message stringlengths 2 28.7k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 21 109k | cluster float64 7 7 | __index_level_0__ int64 42 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A chessboard n × m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i - 1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.
The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 5000). The second line contains integer x (1 ≤ x ≤ 109).
Output
Print how many squares will be painted exactly x times.
Examples
Input
3 3
1
Output
4
Input
3 3
2
Output
1
Input
1 1
1
Output
1
Submitted Solution:
```
import itertools
import math
n, m = [int(k) for k in input().split()]
x = int(input())
if n-2*(x-1) < 1 or m-2*(x-1) < 1:
print(0)
elif n-2*(x-1) == 1 or m-2*(x-1) == 1:
print((n+m-4*(x-1))//2)
else: print(n+m-2 - 4*(x-1))
``` | instruction | 0 | 60,129 | 7 | 120,258 |
Yes | output | 1 | 60,129 | 7 | 120,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A chessboard n × m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i - 1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.
The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 5000). The second line contains integer x (1 ≤ x ≤ 109).
Output
Print how many squares will be painted exactly x times.
Examples
Input
3 3
1
Output
4
Input
3 3
2
Output
1
Input
1 1
1
Output
1
Submitted Solution:
```
def calculate_sides(n, m):
if n == 1:
return m // 2 if m % 2 == 0 else m // 2 + 1
if m == 1:
return n // 2 if n % 2 == 0 else n // 2 + 1
left, right, top, bottom = 0, 0, 0, 0
top = m // 2 if m % 2 == 0 else m // 2 + 1
bottom = n // 2 if n % 2 == 0 else n // 2 + 1
n -= 2
m -= 2
left = n // 2
if m > 0:
right = n // 2 if m % 2 != 0 else n // 2 + 1
left = n // 2 if m % 2 != 0 else n // 2 + 1
return top + bottom + left + right
n, m = list(map(int, input().split()))
x = int(input())
dict = dict()
times = 1
while n > 0 and m > 0:
quantity = calculate_sides(n, m)
dict[times] = quantity
times += 1
n -= 2
m -= 2
print(dict[x] if x in dict else 0 )
``` | instruction | 0 | 60,130 | 7 | 120,260 |
No | output | 1 | 60,130 | 7 | 120,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A chessboard n × m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i - 1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.
The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 5000). The second line contains integer x (1 ≤ x ≤ 109).
Output
Print how many squares will be painted exactly x times.
Examples
Input
3 3
1
Output
4
Input
3 3
2
Output
1
Input
1 1
1
Output
1
Submitted Solution:
```
n, m = map(int, input().split())
x, v = int(input()), 0
x1, y1, x2, y2 = x - 1, x - 1, n - x, m - x
for i in range(x1, x2 + 1):
if i == x1 or i == x2:
v += (y2 - y1 + 1) // 2 + ((i + y1) % 2 == 0 and (i + y2) % 2 == 0)
else:
v += ((i + y1) % 2 == 0) + ((i + y2) % 2 == 0)
print(v)
``` | instruction | 0 | 60,131 | 7 | 120,262 |
No | output | 1 | 60,131 | 7 | 120,263 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A chessboard n × m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i - 1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.
The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 5000). The second line contains integer x (1 ≤ x ≤ 109).
Output
Print how many squares will be painted exactly x times.
Examples
Input
3 3
1
Output
4
Input
3 3
2
Output
1
Input
1 1
1
Output
1
Submitted Solution:
```
n,m=list(map(int,input().split()))
x=int(input())
print(1 if n-2*(x-1)==m-2*(x-1)==1 else max(0,n+m-4*x+2))
``` | instruction | 0 | 60,132 | 7 | 120,264 |
No | output | 1 | 60,132 | 7 | 120,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A chessboard n × m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i - 1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.
The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 5000). The second line contains integer x (1 ≤ x ≤ 109).
Output
Print how many squares will be painted exactly x times.
