text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
import sys
# import math
# import re
# from heapq import *
# from collections import defaultdict as dd
# from collections import OrderedDict as odict
# from collections import Counter as cc
# from collections import deque
sys.setrecursionlimit(10**5)#thsis is must
# mod = 10**9+7; md = 998244353
# m = 2**32
input = lambda: sys.stdin.readline().strip()
inp = lambda: list(map(int,sys.stdin.readline().strip().split()))
# def C(n,r,mod):
# if r>n:
# return 0
# num = den = 1
# for i in range(r):
# num = (num*(n-i))%mod
# den = (den*(i+1))%mod
# return (num*pow(den,mod-2,mod))%mod
# def pfcs(M = 100000):
# pfc = [0]*(M+1)
# for i in range(2,M+1):
# if pfc[i]==0:
# for j in range(i,M+1,i):
# pfc[j]+=1
# return pfc
#______________________________________________________
for _ in range(int(input())):
x,y = inp()
if y>x:
x,y = y,x
ans = 2*y+1 if x!=y else 2*y
x = x-y-1 if x!=y else x-y
ans+= 2*x if x!=0 else 0
print(ans)
```
| 98,100 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
t = int(input())
l= []
for i in range(t):
a, b = map(int, input().split())
s = 0
max_ = max(a, b)
min_ = min(a, b)
s += min_ * 2
if max_ - min_ == 0:
l.append(s)
else:
l.append(s + (max_ - min_) * 2 - 1)
for i in l:
print(i)
```
| 98,101 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
for _ in range(int(input())):
x, y = map(int, input().split())
print(x+y+max(abs(x-y)-1, 0))
```
| 98,102 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
def call():
x,y=map(int,input().split())
t=max(x,y)
if(x==y):
reS=t*2
else:
reS=t*2-1
print(reS)
for _ in range(int(input())):
call()
```
| 98,103 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
t = int(input())
for _ in range(t):
x, y = [int(s) for s in input().split() ]
lastMove = ''
moveCount = 0
actualX = 0
actualY = 0
firstMove = 'x' if x > y else 'y'
while actualX!=x or actualY!=y:
if firstMove == 'y':
if (actualX < x and lastMove == 'right' and actualY == y) or (actualY < y and lastMove == 'up' and actualX == x):
lastMove='none'
moveCount+=1
elif (actualY < y and lastMove != 'up') or (actualX < x and lastMove == 'right'):
#se aproximar em Y
lastMove='up'
actualY+=1
moveCount+=1
elif (actualX < x and lastMove != 'right') or (actualY < y and lastMove == 'up'):
#seguir na direção X OU ja andei na direção y, mudar
lastMove='right'
actualX+=1
moveCount+=1
else:
if (actualX < x and lastMove == 'right' and actualY == y) or (actualY < y and lastMove == 'up' and actualX == x):
lastMove='none'
moveCount+=1
elif (actualX < x and lastMove != 'right') or (actualY < y and lastMove == 'up'):
#seguir na direção X OU ja andei na direção y, mudar
lastMove='right'
actualX+=1
moveCount+=1
elif (actualY < y and lastMove != 'up') or (actualX < x and lastMove == 'right'):
#se aproximar em Y
lastMove='up'
actualY+=1
moveCount+=1
print(moveCount)
```
| 98,104 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
t = int(input())
for _ in range(t):
x, y = (abs(int(number)) for number in input().split(" "))
if x > y:
result = 2 * y + 2 * (x - y) - 1
elif y > x:
result = 2 * x + 2 * (y - x) - 1
else:
result = 2 * x
print(result)
```
| 98,105 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Tags: math
Correct Solution:
```
import sys
input=sys.stdin.readline
from collections import defaultdict as dc
from collections import Counter
from bisect import bisect_right, bisect_left
import math
from operator import itemgetter
from heapq import heapify, heappop, heappush
for _ in range(int(input())):
n,m=map(int,input().split())
if n==m:
print(2*n)
else:
print(2*max(n,m)-1)
```
| 98,106 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
""" Educational Codeforces Round 98 (Rated for Div. 2) | A - Robot Program """
try:
for _ in range(int(input())):
a, b = map(int, input().split())
ans = 0
if a == b:
ans = (a + b)
else:
ans = a + b + (abs(a - b) - 1)
print(ans)
except EOFError as e:
pass
```
Yes
| 98,107 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
for _ in range(int(input())):
n,m=[int(x) for x in input().split()]
print(n+m+max(0,abs(m-n)-1))
```
Yes
| 98,108 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
import sys
input = sys.stdin.readline
from collections import *
t = int(input())
for _ in range(t):
x, y = map(int, input().split())
m, M = min(x, y), max(x, y)
d = M-m
ans = 2*m
if d>0:
ans += 2*d-1
print(ans)
```
Yes
| 98,109 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
a=int(input(""))
for i in range(a):
x, y = map(int, input().split())
if x==y:
print(x+y)
else:
print(max(x,y)*2-1)
```
Yes
| 98,110 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
for _ in range(int(input())):
a,b = map(int,input().split())
print(max(a,b)*2-1)
```
No
| 98,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
def program():
a,b=[int(x) for x in input().split()]
if a >= 2*b:
#print("2a={} and b={}".format(2*a,b))
print(2*a-1)
else:
print(a+b)
if __name__ == "__main__":
test=int(input())
for i in range(test):
program()
```
No
| 98,112 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
t = int(input())
for i in range(t):
inp = input()
x, y = int(inp[0]), int(inp[2])
if abs(x - y) > 1:
if x > y:
print(2 * x - 1)
else:
print(2 * y - 1)
else:
print(x + y)
```
No
| 98,113 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an infinite 2-dimensional grid. The robot stands in cell (0, 0) and wants to reach cell (x, y). Here is a list of possible commands the robot can execute:
* move north from cell (i, j) to (i, j + 1);
* move east from cell (i, j) to (i + 1, j);
* move south from cell (i, j) to (i, j - 1);
* move west from cell (i, j) to (i - 1, j);
* stay in cell (i, j).
The robot wants to reach cell (x, y) in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach (x, y) from (0, 0)?
Input
The first line contains a single integer t (1 β€ t β€ 100) β the number of testcases.
Each of the next t lines contains two integers x and y (0 β€ x, y β€ 10^4) β the destination coordinates of the robot.
Output
For each testcase print a single integer β the minimum number of commands required for the robot to reach (x, y) from (0, 0) if no command is allowed to be executed two or more times in a row.
Example
Input
5
5 5
3 4
7 1
0 0
2 0
Output
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.
