
ans = n*m
for i in range(a, n+1):
for j in range(b, m+1):
ans = min(ans, y[i][j]-y[i-a][j]-y[i][j-b]+y[i-a][j-b])
return ans
print(min(solve(n, m, x), solve(m, n, list(map(list, zip(*x))))))
``` | instruction | 0 | 77,108 | 23 | 154,216 |
Yes | output | 1 | 77,108 | 23 | 154,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
import re
import sys
exit=sys.exit
from bisect import bisect_left as bsl,bisect_right as bsr
from collections import Counter,defaultdict as ddict,deque
from functools import lru_cache
cache=lru_cache(None)
from heapq import *
from itertools import *
from math import inf
from pprint import pprint as pp
enum=enumerate
ri=lambda:int(rln())
ris=lambda:list(map(int,rfs()))
rln=sys.stdin.readline
rl=lambda:rln().rstrip('\n')
rfs=lambda:rln().split()
cat=''.join
catn='\n'.join
mod=1000000007
d4=[(0,-1),(1,0),(0,1),(-1,0)]
d8=[(-1,-1),(0,-1),(1,-1),(-1,0),(1,0),(-1,1),(0,1),(1,1)]
########################################################################
def solve(a,b):
ans=inf
for r in range(m-a+1):
for c in range(n-b+1):
ans=min(ans,count(r,c,a,b))
return ans
def count(r,c,a,b):
ret=0
for i in range(r,r+a):
for j in range(c,c+b):
ret+=grid[i][j]
return ret
m,n=ris()
grid=[ris() for _ in range(m)]
a,b=ris()
print(min(solve(a,b),solve(b,a)))
``` | instruction | 0 | 77,109 | 23 | 154,218 |
Yes | output | 1 | 77,109 | 23 | 154,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
n, m = map(int, input().split())
a = []
ans = 1e10
for i in range(n):
temp = input().split()
a.append(temp)
n1, m1 = map(int, input().split())
for i in range(n):
for j in range(m):
#
now = 0
b = False
for i1 in range(n1):
for j1 in range(m1):
try:
if a[i + i1][j + j1] == '1':
now += 1
except Exception:
b = 1
break
if b == True:
now = 1e10
break
ans = min(ans, now)
now = 0
b = False
for i1 in range(m1):
for j1 in range(n1):
try:
if a[i + i1][j + j1] == '1':
now += 1
except Exception:
b = True
break
if b == True:
now = 1e10
break
ans = min(ans, now)
print(ans)
``` | instruction | 0 | 77,110 | 23 | 154,220 |
Yes | output | 1 | 77,110 | 23 | 154,221 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
def findHouse(n,m,house,a,b):
resTab1 = []
resTab2 = []
#First side
for i in range(n):
row1 = []
for j in range(m):
areaSum1 = 0
if i + b <= n and j + a <= m:
for k in range(i,i+b):
for l in range(j,j+a):
areaSum1 += house[k][l]
else:
areaSum1 = None
row1.append(areaSum1)
resTab1.append(row1)
#SecondSide
for i in range(n):
row2 = []
for j in range(m):
areaSum2 = 0
if i + a <= n and j + b <= m:
for k in range(i,i+a):
for l in range(j,j+b):
areaSum2 += house[k][l]
else:
areaSum2 = None
row2.append(areaSum2)
resTab2.append(row2)
minTree = float('inf')
res = []
for i in range(n):
for j in range(m):
if resTab1[i][j] != None:
res.append(resTab1[i][j])
if resTab2[i][j]!= None:
res.append(resTab2[i][j])
#print(resTab1)
#print(resTab2)
#print(min(res))
return min(res)
n,m = [int(a) for a in input().split()]
house = []
for i in range(n):
house.append([int(a) for a in input().split() ])
a,b = [int(a) for a in input().split() ]
print(findHouse(n,m,house,a,b))
``` | instruction | 0 | 77,111 | 23 | 154,222 |
Yes | output | 1 | 77,111 | 23 | 154,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
n, m = map(int, input().split())
t = [[0] * (m + 1)] + [[] for i in range(n)]
t[1] = [0] + list(map(int, input().split()))
for j in range(2, m + 1): t[1][j] += t[1][j - 1]
for i in range(2, n + 1):
t[i] = [0] + list(map(int, input().split()))
for j in range(2, m + 1): t[i][j] += t[i][j - 1]
for j in range(1, m + 1): t[i][j] += t[i - 1][j]
b, a = map(int, input().split())
print(min(t[i + a][j + b] + t[i][j] - t[i + a][j] - t[i][j + b] for i in range(n - a + 1) for j in range(m - b + 1)))
``` | instruction | 0 | 77,112 | 23 | 154,224 |