Examples
Input
3 3
1
Output
4
Input
3 3
2
Output
1
Input
1 1
1
Output
1
Submitted Solution:
```
n,m = list(map(int, input().split(" ")))
timesleft = int(input())
print(((n-(timesleft-1)*2) * (m-(timesleft-1)*2)+1)//2)
``` | instruction | 0 | 60,133 | 7 | 120,266 |
No | output | 1 | 60,133 | 7 | 120,267 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,447 | 7 | 120,894 |
"Correct Solution:
```
n=int(input())
s=input()
print("Yes" if s.count("R")>n/2 else "No")
``` | output | 1 | 60,447 | 7 | 120,895 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,448 | 7 | 120,896 |
"Correct Solution:
```
N=input()
s=list(input())
r=s.count("R")
b=s.count("B")
if r>b:
print("Yes")
else:
print("No")
``` | output | 1 | 60,448 | 7 | 120,897 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,449 | 7 | 120,898 |
"Correct Solution:
```
print('Yes'if int(input())/2<input().count('R')else'No')
``` | output | 1 | 60,449 | 7 | 120,899 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,450 | 7 | 120,900 |
"Correct Solution:
```
print('YNeos'[int(input())<=input().count('B')*2::2])
``` | output | 1 | 60,450 | 7 | 120,901 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,451 | 7 | 120,902 |
"Correct Solution:
```
a=input()
x=input()
b=x.count("B")
r=x.count("R")
if r>b:
print("Yes")
else:
print("No")
``` | output | 1 | 60,451 | 7 | 120,903 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,452 | 7 | 120,904 |
"Correct Solution:
```
n=input()
s=input()
print("Yes"if s.count("R")>s.count("B")else"No")
``` | output | 1 | 60,452 | 7 | 120,905 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,453 | 7 | 120,906 |
"Correct Solution:
```
_ = input()
s = input()
print("Yes") if s.count("R") > s.count("B") else print("No")
``` | output | 1 | 60,453 | 7 | 120,907 |
Provide a correct Python 3 solution for this coding contest problem.
There are N people numbered 1 to N. Each person wears a red hat or a blue hat.
You are given a string s representing the colors of the people. Person i wears a red hat if s_i is `R`, and a blue hat if s_i is `B`.
Determine if there are more people wearing a red hat than people wearing a blue hat.
Constraints
* 1 \leq N \leq 100
* |s| = N
* s_i is `R` or `B`.
Input
Input is given from Standard Input in the following format:
N
s
Output
If there are more people wearing a red hat than there are people wearing a blue hat, print `Yes`; otherwise, print `No`.
Examples
Input
4
RRBR
Output
Yes
Input
4
BRBR
Output
No | instruction | 0 | 60,454 | 7 | 120,908 |
"Correct Solution:
```
N = int(input())
s = [i for i in input()]
c = s.count('R')
print(['No','Yes'][c > N-c])
``` | output | 1 | 60,454 | 7 | 120,909 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,471 | 7 | 122,942 |
Tags: math, number theory
Correct Solution:
```
import math as m
def innput():
return [int(i) for i in input().split()]
def prime(x):
if x % 2 == 0 or x == 1:
return False
f = True
lim = m.ceil(m.sqrt(x)) + 1
i = 3
while i < lim:
if m.ceil(x/i) == m.floor(x/i):
return False
i += 2
return True
def main():
n = innput()[0]
for i in range(n):
b, a = innput()
c = (b+a)*(b-a)
if prime(c):
print("YES")
else:
print("NO")
main()
``` | output | 1 | 61,471 | 7 | 122,943 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,472 | 7 | 122,944 |
Tags: math, number theory
Correct Solution:
```
def criba_eratostenes(n,s):
multiplos = set()
for i in range(2, n+1):
if i not in multiplos:
multiplos.update(range(i*i, n+1, i))
if s%i == 0:
print("NO")
break;
else:
print("YES")
n = int(input())
for i in range(n):
linea = input()
primero = int(linea[:linea.find(" ")])
segundo = int(linea[linea.find(" "):])
cuadrado = primero**2 - segundo**2
p = primero- segundo
if p == 1:
criba_eratostenes(int(cuadrado**(1/2)),cuadrado)
else:
print("NO")
``` | output | 1 | 61,472 | 7 | 122,945 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,473 | 7 | 122,946 |