Submitted Solution:
```
# This is a sample Python script.
# Press Shift+F10 to execute it or replace it with your code.
# Press Double Shift to search everywhere for classes, files, tool windows, actions, and settings.
# Use a breakpoint in the code line below to debug your sc # Press Ctrl+F8 to toggle the breakpoint.
# Press the green button in the gutter to run t
# See PyCharm help at https://www.jetbrains.com/help/pycharm/
t = int(input())
for i in range(t):
inputValues = input().split()
x = int(inputValues[0])
y = int(inputValues[1])
x = abs(x)
if x != 0:
abc = x+(x-1)
else:
abc = 0
print(abc)
```
No
| 98,114 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
import sys
#input = sys.stdin.readline
for _ in range(int(input())):
n=int(input())
a=[]
for i in range(n):
temp=input()
a.append([])
for k in temp:
a[-1].append(int(k))
input()
b=[]
for i in range(n):
temp=input()
b.append([])
for k in temp:
b[-1].append(int(k))
f=True
for i in range(n):
if a[0][i]!=b[0][i]:
new=''
for j in range(n):
a[j][i]^=1
for i in range(n):
if a[i]!=b[i]:
new=''
for j in range(n):
a[i][j]^=1
if a[i]!=b[i]:
f=False
break
if f==False:
print('NO')
else:
print('YES')
```
| 98,115 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
def check(r, i, j):
return r[i][j]^r[i+1][j+1] == r[i+1][j]^r[i][j+1]
for _ in range(int(input())):
n = int(input())
a = [list(map(int, list(input()))) for i in range(n)]
input()
b = [list(map(int, list(input()))) for i in range(n)]
r = []
for i in range(n):
r.append([])
for j in range(n):
r[i].append(a[i][j]^b[i][j])
#print(a,b,r)
i = 0
j = n-1
ans = 'YES'
for i in range(n-1):
for j in range(n-1):
if not check(r, i, j):
ans = 'NO'
break
print(ans)
```
| 98,116 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
a=[]
for j in range(n):
s=input()
c=[]
for k in s:
c.append(int(k))
a.append(c)
p=input()
b = []
for j in range(n):
s = input()
c = []
for k in s:
c.append(int(k))
b.append(c)
res=[[0 for i in range(n)] for j in range(n)]
for i in range(n):
for j in range(n):
if a[i][j]!=b[i][j]:
res[i][j]=1
if n==1:
print("YES")
else:
flag=1
i=0
while(i<n-1):
p=abs(res[0][i]-res[0][i+1])
j=1
while(j<n):
q=abs(res[j][i]-res[j][i+1])
if p!=q:
flag=0
break
j+=1
i+=1
if flag:
print("YES")
else:
print("NO")
```
| 98,117 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
import sys
from bisect import bisect_left
input = sys.stdin.readline
def solve():
n = int(input())
a = [None]*n
for i in range(n):
a[i] = list(map(int,input().strip()))
input()
for i in range(n):
j = 0
for c in map(int,input().strip()):
a[i][j] ^= c
j += 1
one = a[0]
two = [i^1 for i in a[0]]
for j in range(1, n):
if a[j] != one and a[j] != two:
print("NO")
return
print("YES")
for i in range(int(input())):
solve()
```
| 98,118 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
import sys
input = sys.stdin.readline
from collections import *
from bisect import *
for _ in range(int(input())):
n = int(input())
a = [list(map(int, input()[:-1])) for _ in range(n)]
input()
b = [list(map(int, input()[:-1])) for _ in range(n)]
flag = [False]*n
for i in range(n):
if a[0][i]!=b[0][i]:
flag[i] = True
ok = True
for i in range(1, n):
c = []
for j in range(n):
if flag[j]:
c.append(1^a[i][j])
else:
c.append(a[i][j])
xor = [c[j]^b[i][j] for j in range(n)]
if not (xor==[0]*n or xor==[1]*n):
ok = False
break
if ok:
print('YES')
continue
flag = [False]*n
for i in range(n):
if a[0][i]==b[0][i]:
flag[i] = True
ok = True
for i in range(1, n):
c = []
for j in range(n):
if flag[j]:
c.append(1^a[i][j])
else:
c.append(a[i][j])
xor = [c[j]^b[i][j] for j in range(n)]
if not (xor==[0]*n or xor==[1]*n):
ok = False
break
if ok:
print('YES')
else:
print('NO')
```
| 98,119 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
import sys
input = lambda: sys.stdin.readline().rstrip()
T = int(input())
for _ in range(T):
N = int(input())
A = [[int(a) for a in input()] for _ in range(N)]
input()
for i in range(N):
for j, a in enumerate([int(a) for a in input()]):
A[i][j] ^= a
if A[0][0]:
for j in range(N):
A[0][j] ^= 1
for j in range(N):
if A[0][j]:
for i in range(N):
A[i][j] ^= 1
for i in range(1, N):
if A[i][0]:
for j in range(N):
A[i][j] ^= 1
print("YES" if sum(sum(a) for a in A) == 0 else "NO")
```
| 98,120 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
from math import gcd, ceil
def prod(a, mod=10**9+7):
ans = 1
for each in a:
ans = (ans * each) % mod
return ans
def lcm(a, b): return a * b // gcd(a, b)
def binary(x, length=16):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
for _ in range(int(input()) if True else 1):
n = int(input())
#n, k = map(int, input().split())
#a, b = map(int, input().split())
#c, d = map(int, input().split())
#a = list(map(int, input().split()))
#b = list(map(int, input().split()))
#s = input()
a = []
b = []
for i in range(n):
a += [[int(k) for k in input()]]
s = input()
for i in range(n):
b += [[int(k) for k in input()]]
if n == 1:
print("YES")
continue
v = [-1]*n
h = [0]*n
v[0] = 0
pos = True
i = 0
for j in range(n):
diff = (b[i][j] - a[i][j]) % 2
# (v[i] + h[j]) = diff (mod 2)
h[j] = (diff - v[i]) % 2
for i in range(1, n):
for j in range(n):
diff = (b[i][j] - a[i][j]) % 2
vi = (diff - h[j]) % 2
if v[i] == -1:
v[i] = vi
elif v[i] != vi:
pos = False
break
if not pos:break
if pos:
print("YES")
continue
v = [-1] * n
h = [0] * n
v[0] = 1
pos = True
i = 0
for j in range(n):
diff = (b[i][j] - a[i][j]) % 2
# (v[i] + h[j]) = diff (mod 2)
h[j] = (diff - v[i]) % 2
for i in range(1, n):
for j in range(n):
diff = (b[i][j] - a[i][j]) % 2
vi = (diff - h[j]) % 2
if v[i] == -1:
v[i] = vi
elif v[i] != vi:
pos = False
break
if not pos: break
if pos:
print("YES")
continue
print("NO")
```
| 98,121 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Tags: 2-sat, brute force, constructive algorithms
Correct Solution:
```
import sys
input = sys.stdin.readline
t = int(input())
for _ in range(t):
n = int(input())
mat_a = []
mat_b = []
for i in range(n):
row = list(input())
mat_a.append(row)
extra = input()
for i in range(n):
row = list(input())
mat_b.append(row)
possible = True
rows = [0] * n
columns = [0] * n
for i in range(n):
for j in range(n):
if not possible: break
element_a = int(mat_a[i][j])
element_b = int(mat_b[i][j])
if (element_a ^ rows[i] ^ columns[j]) != element_b:
if i == 0 and j == 0:
rows[i] = 1
elif i == 0:
columns[j] = 1
elif j == 0:
rows[i] = 1
else:
possible = False
break
print("YES" if possible else "NO")
```
| 98,122 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
#CFR-697-F
for _ in range(int(input())):
n = int(input())
A = [tuple(map(int, input())) for _ in range(n)]
e = input()
B = [tuple(map(int, input())) for _ in range(n)]
V = [[A[i][j]^B[i][j] for j in range(n)] for i in range(n)]
#print(V)
if V[0] == [0]*n:
flag = 1
for i in range(1, n):
if V[i] != [0]*n and V[i] != [1]*n:
flag = 0
break
if flag:
print('YES')
else:
print('NO')
else:
flag = 1
for i in range(1,n):
W = [V[i][j]^V[0][j] for j in range(n)]
if W != [0]*n and W != [1]*n:
flag = 0
break
if flag:
print('YES')
else:
print('NO')
```
Yes
| 98,123 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
a=[]
for i in range(n):
a.append(input())
b=[]
input()
for i in range(n):
b.append(input())
grid=[]
for i in range(n):
grid.append([])
for j in range(n):
if a[i][j]==b[i][j]:
grid[-1].append(0)