No | output | 1 | 77,112 | 23 | 154,225 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
z=map(int,input().split())
g=range
n,m=z
M=[]
for i in g(n):
M+=list(map(int,input().split()))
print(M)
p=list(map(int,input().split()))
print(p)
# this is supposed to be at least (a,b) && (a,b) in dimensions
R=[[0 for x in g(m)]for y in g(n)]
x=2500
for k in g(2):
for r in g(n-p[k]+1):
for c in g(m-p[1-k]+1):
if(0==c):
if(0==r):
R[0][0]=0
for u in g(p[k]):
for v in g(p[1-k]):
R[0][0]+=M[u*m+v]
else:
R[r][c]=R[r-1][c]
for v in g(c,c+p[1-k]):
R[r][c]-=M[(r-1)*m+v]
R[r][c]+=M[(r+p[k]-1)*m+v]
else:
R[r][c]=R[r][c-1]
for u in g(r,r+p[k]):
t=1
R[r][c]-=M[u*m+c-1]
R[r][c]+=M[u*m+c+p[1-k]-1]
x=min(x,R[r][c])
print(x)
``` | instruction | 0 | 77,113 | 23 | 154,226 |
No | output | 1 | 77,113 | 23 | 154,227 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
import re
import sys
exit=sys.exit
from bisect import bisect_left as bsl,bisect_right as bsr
from collections import Counter,defaultdict as ddict,deque
from functools import lru_cache
cache=lru_cache(None)
from heapq import *
from itertools import *
from math import inf
from pprint import pprint as pp
enum=enumerate
ri=lambda:int(rln())
ris=lambda:list(map(int,rfs()))
rln=sys.stdin.readline
rl=lambda:rln().rstrip('\n')
rfs=lambda:rln().split()
cat=''.join
catn='\n'.join
mod=1000000007
d4=[(0,-1),(1,0),(0,1),(-1,0)]
d8=[(-1,-1),(0,-1),(1,-1),(-1,0),(1,0),(-1,1),(0,1),(1,1)]
########################################################################
def solve(a,b):
ans=inf
for r in range(m-a+1):
for c in range(n-b+1):
if not (r==0 or r+a==m or c==0 or c+b==n):
continue
ans=min(ans,count(r,c,a,b))
return ans
def count(r,c,a,b):
ret=0
for i in range(r,r+a):
for j in range(c,c+b):
ret+=grid[i][j]
return ret
m,n=ris()
grid=[ris() for _ in range(m)]
a,b=ris()
print(min(solve(a,b),solve(b,a)))
``` | instruction | 0 | 77,114 | 23 | 154,228 |
No | output | 1 | 77,114 | 23 | 154,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya has a beautiful garden where wonderful fruit trees grow and yield fantastic harvest every year. But lately thieves started to sneak into the garden at nights and steal the fruit too often. Vasya can’t spend the nights in the garden and guard the fruit because there’s no house in the garden! Vasya had been saving in for some time and finally he decided to build the house. The rest is simple: he should choose in which part of the garden to build the house. In the evening he sat at his table and drew the garden’s plan. On the plan the garden is represented as a rectangular checkered field n × m in size divided into squares whose side length is 1. In some squares Vasya marked the trees growing there (one shouldn’t plant the trees too close to each other that’s why one square contains no more than one tree). Vasya wants to find a rectangular land lot a × b squares in size to build a house on, at that the land lot border should go along the lines of the grid that separates the squares. All the trees that grow on the building lot will have to be chopped off. Vasya loves his garden very much, so help him choose the building land lot location so that the number of chopped trees would be as little as possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 50) which represent the garden location. The next n lines contain m numbers 0 or 1, which describe the garden on the scheme. The zero means that a tree doesn’t grow on this square and the 1 means that there is a growing tree. The last line contains two integers a and b (1 ≤ a, b ≤ 50). Note that Vasya can choose for building an a × b rectangle as well a b × a one, i.e. the side of the lot with the length of a can be located as parallel to the garden side with the length of n, as well as parallel to the garden side with the length of m.