Tags: math, number theory
Correct Solution:
```
t = int(input())
for _ in range(t):
A,B = map(int, input().split())
if A-B > 1:
print('NO')
else:
A += B
i = 2
while i**2 <= A:
if A%i == 0:
print('NO')
break
i+=1
else:
print('YES')
``` | output | 1 | 61,473 | 7 | 122,947 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,474 | 7 | 122,948 |
Tags: math, number theory
Correct Solution:
```
t = int(input())
def _try_composite(a, d, n, s):
if pow(a, d, n) == 1:
return False
for i in range(s):
if pow(a, 2**i * d, n) == n-1:
return False
return True # n is definitely composite
def is_prime(n, _precision_for_huge_n=16):
if n in _known_primes or n in (0, 1):
return True
if any((n % p) == 0 for p in _known_primes):
return False
d, s = n - 1, 0
while not d % 2:
d, s = d >> 1, s + 1
# Returns exact according to http://primes.utm.edu/prove/prove2_3.html
if n < 1373653:
return not any(_try_composite(a, d, n, s) for a in (2, 3))
if n < 25326001:
return not any(_try_composite(a, d, n, s) for a in (2, 3, 5))
if n < 118670087467:
if n == 3215031751:
return False
return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7))
if n < 2152302898747:
return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11))
if n < 3474749660383:
return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11, 13))
if n < 341550071728321:
return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11, 13, 17))
# otherwise
return not any(_try_composite(a, d, n, s)
for a in _known_primes[:_precision_for_huge_n])
_known_primes = [2, 3]
_known_primes += [x for x in range(5, 1000, 2) if is_prime(x)]
for i in range(t):
[a,b] = [int(x) for x in input().split(" ")]
if a-b != 1:
print("NO")
else:
if is_prime(a+b):
print("YES")
else:
print("NO")
``` | output | 1 | 61,474 | 7 | 122,949 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,475 | 7 | 122,950 |
Tags: math, number theory
Correct Solution:
```
from math import sqrt
def era(n):
i = 2
limit = int(sqrt(n))+1
while (i<limit):
if (n%i==0):
return True
i+=1
return False
t = int(input())
for i in range(t):
a, b = [int(x) for x in input().split()]
c = a+b
z = era(c)
if (a-b==1) and (not z):
print("YES")
else:
print("NO")
``` | output | 1 | 61,475 | 7 | 122,951 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,476 | 7 | 122,952 |
Tags: math, number theory
Correct Solution:
```
def main():
n = int(input())
L = [None] * n
for i in range(n):
L[i] = (int(x) for x in input().split())
solver(L)
def primeSieve(n):
booleans = [True] * (n + 1)
booleans[0] = False
booleans[1] = False
for x in range(2, int(n**0.5) + 1):
if booleans[x] == True:
for y in range(x**2, n + 1, x):
booleans[y] = False
return booleans
def isPrime(n):
if n < 2:
return False
elif n % 2 == 0:
return n == 2
else:
for x in range(3, int(n**0.5) + 1, 2):
if n % x == 0:
return False
return True
def solver(L):
for (a, b) in L:
if a - b == 1 and isPrime(a + b):
print("YES")
else:
print("NO")
def solver2(L):
primes = primeSieve(10**3)
for (a, b) in L:
#if isPrime(a**2 - b**2):
if primes[a**2 - b**2]:
print("YES")
else:
print("NO")
#solver([(6, 5), (16, 13), (61690850361, 24777622630), (34, 33)])
#for i in range(1, 20):
#print(i, isPrime(i)),
main()
``` | output | 1 | 61,476 | 7 | 122,953 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,477 | 7 | 122,954 |
Tags: math, number theory
Correct Solution:
```
def is_prime(num):
for div in range(2, int(num ** 0.5) + 1):
if num % div == 0:
return False
return True
def read_nums():
return list(map(int, input().split()))
t = int(input())
for _ in range(t):
a, b = read_nums()
if a - b != 1:
print('NO')
else:
if is_prime(a + b):
print('YES')
else:
print('NO')
``` | output | 1 | 61,477 | 7 | 122,955 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b < a). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).