else:
grid[-1].append(1)
first=[]
second=[]
for i in range(n):
if grid[i][0]==grid[0][0]:
first.append(0)
else:
first.append(1)
for i in range(n):
if grid[0][i]==grid[0][0]:
second.append(0)
else:
second.append(1)
flag=0
for i in range(n):
for j in range(n):
if 1^(grid[i][j]==grid[0][0])^(first[i]^second[j]):
flag=1
break
if flag:
break
if flag:
print('NO')
else:
print('YES')
```
Yes
| 98,124 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
start = []
for _ in range(n):
start.append([int(i) for i in input()])
input()
target = []
for _ in range(n):
target.append([int(i) for i in input()])
# for row in start:
# print(*row)
# print()
# for row in target:
# print(*row)
# print()
for row in range(n):
for col in range(n):
if target[row][col] == 1:
start[row][col] = 1 - start[row][col]
passed = True
val = start[0][0]
for row in range(n-1):
for col in range(n-1):
v = start[row][col]
if not(v == start[row+1][col+1] and v != start[row+1][col] and v != start[row][col+1]):
passed = False
if not passed:
break
if not passed:
break
if passed:
print('YES')
else:
switch_val = n//2 + 1
for row in start:
if sum(row) >= switch_val:
for i in range(n):
row[i] = 1 - row[i]
# for row in start:
# print(*row)
# print()
start = list(map(list, zip(*start)))
switch_val = n//2 + 1
for row in start:
if sum(row) >= switch_val:
for i in range(n):
row[i] = 1 - row[i]
# for row in start:
# print(*row)
# print()
out = 'YES'
for col in range(n):
x = sum(row[col] for row in start)
if not (x == 0 or x == n):
out = 'NO'
break
print(out)
```
Yes
| 98,125 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
from sys import stdin
from collections import defaultdict
t = int(stdin.readline())
def duoc(mata, matb):
mau = []
for col in range(n):
mau.append(1 - (mata[0][col] == matb[0][col]))
for row in range(1, n):
hang = []
for col in range(n):
if mata[row][col] == matb[row][col]:
if mau == 1:
hang.append(1)
else:
hang.append(0)
else:
if mau == 1:
hang.append(0)
else:
hang.append(1)
moc = (hang[0] + mau[0]) % 2
for col in range(1, n):
if (hang[col] + mau[col]) % 2 != moc:
return False
return True
for _ in range(t):
mata = []
matb = []
n = int(stdin.readline())
for row in range(n):
mata.append(stdin.readline()[:-1])
blank = stdin.readline()
for row in range(n):
matb.append(stdin.readline()[:-1])
if duoc(mata, matb) == True:
print('yes')
else:
print('no')
```
Yes
| 98,126 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
test=int(input())
for testcase in range(test):
n=int(input())
a=[]
b=[]
for i in range(n):
s=input()
arr=[int(x) for x in s]
a.append(arr)
space=input()
for i in range(n):
s=input()
arr=[int(x) for x in s]
b.append(arr)
if(n==1):
print("YES")
continue
for i in range(n):
if(a[0][i]!=b[0][i]):
for j in range(n):
a[j][i]=a[j][i]^1
last=True
for i in range(1,n):
flag=True
for j in range(n):
if(a[i][j]!=b[i][j]):
if(flag==True and j<n-1):
flag=False
for k in range(n):
a[i][k]=a[i][k]^1
else:
print("NO")
last=False
break
if(last==False):
break
else:
print("YES")
```
No
| 98,127 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
for _ in range(int(input())):
A = [int(input(), 2) for _ in range(int(input()))]
input()
for i, a in enumerate(A):
A[i] = a ^ int(input(), 2)
t = A.pop()
for a in A:
a ^= t
if a & (a + 1):
print('NO')
break
else:
print('YES')
```
No
| 98,128 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
import sys, io, os
if os.environ['USERNAME']=='kissz':
inp=open('in.txt','r').readline
def debug(*args):
print(*args,file=sys.stderr)
else:
inp=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def debug(*args):
pass
# SCRIPT STARTS HERE
for _ in range(int(inp())):
n=int(inp())
A=[]
for _ in range(n):
A.append([*map(int,list(inp().strip()))])
inp()
B=[]
for _ in range(n):
B.append([*map(int,list(inp().strip()))])
debug(A,B)
for i in range(n):
if A[0][i]!=B[0][i]:
for j in range(n):
A[j][i]=1-A[j][i]
for j in range(1,n):
if A[j][0]!=B[j][0]:
for i in range(n):
A[j][i]=1-A[j][i]
if A==B:
print('YES')
else:
print('NO')
```
No
| 98,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two binary square matrices a and b of size n Γ n. A matrix is called binary if each of its elements is equal to 0 or 1. You can do the following operations on the matrix a arbitrary number of times (0 or more):
* vertical xor. You choose the number j (1 β€ j β€ n) and for all i (1 β€ i β€ n) do the following: a_{i, j} := a_{i, j} β 1 (β β is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)).
* horizontal xor. You choose the number i (1 β€ i β€ n) and for all j (1 β€ j β€ n) do the following: a_{i, j} := a_{i, j} β 1.
Note that the elements of the a matrix change after each operation.
For example, if n=3 and the matrix a is: $$$ \begin{pmatrix} 1 & 1 & 0 \\\ 0 & 0 & 1 \\\ 1 & 1 & 0 \end{pmatrix} $$$ Then the following sequence of operations shows an example of transformations:
* vertical xor, j=1. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 1 & 0 & 1 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* horizontal xor, i=2. $$$ a= \begin{pmatrix} 0 & 1 & 0 \\\ 0 & 1 & 0 \\\ 0 & 1 & 0 \end{pmatrix} $$$
* vertical xor, j=2. $$$ a= \begin{pmatrix} 0 & 0 & 0 \\\ 0 & 0 & 0 \\\ 0 & 0 & 0 \end{pmatrix} $$$
Check if there is a sequence of operations such that the matrix a becomes equal to the matrix b.
Input
The first line contains one integer t (1 β€ t β€ 1000) β the number of test cases. Then t test cases follow.
The first line of each test case contains one integer n (1 β€ n β€ 1000) β the size of the matrices.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix a.
An empty line follows.
The following n lines contain strings of length n, consisting of the characters '0' and '1' β the description of the matrix b.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, output on a separate line:
* "YES", there is such a sequence of operations that the matrix a becomes equal to the matrix b;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
3
3
110
001
110
000
000
000
3
101
010
101
010
101
010
2
01
11
10
10
Output
YES
YES
NO
Note
The first test case is explained in the statements.
In the second test case, the following sequence of operations is suitable:
* horizontal xor, i=1;
* horizontal xor, i=2;
* horizontal xor, i=3;
It can be proved that there is no sequence of operations in the third test case so that the matrix a becomes equal to the matrix b.
Submitted Solution:
```
def checkZero(mat,n):
for i in range(1,n):
if mat[i]!=mat[i-1]:
for j in range(n):
mat[i][j]^=1
if mat[i]!=mat[i-1]:
return False
return True
for _ in range(int(input())):
n=int(input())
a=[]
b=[]
for i in range(n):
a.append(list(map(int,list(input()))))
input()
for i in range(n):
b.append(list(map(int,list(input()))))
if checkZero(a,n)==True and checkZero(b,n)==True:
print('YES')
else:
print('NO')
```
No
| 98,130 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is extremely busy: he is renovating his house! He needs to hand wallpaper, assemble furniture throw away trash.
Kostya is buying tiles for bathroom today. He is standing in front of a large square stand with tiles in a shop. The stand is a square of n Γ n cells, each cell of which contains a small tile with color c_{i,\,j}. The shop sells tiles in packs: more specifically, you can only buy a subsquare of the initial square.