Output
Print the minimum number of trees that needs to be chopped off to select a land lot a × b in size to build a house on. It is guaranteed that at least one lot location can always be found, i. e. either a ≤ n and b ≤ m, or a ≤ m и b ≤ n.
Examples
Input
2 2
1 0
1 1
1 1
Output
0
Input
4 5
0 0 1 0 1
0 1 1 1 0
1 0 1 0 1
1 1 1 1 1
2 3
Output
2
Note
In the second example the upper left square is (1,1) and the lower right is (3,2).
Submitted Solution:
```
n, m = map(int, input().split())
t = [[0] * (m + 1)] + [[] for i in range(n)]
t[1] = [0] + list(map(int, input().split()))
for j in range(2, m + 1): t[1][j] += t[1][j - 1]
for i in range(2, n + 1):
t[i] = [0] + list(map(int, input().split()))
for j in range(2, m + 1): t[i][j] += t[i][j - 1]
for j in range(1, m + 1): t[i][j] += t[i - 1][j]
a, b = map(int, input().split())
print(min(t[i + a][j + b] + t[i][j] - t[i + a][j] - t[i][j + b] for i in range(n - a + 1) for j in range(m - b + 1)))
``` | instruction | 0 | 77,115 | 23 | 154,230 |
No | output | 1 | 77,115 | 23 | 154,231 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n.
Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.
Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.
Input
The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.
Output
The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square.
Examples
Input
6
Output
1
Input
20
Output
4
Note
There is only one way to divide the stick in the first sample {1, 1, 2, 2}.
Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work.
Submitted Solution:
```
n=int(input())
print( 0 if n&1 else (n//2 -1)//2 )
``` | instruction | 0 | 77,143 | 23 | 154,286 |
Yes | output | 1 | 77,143 | 23 | 154,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n.
Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.
Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.
Input
The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.
Output
The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square.
Examples
Input
6
Output
1
Input
20
Output
4
Note
There is only one way to divide the stick in the first sample {1, 1, 2, 2}.
Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work.
Submitted Solution:
```
s = int(input())
if s%2 != 0:
print(0)
else:
s = s//2
if s%2 == 0:
print(s//2 - 1)
else:
print(s//2)
``` | instruction | 0 | 77,144 | 23 | 154,288 |
Yes | output | 1 | 77,144 | 23 | 154,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n.
Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.
Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.
Input
The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.
Output
The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square.
Examples
Input
6
Output
1
Input
20
Output
4
Note
There is only one way to divide the stick in the first sample {1, 1, 2, 2}.
Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work.
Submitted Solution:
```
n = int(input())
if n % 2 != 0:
print(0)
exit()
if (n/2) % 2 == 0:
n -= 2
l = int(n/4)
print(l)
``` | instruction | 0 | 77,145 | 23 | 154,290 |
Yes | output | 1 | 77,145 | 23 | 154,291 |
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