Alice would like to know whether the area of her cloth expressed in square centimeters is [prime.](https://en.wikipedia.org/wiki/Prime_number) Could you help her to determine it?
Input
The first line contains a number t (1 ≤ t ≤ 5) — the number of test cases.
Each of the next t lines describes the i-th test case. It contains two integers a and b~(1 ≤ b < a ≤ 10^{11}) — the side length of Alice's square and the side length of the square that Bob wants.
Output
Print t lines, where the i-th line is the answer to the i-th test case. Print "YES" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print "NO".
You can print each letter in an arbitrary case (upper or lower).
Example
Input
4
6 5
16 13
61690850361 24777622630
34 33
Output
YES
NO
NO
YES
Note
The figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is 6^2 - 5^2 = 36 - 25 = 11, which is prime, so the answer is "YES".
<image>
In the second case, the area is 16^2 - 13^2 = 87, which is divisible by 3.
<image>
In the third case, the area of the remaining piece is 61690850361^2 - 24777622630^2 = 3191830435068605713421. This number is not prime because 3191830435068605713421 = 36913227731 ⋅ 86468472991 .
In the last case, the area is 34^2 - 33^2 = 67. | instruction | 0 | 61,478 | 7 | 122,956 |
Tags: math, number theory
Correct Solution:
```
read = lambda: map(int, input().split())
def prime(x):
d = 2
while d*d<= x:
if x % d == 0: return 0
d += 1
return 1
t = int(input())
res = ""
for i in range(t):
a, b = read()
res += "YES\n" if a-b==1 and prime(a+b) else "NO\n"
print(res)
``` | output | 1 | 61,478 | 7 | 122,957 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
def ans():
H, W = map(int,input().split())
HW = [input() for _ in range(H)]
HW = ["".join(hw) for hw in zip(*HW) if hw.count("#") > 0]
HW = ["".join(hw) for hw in zip(*HW) if hw.count("#") > 0]
print("\n".join(HW))
ans()
``` | instruction | 0 | 62,117 | 7 | 124,234 |
Yes | output | 1 | 62,117 | 7 | 124,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
h,w = map(int, input().split())
a=[]
A=[[i for i in input()] for _ in range(h)]
B=[x for x in A if "#" in x]
C = zip(*[y for y in zip(*B) if "#" in y])
for d in C:print("".join(d))
``` | instruction | 0 | 62,118 | 7 | 124,236 |
Yes | output | 1 | 62,118 | 7 | 124,237 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
h,w=map(int,input().split())
a=[list(input()) for _ in range(h)]
s=[]
for i in a:
if(i.count("#")!=0):s.append(i)
a = [list(x) for x in zip(*s)]
s=[]
for i in a:
if(i.count("#")!=0):s.append(i)
a = [list(x) for x in zip(*s)]
for i in a:print("".join(i))
``` | instruction | 0 | 62,119 | 7 | 124,238 |
Yes | output | 1 | 62,119 | 7 | 124,239 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
h, w = map(int, input().split())
grid = [list(input()) for i in range(h)]
for i in range(2):
grid = [col for col in grid if '#' in col ]
grid = list(map(list, (zip(*grid))))
for g in grid:
print(''.join(g))
``` | instruction | 0 | 62,120 | 7 | 124,240 |
Yes | output | 1 | 62,120 | 7 | 124,241 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
h,w=map(int,input().split())
a=[list(input().split()) for _ in range(h)]
#タテのチェック
for i in range(w):
tmp=0
for j in range(h):