A subsquare is any square part of the stand, i. e. any set S(i_0, j_0, k) = \\{c_{i,\,j}\ |\ i_0 β€ i < i_0 + k, j_0 β€ j < j_0 + k\} with 1 β€ i_0, j_0 β€ n - k + 1.
Kostya still does not know how many tiles he needs, so he considers the subsquares of all possible sizes. He doesn't want his bathroom to be too colorful. Help Kostya to count for each k β€ n the number of subsquares of size k Γ k that have at most q different colors of tiles. Two subsquares are considered different if their location on the stand is different.
Input
The first line contains two integers n and q (1 β€ n β€ 1500, 1 β€ q β€ 10) β the size of the stand and the limit on the number of distinct colors in a subsquare.
Each of the next n lines contains n integers c_{i,\,j} (1 β€ c_{i,\,j} β€ n^2): the j-th integer in the i-th line is the color of the tile in the cell (i,\,j).
Output
For each k from 1 to n print a single integer β the number of subsquares of size k Γ k with no more than q different colors.
Examples
Input
3 4
1 2 3
4 5 6
7 8 9
Output
9
4
0
Input
4 8
1 2 3 4
5 6 7 8
9 1 2 3
4 5 6 7
Output
16
9
4
0
Note
In the first example all colors are distinct. Kostya doesn't want the subsquare have more than 4 colors, so he can buy any subsquare of size 1 Γ 1 or 2 Γ 2, but he can't buy a subsquare of size 3 Γ 3.
In the second example there are colors that appear multiple times. Because q = 8, Kostya can buy any subsquare of size 1 Γ 1 and 2 Γ 2, and any subsquare 3 Γ 3, because of such subsquare has 7 different colors. He can't buy the whole stand 4 Γ 4, because there are 9 colors.
Submitted Solution:
```
s=input().split(" ")
n=int(s[0])
q=int(s[1])
l=[]
for i in range(n):
l.append(input().split(" "))
for j in range(n):
l[-1][j]=int(l[-1][j])
x=[]
for i in range(n):
x.append([])
for j in range(n):
x[i].append({l[i][j]:""})
if q==0:
print(0)
s=0
else:
print(n*n)
s=n*n
for p in range(1,n):
if s==0:
break
s=0
x.pop()
for i in range(n-p):
x[i].pop()
for j in range(n-p):
if len(x[i][j])<=q:
for k in range(j,j+p+1):
x[i][j].update({l[i+p][k]:""})
if len(x[i][j])>q:
break
if len(x[i][j])<=q:
for k in range(i,i+p+1):
x[i][j].update({l[k][j+p]:""})
if len(x[i][j])>q:
break
if len(x[i][j])<=q:
s+=1
print(s)
```
No
| 98,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is extremely busy: he is renovating his house! He needs to hand wallpaper, assemble furniture throw away trash.
Kostya is buying tiles for bathroom today. He is standing in front of a large square stand with tiles in a shop. The stand is a square of n Γ n cells, each cell of which contains a small tile with color c_{i,\,j}. The shop sells tiles in packs: more specifically, you can only buy a subsquare of the initial square.
A subsquare is any square part of the stand, i. e. any set S(i_0, j_0, k) = \\{c_{i,\,j}\ |\ i_0 β€ i < i_0 + k, j_0 β€ j < j_0 + k\} with 1 β€ i_0, j_0 β€ n - k + 1.
Kostya still does not know how many tiles he needs, so he considers the subsquares of all possible sizes. He doesn't want his bathroom to be too colorful. Help Kostya to count for each k β€ n the number of subsquares of size k Γ k that have at most q different colors of tiles. Two subsquares are considered different if their location on the stand is different.
Input
The first line contains two integers n and q (1 β€ n β€ 1500, 1 β€ q β€ 10) β the size of the stand and the limit on the number of distinct colors in a subsquare.
Each of the next n lines contains n integers c_{i,\,j} (1 β€ c_{i,\,j} β€ n^2): the j-th integer in the i-th line is the color of the tile in the cell (i,\,j).
Output
For each k from 1 to n print a single integer β the number of subsquares of size k Γ k with no more than q different colors.
Examples
Input
3 4
1 2 3
4 5 6
7 8 9
Output
9
4
0
Input
4 8
1 2 3 4
5 6 7 8
9 1 2 3
4 5 6 7
Output
16
9
4
0
Note
In the first example all colors are distinct. Kostya doesn't want the subsquare have more than 4 colors, so he can buy any subsquare of size 1 Γ 1 or 2 Γ 2, but he can't buy a subsquare of size 3 Γ 3.
In the second example there are colors that appear multiple times. Because q = 8, Kostya can buy any subsquare of size 1 Γ 1 and 2 Γ 2, and any subsquare 3 Γ 3, because of such subsquare has 7 different colors. He can't buy the whole stand 4 Γ 4, because there are 9 colors.
Submitted Solution:
```
False
```
No
| 98,132 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Monocarp plays a computer game called "Goblins and Gnomes". In this game, he manages a large underground city of gnomes and defends it from hordes of goblins.
The city consists of n halls and m one-directional tunnels connecting them. The structure of tunnels has the following property: if a goblin leaves any hall, he cannot return to that hall.
The city will be attacked by k waves of goblins; during the i-th wave, i goblins attack the city. Monocarp's goal is to pass all k waves.
The i-th wave goes as follows: firstly, i goblins appear in some halls of the city and pillage them; at most one goblin appears in each hall. Then, goblins start moving along the tunnels, pillaging all the halls in their path.
Goblins are very greedy and cunning, so they choose their paths so that no two goblins pass through the same hall. Among all possible attack plans, they choose a plan which allows them to pillage the maximum number of halls. After goblins are done pillaging, they leave the city.
If all halls are pillaged during the wave β Monocarp loses the game. Otherwise, the city is restored. If some hall is pillaged during a wave, goblins are still interested in pillaging it during the next waves.
Before each wave, Monocarp can spend some time preparing to it. Monocarp doesn't have any strict time limits on his preparations (he decides when to call each wave by himself), but the longer he prepares for a wave, the fewer points he gets for passing it. If Monocarp prepares for the i-th wave for t_i minutes, then he gets max(0, x_i - t_i β
y_i) points for passing it (obviously, if he doesn't lose in the process).
While preparing for a wave, Monocarp can block tunnels. He can spend one minute to either block all tunnels leading from some hall or block all tunnels leading to some hall. If Monocarp blocks a tunnel while preparing for a wave, it stays blocked during the next waves as well.
Help Monocarp to defend against all k waves of goblins and get the maximum possible amount of points!
Input
The first line contains three integers n, m and k (2 β€ n β€ 50; 0 β€ m β€ (n(n - 1))/(2); 1 β€ k β€ n - 1) β the number of halls in the city, the number of tunnels and the number of goblin waves, correspondely.
Next m lines describe tunnels. The i-th line contains two integers u_i and v_i (1 β€ u_i, v_i β€ n; u_i β v_i). It means that the tunnel goes from hall u_i to hall v_i. The structure of tunnels has the following property: if a goblin leaves any hall, he cannot return to that hall. There is at most one tunnel between each pair of halls.
Next k lines describe the scoring system. The i-th line contains two integers x_i and y_i (1 β€ x_i β€ 10^9; 1 β€ y_i β€ 10^9). If Monocarp prepares for the i-th wave for t_i minutes, then he gets max(0, x_i - t_i β
y_i) points for passing it.
Output
Print the optimal Monocarp's strategy in the following format:
At first, print one integer a (k β€ a β€ 2n + k) β the number of actions Monocarp will perform. Next, print actions themselves in the order Monocarp performs them. The i-th action is described by a single integer b_i (-n β€ b_i β€ n) using the following format:
* if b_i > 0 then Monocarp blocks all tunnels going out from the hall b_i;
* if b_i < 0 then Monocarp blocks all tunnels going into the hall |b_i|;
* if b_i = 0 then Monocarp calls the next goblin wave.
You can't repeat the same block action b_i several times. Monocarp must survive all waves he calls (goblins shouldn't be able to pillage all halls). Monocarp should call exactly k waves and earn the maximum possible number of points in total.
If there are several optimal strategies β print any of them.
Examples
Input
5 4 4
1 2
2 3
4 3
5 3
100 1
200 5
10 10
100 1
Output
6
-2 -3 0 0 0 0
Input
5 4 4
1 2
2 3
4 3
5 3
100 100
200 5
10 10
100 1
Output
6
0 -3 0 0 1 0
Input
5 10 1
1 2
1 3
1 4
1 5
5 2
5 3
5 4
4 2
4 3
2 3
100 100
Output
6
1 2 3 4 5 0
Note
In the first example, Monocarp, firstly, block all tunnels going in hall 2, secondly β all tunnels going in hall 3, and after that calls all waves. He spent two minutes to prepare to wave 1, so he gets 98 points for it. He didn't prepare after that, that's why he gets maximum scores for each of next waves (200, 10 and 100). In total, Monocarp earns 408 points.
In the second example, Monocarp calls for the first wave immediately and gets 100 points. Before the second wave he blocks all tunnels going in hall 3. He spent one minute preparing to the wave, so he gets 195 points. Monocarp didn't prepare for the third wave, so he gets 10 points by surviving it. Before the fourth wave he blocks all tunnels going out from hall 1. He spent one minute, so he gets 99 points for the fourth wave. In total, Monocarp earns 404 points.
In the third example, it doesn't matter how many minutes Monocarp will spend before the wave, since he won't get any points for it. That's why he decides to block all tunnels in the city, spending 5 minutes. He survived the wave though without getting any points.
Submitted Solution:
```
a=input()
if a==('Aska'):
print(a)
```
No
| 98,133 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Tags: brute force
Correct Solution:
```
x,y=input(),input()
res=[0]*len(x)
dicc ={i:[] for i in "abcdefghijklmnopqrstuvwxyz"}
for i,j in enumerate(x):
dicc[j].append(i)
for i in y:
for j in dicc[i]:
res[j]+=1
res=[0]+res
print(len(y)-max(res))
```
| 98,134 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Tags: brute force
Correct Solution:
```
#------------------------template--------------------------#
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
ALPHA='abcdefghijklmnopqrstuvwxyz'
M=10**9+7
EPS=1e-6
def value():return tuple(map(int,input().split()))
def array():return [int(i) for i in input().split()]
def Int():return int(input())
def Str():return input()
def arrayS():return [i for i in input().split()]
#-------------------------code---------------------------#
# vsInput()
def cost(x):
ans=0
for i in range(len(t)):
ans+=s[i+x]!=t[i]
return ans
s=input()
t=input()
n=len(s)
ans=inf
s='/'*(len(t))+s+'/'*(len(t))
for i in range(n+2*len(t)-len(t)):
ans=min(ans,cost(i))
print(ans)
```
| 98,135 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Tags: brute force
Correct Solution:
```
aa = input()
bb = input()
if len(aa) >= len(bb):
p = aa
q = bb
else:
p = aa
q = bb
maxc = 0
for i in range(1,len(p)+len(q)):
k1 = max(0,i-len(q))
k2 = min(i,len(p))
a = p[k1:k2]
if i < len(q):
b = q[-i:]
elif i > len(p):
b = q[:-(i-len(p))]
else:
b = q
c = 0
for j in range(len(a)):
if a[j] == b[j]:
c += 1
if c > maxc:
maxc = c
print(len(bb)-maxc)
```
| 98,136 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Tags: brute force
Correct Solution:
```
x,y=input(),input()
t=[0]*len(x)
p={i:[] for i in "abcdefghijklmnopqrstuvwxyz"}
for i,j in enumerate(x):
p[j].append(i)
#print(p)
for i in y:
for j in p[i]:
t[j]+=1
t=[0]+t
print(len(y)-max(t))
# Made By Mostafa_Khaled
```
| 98,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Submitted Solution:
```
#------------------------template--------------------------#
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
ALPHA='abcdefghijklmnopqrstuvwxyz'
M=10**9+7
EPS=1e-6
def value():return tuple(map(int,input().split()))
def array():return [int(i) for i in input().split()]
def Int():return int(input())
def Str():return input()
def arrayS():return [i for i in input().split()]
#-------------------------code---------------------------#
# vsInput()
def cost(x):
temp=s[x:]
ans=0
i=0
while(i<len(t) and t[i]!=temp[0]):
i+=1
ans+=1
start=i
while(i<len(t) and i-start<len(temp)):
ans+=t[i]!=temp[i-start]
i+=1
# print(ans)
ans+=len(t)-i
# print(temp,ans,i)
return ans
s=input()
t=input()
n=len(s)
ans=inf
for i in range(n):
ans=min(ans,cost(i))
s=s[::-1]
t=t[::-1]
for i in range(n):
ans=min(ans,cost(i))
print(ans)
```
No
| 98,138 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Submitted Solution:
```
s= input()
s1 = input()
count =1
for i in range(len(s1)):
if s1[:count] in s:
count+=1
if count==1:
for i in set(s1):
if i in s:
count+=1
print(len(s1)-count+1)
```
No
| 98,139 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Submitted Solution:
```
s= input()
s1 = input()
count =1
for i in range(len(s1)):
if s1[:count] in s:
count+=1
print(len(s1)-count+1)
```
No
| 98,140 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s.
String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".
Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions:
* Insert one letter to any end of the string.
* Delete one letter from any end of the string.
* Change one letter into any other one.
Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u.
Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it.
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.
Output
Print the only integer β the minimum number of changes that Dr. Moriarty has to make with the string that you choose.
Examples
Input
aaaaa
aaa
Output
0
Input
abcabc
bcd
Output
1
Input
abcdef
klmnopq
Output
7
Note
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes.
In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.
In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.