if a[j][i]=="#":
tmp=1
if tmp==0:
for j in range(h):
a[j][i]="0"
#ヨコのチェック
for i in range(h):
if not "#" in a[i][:]:
a[i][:]=[0]*w
for i in range(h):
tmpl=[]
for j in range(w):
if not a[i][j]=="0":
tmpl.append(a[i][j])
if "#" in tmpl or "." in tmpl:
print(" ".join(tmpl))
``` | instruction | 0 | 62,121 | 7 | 124,242 |
No | output | 1 | 62,121 | 7 | 124,243 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
a,b=map(int,input().split())
c=[]
for i in range(a):
g=input()
if "#" not in g:
continue
d=list(g)
c.append(d)
l=len(c)
p=[]
for i in range(b):
for j in range(l):
if c[j][i]=="#":
p.append(i)
continue
for i in range(l):
for j in range(len(p)):
if j == len(p)-1:
print(c[i][p[j]])
continue
print(c[i][p[j]],end="")
``` | instruction | 0 | 62,122 | 7 | 124,244 |
No | output | 1 | 62,122 | 7 | 124,245 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
import numpy as np
H,W = map(int,input().split())
matrix = np.array([])
for i in range(H):
temp = list(input())
matrix = np.append(matrix,temp)
count = []
row = 0
index = 0
for i in range(0,H*(W-1)+1,W):
if matrix[i] == "." and matrix[i+1] == "." and matrix[i+2] == ".":
count = np.append(count,i)
count = np.append(count,i+1)
count = np.append(count,i+2)
row += 1
for i in range(0,W):
if matrix[i] == "." and matrix[i+3] == "." and matrix[i+6] == ".":
count = np.append(count,i)
count = np.append(count,i+3)
count = np.append(count,i+6)
index += 1
count = [int(s) for s in list(set(count))]
count = sorted(count,reverse=True)
for i in count:
matrix = np.delete(matrix,[i],None)
matrix = matrix.reshape(H-row,W-index)
for i in range(H-row):
print()
for s in matrix[i]:
print(s,end="")
``` | instruction | 0 | 62,123 | 7 | 124,246 |
No | output | 1 | 62,123 | 7 | 124,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid of squares with H horizontal rows and W vertical columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j). Each square is black or white. The color of the square is given as an H-by-W matrix (a_{i, j}). If a_{i, j} is `.`, the square (i, j) is white; if a_{i, j} is `#`, the square (i, j) is black.
Snuke is compressing this grid. He will do so by repeatedly performing the following operation while there is a row or column that consists only of white squares:
* Operation: choose any one row or column that consists only of white squares, remove it and delete the space between the rows or columns.
It can be shown that the final state of the grid is uniquely determined regardless of what row or column is chosen in each operation. Find the final state of the grid.
Constraints
* 1 \leq H, W \leq 100
* a_{i, j} is `.` or `#`.
* There is at least one black square in the whole grid.
Input
Input is given from Standard Input in the following format:
H W
a_{1, 1}...a_{1, W}
:
a_{H, 1}...a_{H, W}
Output
Print the final state of the grid in the same format as input (without the numbers of rows and columns); see the samples for clarity.
Examples
Input
4 4
##.#
....
##.#
.#.#
Output
###
###
.##
Input
4 4
.#
....
.#
.#.#
Output
.##
Input
3 3
..
.#.
..#
Output
..
.#.
..#
Input
4 5
.....
.....
..#..
.....
Output
Input
7 6
......
....#.
.#....
..#...
..#...
......
.#..#.
Output
..#
..
.#.
.#.