Submitted Solution:
```
#------------------------template--------------------------#
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
ALPHA='abcdefghijklmnopqrstuvwxyz'
M=10**9+7
EPS=1e-6
def value():return tuple(map(int,input().split()))
def array():return [int(i) for i in input().split()]
def Int():return int(input())
def Str():return input()
def arrayS():return [i for i in input().split()]
#-------------------------code---------------------------#
# vsInput()
def cost(x):
temp=s[x:+len(t)]
ans=len(t)-len(temp)
for i in range(len(temp)):
ans+=t[i]!=temp[i]
return ans
s=input()
t=input()
n=len(s)
ans=len(t)
for i in range(n):
ans=min(ans,cost(i))
print(ans)
```
No
| 98,141 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
import sys
def getMultiLineInput() -> []:
lines = []
while True:
try:
lines.append(input())
except EOFError:
break
return lines
def printResult(number: int, inputs: []):
#
result = 0
#
for i in range(0, number - 1):
tValue = 0
while i + pow(2, tValue) < number:
tValue += 1
t_last = i + pow(2, tValue - 1)
val = inputs[i]
inputs[i] -= val
inputs[t_last] += val
result += val
print(result)
# main
inputs = getMultiLineInput()
count = int(inputs[0])
inputs = list(map(lambda x: int(x), inputs[1].split()))
printResult(count, inputs)
```
| 98,142 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
__author__ = 'Esfandiar'
from math import log2
n = int(input())
a = list(map(int,input().split()))
res = 0
for i in range(n-1):
res+=a[i]
print(res)
y=n-(i+1)
a[i+(2**(int(log2(y))))]+=a[i]
```
| 98,143 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
from math import inf,sqrt,floor,ceil
from collections import Counter,defaultdict,deque
from heapq import heappush as hpush,heappop as hpop,heapify as h
from operator import itemgetter
from itertools import product
from bisect import bisect_left,bisect_right
#for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split( )))
ans=0
for i in range(n-1):
start=1
while i+start*2<n:
start*=2
a[i+start]+=a[i]
ans+=a[i]
print(ans)
```
| 98,144 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
import sys
import math
#to read string
get_string = lambda: sys.stdin.readline().strip()
#to read list of integers
get_int_list = lambda: list( map(int,sys.stdin.readline().strip().split()) )
#to read integers
get_int = lambda: int(sys.stdin.readline())
#--------------------------------WhiteHat010--------------------------------------#
n = get_int()
lst = get_int_list()
prev = 0
for i in range(n-1):
t = int( math.log( n-i-1 , 2 ) )
prev = prev + lst[i]
lst[2**t + i] += lst[i]
print(prev)
```
| 98,145 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
mod = 1000000007
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())
n=ii()
l=il()
i=0
while 2**i<=n-1:
i+=1
i-=1
sm=0
for j in range(n-1):
if j+2**i>n-1:
i-=1
sm+=l[j]
l[j+2**i]+=l[j]
print(sm)
if n==1:
print(0)
```
| 98,146 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
def findP2(n):
l = len(bin(n)) - 3
l = "1" + "0" * l
l = int(l, 2)
if l == n: l //= 2
return l
N = int(input())
L = list(map(int, input().split()))
last = 0
for i in range(N - 1):
tp2 = findP2(N - i)
last += L[i]
L[tp2 + i] += L[i]
L[i] = 0
print(last)
```
| 98,147 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
import math
n=int(input())
a=list(map(int,input().split()))
l=[]
c=0
for i in range(1,n):
p=(math.floor(math.log2(n-i)))
l.append(p)
c=c+a[i-1]
a[i+2**p-1]=a[i+2**p-1]+a[i-1]
print(c)
```
| 98,148 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Tags: greedy
Correct Solution:
```
from collections import deque, defaultdict, Counter
from itertools import product, groupby, permutations, combinations, accumulate
from math import gcd, floor, inf, log2, sqrt, log10
from bisect import bisect_right, bisect_left
from statistics import mode
from string import ascii_uppercase
power_of_two = lambda number: int(log2(number))
num = int(input())
arr = list(map(int, input().split()))
new_arr = arr[::]
for i, n in enumerate(arr[:-1], start=1):
t = power_of_two(num-i)
ind = i + 2**t -1
new_arr[ind] += new_arr[i-1]
presum = list(accumulate(new_arr))
presum.pop()
for i in presum:
print(i)
```
| 98,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Submitted Solution:
```
def main():
from math import floor, log2
n = int(input())
numbers = [0] + [int(_) for _ in input().split()]
moves = [0] * (n + 1)
for i in range(1, n):
t = floor(log2(n - i))
j = i + 2 ** t
moves[i] = numbers[i]
numbers[j] += numbers[i]
numbers[i] = 0
for i in range(2, n):
moves[i] += moves[i - 1]
print('\n'.join([str(moves[i]) for i in range(1, n)]))
if __name__ == '__main__':
main()
```
Yes
| 98,150 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Submitted Solution:
```
import math
def calc_max_pow(i, n):
return int(math.log(n - i, 2) // 1)
n = int(input())
sequence = input().split(' ')
for i in range(n):
sequence[i] = int(sequence[i])
moves_before = 0
for i in range(n - 1):
moves_before += sequence[i]
print(moves_before)
max_pow_to_move = calc_max_pow(i + 1, n)
move_to = pow(2, max_pow_to_move) + i
sequence[move_to] += sequence[i]
```
Yes
| 98,151 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Submitted Solution:
```
from math import log2
c = 0
n = int(input())
a = list(map(int, input().split()))
for i in range(n - 1):
c += a[i]
j = 2 ** int(log2(n - i-1)) + i
a[j] += a[i]
print(c)
```
Yes
| 98,152 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Submitted Solution:
```
from math import log2
n = int(input())
a = list(map(int,input().split()))
res = 0
for i in range(n-1):
res+=a[i]
print(res)
y=n-(i+1)
a[i+(2**(int(log2(y))))]+=a[i]
```
Yes
| 98,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Submitted Solution:
```
mod = 1000000007
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())
n=ii()
l=il()
i=0
while 2**i<n-1:
i+=1
i-=1
sm=0
for j in range(n-1):
if j+2**i>n-1:
i-=1
sm+=l[j]
l[j+2**i]+=l[j]
print(sm)
```
No
| 98,154 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 β€ i β€ n) such that ai > 0 and an integer t (t β₯ 0) such that i + 2t β€ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 β€ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 β€ ai β€ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 β€ n β€ 300
The input limitations for getting 50 points are:
* 1 β€ n β€ 2000
The input limitations for getting 100 points are:
* 1 β€ n β€ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
Submitted Solution:
```
mod = 1000000007
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())
n=ii()
l=il()
i=0
while 2**i<n-1:
i+=1
i-=1
sm=0
for j in range(n-1):
if j+2**i>n-1:
i-=1
sm+=l[j]
l[j+2**i]+=l[j]
print(sm)
if n==1:
print(0)
```
No
| 98,155 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pete and Bob invented a new interesting game. Bob takes a sheet of paper and locates a Cartesian coordinate system on it as follows: point (0, 0) is located in the bottom-left corner, Ox axis is directed right, Oy axis is directed up. Pete gives Bob requests of three types:
* add x y β on the sheet of paper Bob marks a point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is not yet marked on Bob's sheet at the time of the request.
* remove x y β on the sheet of paper Bob erases the previously marked point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is already marked on Bob's sheet at the time of the request.
* find x y β on the sheet of paper Bob finds all the marked points, lying strictly above and strictly to the right of point (x, y). Among these points Bob chooses the leftmost one, if it is not unique, he chooses the bottommost one, and gives its coordinates to Pete.
Bob managed to answer the requests, when they were 10, 100 or 1000, but when their amount grew up to 2Β·105, Bob failed to cope. Now he needs a program that will answer all Pete's requests. Help Bob, please!
Input
The first input line contains number n (1 β€ n β€ 2Β·105) β amount of requests. Then there follow n lines β descriptions of the requests. add x y describes the request to add a point, remove x y β the request to erase a point, find x y β the request to find the bottom-left point. All the coordinates in the input file are non-negative and don't exceed 109.
Output
For each request of type find x y output in a separate line the answer to it β coordinates of the bottommost among the leftmost marked points, lying strictly above and to the right of point (x, y). If there are no points strictly above and to the right of point (x, y), output -1.
Examples
Input
7
add 1 1
add 3 4
find 0 0
remove 1 1
find 0 0
add 1 1
find 0 0
Output
1 1
3 4
1 1
Input
13
add 5 5
add 5 6
add 5 7
add 6 5
add 6 6
add 6 7
add 7 5
add 7 6
add 7 7
find 6 6
remove 7 7
find 6 6
find 4 4
Output
7 7
-1
5 5
Submitted Solution:
```
import bisect
n = int(input())
points = list()
x_points = list()
corresponding_y_points = list()
y_points = list()
corresponding_x_points = list()
def insert_point(point):
index = bisect.bisect(points, point)
points.insert(index, point)
index = bisect.bisect(x_points, point[0])
x_points.insert(index, point[0])
corresponding_y_points.insert(index, point[1])
index = bisect.bisect(y_points, point[1])
y_points.insert(index, point[1])
corresponding_x_points.insert(index, point[0])
def find_first_and_second_point(point, x=True):
if x:
first_point = point[0]
second_point = point[1]
else:
first_point = point[1]
second_point = point[0]
return first_point, second_point
def find_index_point_to_remove(ordered_points, corresponding_points, point, x=True):
first_point, second_point = find_first_and_second_point(point, x)
first_index = bisect.bisect_left(ordered_points, first_point)
second_index = first_index
for index in range(first_index, len(ordered_points)):
if ordered_points[index] != ordered_points[first_index]:
break
if corresponding_points[index] == second_point:
second_index = index
break
return second_index
def remove_point(point):
points.remove(point)
del corresponding_y_points[find_index_point_to_remove(x_points, corresponding_y_points, point)]
x_points.remove(current_point[0])
del corresponding_x_points[find_index_point_to_remove(y_points, corresponding_x_points, point, False)]
y_points.remove(current_point[1])
def find_point(ordered_points, corresponding_points, point, x=True):
first_point, second_point = find_first_and_second_point(point, x)
first_index = bisect.bisect_left(ordered_points, first_point + 1)
if first_index >= len(ordered_points):
return -1, -1
found = False
for index in range(first_index, len(ordered_points)):
if corresponding_points[index] > second_point:
first_index = index
found = True
break
if not found:
return -1, -1
min_point = corresponding_points[first_index]
second_index = first_index
for index in range(first_index + 1, len(ordered_points)):
if ordered_points[index] != ordered_points[first_index]:
break
if corresponding_points[index] < min_point:
min_point = corresponding_points[index]
second_index = index
return first_index, second_index
for _ in range(n):
request = input().split()
current_point = (int(request[1]), int(request[2]))
if "add" in request:
insert_point(current_point)
elif "remove" in request:
remove_point(current_point)
else:
first_index_x, first_index_y = find_point(x_points, corresponding_y_points, current_point)
second_index_y, second_index_x = find_point(y_points, corresponding_x_points, current_point, False)
if first_index_x == -1 and second_index_x == -1:
print("-1")
else:
if x_points[first_index_x] > current_point[0] and corresponding_y_points[first_index_y] > current_point[1]:
print(x_points[first_index_x], corresponding_y_points[first_index_y])
elif corresponding_x_points[second_index_x] > current_point[0] and y_points[second_index_y] > current_point[1]:
print(corresponding_x_points[second_index_x], y_points[second_index_y])
else:
print("-1")
```
No
| 98,156 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pete and Bob invented a new interesting game. Bob takes a sheet of paper and locates a Cartesian coordinate system on it as follows: point (0, 0) is located in the bottom-left corner, Ox axis is directed right, Oy axis is directed up. Pete gives Bob requests of three types:
* add x y β on the sheet of paper Bob marks a point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is not yet marked on Bob's sheet at the time of the request.
* remove x y β on the sheet of paper Bob erases the previously marked point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is already marked on Bob's sheet at the time of the request.
* find x y β on the sheet of paper Bob finds all the marked points, lying strictly above and strictly to the right of point (x, y). Among these points Bob chooses the leftmost one, if it is not unique, he chooses the bottommost one, and gives its coordinates to Pete.
Bob managed to answer the requests, when they were 10, 100 or 1000, but when their amount grew up to 2Β·105, Bob failed to cope. Now he needs a program that will answer all Pete's requests. Help Bob, please!
Input
The first input line contains number n (1 β€ n β€ 2Β·105) β amount of requests. Then there follow n lines β descriptions of the requests. add x y describes the request to add a point, remove x y β the request to erase a point, find x y β the request to find the bottom-left point. All the coordinates in the input file are non-negative and don't exceed 109.
Output
For each request of type find x y output in a separate line the answer to it β coordinates of the bottommost among the leftmost marked points, lying strictly above and to the right of point (x, y). If there are no points strictly above and to the right of point (x, y), output -1.
Examples
Input
7
add 1 1
add 3 4
find 0 0
remove 1 1
find 0 0
add 1 1
find 0 0
Output
1 1
3 4
1 1
Input
13
add 5 5
add 5 6
add 5 7
add 6 5
add 6 6
add 6 7
add 7 5
add 7 6
add 7 7
find 6 6
remove 7 7
find 6 6
find 4 4
Output
7 7
-1
5 5
Submitted Solution:
```
a=[]
n=0
for i in range(int(input())):
b,x,y=input().split()
x=int(x)
y=int(y)
c=n/2
d=round(c/2)
d=min(d,n-1)
d=max(d,0)
while round(c)>0:
if a[d][0]>x and a[d][1]>y:
d+=round(c/2)
d=min(d,n-1)
d=max(d,0)
else:
d-=round(c/2)
d=min(d,n-1)
d=max(d,0)
c/=2
while 0<d and a[d][0]>x and a[d][1]>y:
d-=1
while d<n-1 and (a[d][0]<=x or a[d][1]<=y):
d+=1
if b=='add':
n+=1
if d>=n-1 or (a[d][0]>=x and a[d][1]>=y):
a=a[:d]+[[x,y]]+a[d:]
else:
a=a[:d+1]+[[x,y]]+a[d+1:]
elif b=='remove':
d+=1
d=min(d,n-1)
while a[d][0]!=x and a[d][1]!=y:
d-=1
a=a[:d]+a[d+1:]
n-=1
else:
if d>=n or (d==n-1 and (a[d][0]==x or a[d][1]==y)):
print(-1)
else:
if a[d][0]==x or a[d][1]==y:
print(*a[d+1])
else:
print(*a[d])
```
No
| 98,157 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pete and Bob invented a new interesting game. Bob takes a sheet of paper and locates a Cartesian coordinate system on it as follows: point (0, 0) is located in the bottom-left corner, Ox axis is directed right, Oy axis is directed up. Pete gives Bob requests of three types:
* add x y β on the sheet of paper Bob marks a point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is not yet marked on Bob's sheet at the time of the request.
* remove x y β on the sheet of paper Bob erases the previously marked point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is already marked on Bob's sheet at the time of the request.
* find x y β on the sheet of paper Bob finds all the marked points, lying strictly above and strictly to the right of point (x, y). Among these points Bob chooses the leftmost one, if it is not unique, he chooses the bottommost one, and gives its coordinates to Pete.
Bob managed to answer the requests, when they were 10, 100 or 1000, but when their amount grew up to 2Β·105, Bob failed to cope. Now he needs a program that will answer all Pete's requests. Help Bob, please!
Input
The first input line contains number n (1 β€ n β€ 2Β·105) β amount of requests. Then there follow n lines β descriptions of the requests. add x y describes the request to add a point, remove x y β the request to erase a point, find x y β the request to find the bottom-left point. All the coordinates in the input file are non-negative and don't exceed 109.
Output
For each request of type find x y output in a separate line the answer to it β coordinates of the bottommost among the leftmost marked points, lying strictly above and to the right of point (x, y). If there are no points strictly above and to the right of point (x, y), output -1.