.#
Submitted Solution:
```
H, W = [int(n) for n in input().split()]
matrix = []
for i in range(H):
matrix.append(list(input()))
white = ['.'] * W
pop_list = []
counter = 0
i = H - 1
while i >= 0:
if matrix[i] == white:
matrix.pop(i)
i -= 1
counter += 1
i -= 1
white = ['.'] * (H - counter)
i = W - 1
while i >= 0:
current_col = [r[i] for r in matrix]
if current_col == white:
for j, r in enumerate(matrix):
matrix[j].pop(i)
i -= 1
i -= 1
for r in matrix:
for rr in r:
print(rr, end = '')
print('\n')
``` | instruction | 0 | 62,124 | 7 | 124,248 |
No | output | 1 | 62,124 | 7 | 124,249 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,918 | 7 | 125,836 |
"Correct Solution:
```
N,M=map(int,input().split())
A=[0]*M
for i in range(M):
A[i]=list(map(int,input().split()))
P=list(map(int,input().split()))
F=0
for i in range(2**N):
E=0
Sui=[0]*N
for j in range(N):
if ((i >> j) & 1):
Sui[j]+=1
for k in range(M):
D=0
for l in range(1,A[k][0]+1):
if Sui[A[k][l]-1]==1:
D+=1
if D%2==P[k]:
E+=1
if E==M:
F+=1
print(F)
``` | output | 1 | 62,918 | 7 | 125,837 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,919 | 7 | 125,838 |
"Correct Solution:
```
from itertools import product
n, m = map(int, input().split())
l = [[int(i) for i in input().split()] for _ in range(m)]
p = [int(i) for i in input().split()]
c = 0
for sw in product((0, 1), repeat=n):
for i in range(m):
if sum(sw[si - 1] for si in l[i][1:]) % 2 != p[i]:
break
else:
c += 1
print(c)
``` | output | 1 | 62,919 | 7 | 125,839 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,920 | 7 | 125,840 |
"Correct Solution:
```
N, M = map(int, input().split())
K = [set(list(map(int, input().split()))[1:]) for _ in range(M)]
P = list(map(int, input().split()))
ans = 0
for i in range(2**N):
S = set([1+j for j in range(N) if 2**j & i])
for j, k in enumerate(K):
if len(S.intersection(k))%2 != P[j]:
break
else:
ans += 1
print(ans)
``` | output | 1 | 62,920 | 7 | 125,841 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,921 | 7 | 125,842 |
"Correct Solution:
```
from itertools import product
n, m = map(int, input().split())
s = [list(map(int, input().split())) for _ in range(m)]
p = list(map(int, input().split()))
print(sum(all(sum(i[b - 1] for b in a[1:]) % 2 == x for a, x in zip(s, p)) for i in product((0, 1), repeat=n)))
``` | output | 1 | 62,921 | 7 | 125,843 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,922 | 7 | 125,844 |
"Correct Solution:
```
N,M=map(int,input().split())
l=[]
for i in range(M):
l.append(list(map(int,input().split()))[1:])
p=list(map(int,input().split()))
ans=0
for i in range(2**N):
isOK=True
for j in range(M):
stat=0
for k in l[j]:
k-=1
if i&(1<<k):
stat=(stat+1)%2
if stat!=p[j]:
isOK=False
if isOK:
ans+=1
print(ans)
``` | output | 1 | 62,922 | 7 | 125,845 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,923 | 7 | 125,846 |
"Correct Solution:
```
N, M = list(map(int, input().split()))
ks = [list(map(int, input().split())) for _ in range(M)]
p = list(map(int, input().split()))
ans = 0
for i in range(1 << N):
for j in range(M):
t = 0
for k in range(1, ks[j][0] + 1):
if i >> (ks[j][k] - 1) & 1:
t += 1
if t % 2 != p[j]:
break
else:
ans += 1
print(ans)
``` | output | 1 | 62,923 | 7 | 125,847 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,924 | 7 | 125,848 |
"Correct Solution:
```
n,m = map(int,input().split())
data = []
for i in range(m):
k,*s = map(int,input().split())
data.append(set(s))
p = list(map(int,input().split()))
ans = 0
for i in range(1<<n):
on = set()
for j in range(n):
if i>>j&1:on.add(j+1)
if all([len(on&data[l])%2==p[l] for l in range(m)]):ans+=1
print(ans)
``` | output | 1 | 62,924 | 7 | 125,849 |
Provide a correct Python 3 solution for this coding contest problem.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8 | instruction | 0 | 62,925 | 7 | 125,850 |
"Correct Solution:
```
N, M = [int(s) for s in input().split()]
S = []
for _ in range(M):
l = [int(s) for s in input().split()]
S.append(l[1:])
P = [int(s) for s in input().split()]
result = 0
for i in range(2 ** N):
if all(sum(["{:0{N}b}".format(i, N=N)[t - 1] == '1' for t in s]) % 2 == P[j] for j, s in enumerate(S)):
result += 1
print(result)
``` | output | 1 | 62,925 | 7 | 125,851 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
# 23:20
n, m = map(int, input().split())
S = [list(map(int, input().split()))[1:] for i in range(m)]
P = list(map(int, input().split()))
ans = 0
for i in range(2**n):
for s, p in zip(S, P):
c = 0
for t in s:
if (i >> t-1) & 1:
c += 1
if c % 2 != p:
break
else:
ans += 1
print(ans)
``` | instruction | 0 | 62,926 | 7 | 125,852 |
Yes | output | 1 | 62,926 | 7 | 125,853 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
n,m=map(int,input().split())
s=[0]*m
for i in range(m):
s[i]=list(map(int,input().split()))
del s[i][0]
p=list(map(int,input().split()))
count=0
for i in range(2**n):
for k in range(m):
temp=0
for j in range(n):
if ((i >> j) & 1) and j+1 in s[k]:
temp=temp+1
if temp%2!=p[k]:
break
else:
count=count+1
print(count)
``` | instruction | 0 | 62,927 | 7 | 125,854 |
Yes | output | 1 | 62,927 | 7 | 125,855 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
N,M = map(int,input().split())
S = []
for m in range(M):
nums = list(map(int,input().split()))
S.append(nums[1:])
#print(S)
p = list(map(int,input().split()))
#print(p)
ans = 0
for bits in range(1<<N):
for m in range(M):
on = 0
for s in S[m]:
on += (bits>>(s-1))&1
if (on&1) != p[m]:
break
else:
ans += 1
print(ans)
``` | instruction | 0 | 62,928 | 7 | 125,856 |
Yes | output | 1 | 62,928 | 7 | 125,857 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
n,m=map(int,input().split())
s=eval('list(map(int,input().split()[1:])),'*m)
*p,=map(int,input().split())
a=0
r=range
for i in r(1<<n):
c=[0]*m
for j in r(n):
for k in r(m):c[k]+=i>>j&1and j+1in s[k]
a+=all(j==i%2for i,j in zip(c,p))
print(a)
``` | instruction | 0 | 62,929 | 7 | 125,858 |
Yes | output | 1 | 62,929 | 7 | 125,859 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
def read_input():
n, m = map(int, input().split())
slist = []
for i in range(m):
temp = list(map(int, input().split()))
k = temp[0]
s = temp[1:]
slist.append((k, s))
p = list(map(int, input().split()))
return n, m, slist, p
def switch_gen(n):
curr = 0
while True:
bincurr = bin(curr)[2:]
if len(bincurr) > n:
return None
bincurr = [int(c) for c in bincurr]
t = [0] * (n - len(bincurr))
t.extend(bincurr)
yield t
curr += 1
def check_condition(switch, slist, plist):
for s, p in zip(slist, plist):
count = 0
for i in s[1]:
if switch[i - 1] == 1:
count += 1
if count % 2 != p:
return False
return True
def submit():
n, m, slist, p = read_input()
count = 0
for switch in switch_gen(n):
if check_condition(switch, slist, p):
count += 1
print(count)
if __name__ == '__main__':
submit()
``` | instruction | 0 | 62,930 | 7 | 125,860 |
No | output | 1 | 62,930 | 7 | 125,861 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
N,M = map(int,input())
K = []
S = []
for i in range(M):
list = input().split()
K.append(int(list[0]))
S.append(map(int,list[1::]))
p = list(map(int,input().split()))
anss = 0
for i in range(2**n):
for j in range(M):
ans = 0
for k in range(N):
if i >> k & 1 and k in K[j]:
ans += 1
if ans % 2 != p[j]:
break
else:
anss += 1
print(ans)
``` | instruction | 0 | 62,931 | 7 | 125,862 |
No | output | 1 | 62,931 | 7 | 125,863 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
n, m = map(int, input().split())
a = [list(map(int, input().split()))[1:] for _ in range(m)]
p = list(map(int, input().split()))
c = 0
for n in range(1 << n):
for i, s in enumerate(a):
if p[i] ^ sum(n >> s-1 & 1 for s_ in s) & 1:
break
else:
c += 1
print(c)
``` | instruction | 0 | 62,932 | 7 | 125,864 |
No | output | 1 | 62,932 | 7 | 125,865 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches that are "on" among these switches is congruent to p_i modulo 2.
How many combinations of "on" and "off" states of the switches light all the bulbs?
Constraints
* 1 \leq N, M \leq 10
* 1 \leq k_i \leq N
* 1 \leq s_{ij} \leq N
* s_{ia} \neq s_{ib} (a \neq b)
* p_i is 0 or 1.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M
Output
Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
Examples
Input
2 2
2 1 2
1 2
0 1
Output
1
Input
2 3
2 1 2
1 1
1 2
0 0 1
Output
0
Input
5 2
3 1 2 5
2 2 3
1 0
Output
8
Submitted Solution:
```
N,M = map(int,input().split())
ks = [list(map(int, input().split()))for i in range(M)]
p = list(map(int, input().split()))
cnt = 0
all_on = 1
ans = 0
for i in range(2**N):
all_on = 1
bits = "0" + str(N) + "b"
sw_line = str(format(i,bits))
for j in range(M):
for k in range(1,ks[j][0]+1):
sw = sw_line[ks[j][k]-1]
if(sw== "1"):
cnt += 1
if(cnt % 2 != p[j]):
all_on = 0
if(all_on == 1):
ans += 1
print(ans)
``` | instruction | 0 | 62,933 | 7 | 125,866 |
No | output | 1 | 62,933 | 7 | 125,867 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.
Find the number of the possible ways to paint the balls.
Constraints
* 1≦N≦1000
* 2≦K≦1000
* The correct answer is at most 2^{31}-1.
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the possible ways to paint the balls.
Examples
Input
2 2
Output
2
Input
1 10
Output
10 | instruction | 0 | 63,001 | 7 | 126,002 |
"Correct Solution:
```
NK=input().split(" ")
N=int(NK[0])
K=int(NK[1])
print(K*(K-1)**(N-1))
``` | output | 1 | 63,001 | 7 | 126,003 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.
Find the number of the possible ways to paint the balls.
Constraints
* 1≦N≦1000
* 2≦K≦1000
* The correct answer is at most 2^{31}-1.
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the possible ways to paint the balls.
Examples
Input
2 2
Output
2
Input
1 10
Output
10 | instruction | 0 | 63,002 | 7 | 126,004 |
"Correct Solution:
```
N, K = list(map(int,input().split()))
ans = K*(K-1)**(N-1)
print(ans)
``` | output | 1 | 63,002 | 7 | 126,005 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.
Find the number of the possible ways to paint the balls.
Constraints
* 1≦N≦1000
* 2≦K≦1000
* The correct answer is at most 2^{31}-1.
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the possible ways to paint the balls.
Examples
Input
2 2
Output
2
Input
1 10
Output
10 | instruction | 0 | 63,003 | 7 | 126,006 |
"Correct Solution:
```
#abc046 b
n,k=map(int,input().split())
ans=k*(k-1)**(n-1)
print(ans)
``` | output | 1 | 63,003 | 7 | 126,007 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.
Find the number of the possible ways to paint the balls.
Constraints
* 1≦N≦1000
* 2≦K≦1000
* The correct answer is at most 2^{31}-1.
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the possible ways to paint the balls.
Examples
Input
2 2
Output
2
Input
1 10
Output
10 | instruction | 0 | 63,004 | 7 | 126,008 |
"Correct Solution:
```
N, K = map(int,input().split())
ans = K * ((K-1)**(N-1))
print(ans)
``` | output | 1 | 63,004 | 7 | 126,009 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.
Find the number of the possible ways to paint the balls.
Constraints
* 1≦N≦1000
* 2≦K≦1000
* The correct answer is at most 2^{31}-1.
Input
The input is given from Standard Input in the following format:
N K
Output
Print the number of the possible ways to paint the balls.
Examples
Input
2 2
Output
2
Input
1 10
Output
10 | instruction | 0 | 63,005 | 7 | 126,010 |
"Correct Solution:
```
n, k = map(int, input().split())
print(k*((k-1)**(n-1)))
``` | output | 1 | 63,005 | 7 | 126,011 |
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