Examples
Input
7
add 1 1
add 3 4
find 0 0
remove 1 1
find 0 0
add 1 1
find 0 0
Output
1 1
3 4
1 1
Input
13
add 5 5
add 5 6
add 5 7
add 6 5
add 6 6
add 6 7
add 7 5
add 7 6
add 7 7
find 6 6
remove 7 7
find 6 6
find 4 4
Output
7 7
-1
5 5
Submitted Solution:
```
l = int(input())
items = []
points = []
for i in range(l):
item = input().split()
item[1] = int(item[1])
item[2] = int(item[2])
items.append(item)
for item in items:
if item[0] == 'add':
points.append(item[1:])
points.sort(key=lambda point: point[0])
elif item[0] == 'remove':
points.remove(item[1:])
else:
check = 0
for point in points:
if point[0] > item[1] and point[1] > item[2]:
check = 1
print(point[0], point[1])
break;
if (not check):
print(-1)
```
No
| 98,158 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pete and Bob invented a new interesting game. Bob takes a sheet of paper and locates a Cartesian coordinate system on it as follows: point (0, 0) is located in the bottom-left corner, Ox axis is directed right, Oy axis is directed up. Pete gives Bob requests of three types:
* add x y β on the sheet of paper Bob marks a point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is not yet marked on Bob's sheet at the time of the request.
* remove x y β on the sheet of paper Bob erases the previously marked point with coordinates (x, y). For each request of this type it's guaranteed that point (x, y) is already marked on Bob's sheet at the time of the request.
* find x y β on the sheet of paper Bob finds all the marked points, lying strictly above and strictly to the right of point (x, y). Among these points Bob chooses the leftmost one, if it is not unique, he chooses the bottommost one, and gives its coordinates to Pete.
Bob managed to answer the requests, when they were 10, 100 or 1000, but when their amount grew up to 2Β·105, Bob failed to cope. Now he needs a program that will answer all Pete's requests. Help Bob, please!
Input
The first input line contains number n (1 β€ n β€ 2Β·105) β amount of requests. Then there follow n lines β descriptions of the requests. add x y describes the request to add a point, remove x y β the request to erase a point, find x y β the request to find the bottom-left point. All the coordinates in the input file are non-negative and don't exceed 109.
Output
For each request of type find x y output in a separate line the answer to it β coordinates of the bottommost among the leftmost marked points, lying strictly above and to the right of point (x, y). If there are no points strictly above and to the right of point (x, y), output -1.
Examples
Input
7
add 1 1
add 3 4
find 0 0
remove 1 1
find 0 0
add 1 1
find 0 0
Output
1 1
3 4
1 1
Input
13
add 5 5
add 5 6
add 5 7
add 6 5
add 6 6
add 6 7
add 7 5
add 7 6
add 7 7
find 6 6
remove 7 7
find 6 6
find 4 4
Output
7 7
-1
5 5
Submitted Solution:
```
import bisect
n = int(input())
points = list()
x_points = list()
corresponding_y_points = list()
for _ in range(n):
request = input().split()
current_point = (int(request[1]), int(request[2]))
if "add" in request:
index = bisect.bisect(points, current_point)
points.insert(index, current_point)
index = bisect.bisect(x_points, current_point[0])
x_points.insert(index, current_point[0])
corresponding_y_points.insert(index, current_point[1])
elif "remove" in request:
points.remove(current_point)
index_x = bisect.bisect_left(x_points, current_point[0])
index_y = index_x
for index in range(index_x, len(x_points)):
if x_points[index] != x_points[index_x]:
break
if corresponding_y_points[index] == current_point[1]:
index_y = index
break
del corresponding_y_points[index_y]
x_points.remove(current_point[0])
else:
try:
index_x = bisect.bisect_left(x_points, current_point[0] + 1)
for index in range(index_x, len(x_points)):
if corresponding_y_points[index] > current_point[1]:
index_x = index
break
y_min = corresponding_y_points[index_x]
index_y = index_x
for index in range(index_x, len(x_points)):
if x_points[index] != x_points[index_x]:
break
if corresponding_y_points[index] < y_min:
y_min = corresponding_y_points[index]
index_y = index
if x_points[index_x] > current_point[0] and corresponding_y_points[index_y] > current_point[1]:
print(x_points[index_x], corresponding_y_points[index_y])
else:
print("-1")
except Exception:
print("-1")
```
No
| 98,159 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A graph is called planar, if it can be drawn in such a way that its edges intersect only at their vertexes.
An articulation point is such a vertex of an undirected graph, that when removed increases the number of connected components of the graph.
A bridge is such an edge of an undirected graph, that when removed increases the number of connected components of the graph.
You've got a connected undirected planar graph consisting of n vertexes, numbered from 1 to n, drawn on the plane. The graph has no bridges, articulation points, loops and multiple edges. You are also given q queries. Each query is a cycle in the graph. The query response is the number of graph vertexes, which (if you draw a graph and the cycle on the plane) are located either inside the cycle, or on it. Write a program that, given the graph and the queries, will answer each query.
Input
The first line contains two space-separated integers n and m (3 β€ n, m β€ 105) β the number of vertexes and edges of the graph. Next m lines contain the edges of the graph: the i-th line contains two space-separated integers ui and vi (1 β€ ui, vi β€ n) β the numbers of vertexes, connecting the i-th edge. The next n lines contain the positions of the planar graph vertexes on the plane: the i-th line contains a pair of space-separated integers xi and yi (|xi|, |yi| β€ 109) β the coordinates of the i-th vertex of the graph on the plane.
The next line contains integer q (1 β€ q β€ 105) β the number of queries. Then follow q lines that describe the queries: the i-th line contains the sequence of space-separated integers ki, a1, a2, ..., aki (1 β€ aj β€ n; ki > 2), where ki is the cycle length in the i-th query, aj are numbers of the vertexes that form a cycle. The numbers of vertexes in the cycle are given in the clockwise or counterclockwise order. The given cycles are simple, that is they cannot go through a graph vertex more than once. The total length of all cycles in all queries does not exceed 105.
It is guaranteed that the given graph contains no bridges, articulation points, loops and multiple edges. It is guaranteed that the edge segments can have common points only at the graph's vertexes.
Output
For each query print a single integer β the number of vertexes inside the cycle or on it. Print the answers in the order, in which the queries follow in the input. Separate the numbers by spaces.
Examples
Input
3 3
1 2
2 3
3 1
0 0
1 0
0 1
1
3 1 2 3
Output
3
Input
5 8
1 2
2 3
3 4
4 1
1 5
2 5
3 5
4 5
0 0
2 0
2 2
0 2
1 1
1
4 1 2 3 4
Output
5
Input
4 5
1 2
2 3
3 4
4 1
2 4
0 0
1 0
1 1
0 1
3
3 1 2 4
3 4 2 3
4 1 2 3 4
Output
3
3
4
Submitted Solution:
```
l=input()
l=l.split(' ')
m=int(l.pop())
n=int(l.pop())
edges=[]
for k in range(m):
l=input()
l=l.split(' ')
b=int(l.pop())
a=int(l.pop())
edges.append([a,b])
positions=[]
for k in range(n):
l=input()
l=l.split(' ')
b=int(l.pop())
a=int(l.pop())
positions.append([a,b])
q=int(input())
queries=[]
for k in range(q):
l=input()
l=l.split(' ')
r=len(l)
liste=[]
for k in range(r):
liste.append(positions[int(l[k])-1])
queries.append(liste)
def distance(a,b):
return sqrt((a[0]-b[0])**2+(a[1]-b[1])**2)
def point_in_poly(x,y,poly):
n = len(poly)
inside = False
p1x,p1y = poly[0]
for i in range(n+1):
p2x,p2y = poly[i % n]
if y > min(p1y,p2y):
if y <= max(p1y,p2y):
if x <= max(p1x,p2x):
if p1y != p2y:
xints = (y-p1y)*(p2x-p1x)/(p2y-p1y)+p1x
if p1x == p2x or x <= xints:
inside = not inside
p1x,p1y = p2x,p2y
return inside
for k in range(q):
V=queries[k]
compteur=0
for point in positions:
if point_in_poly(point[0],point[1],V)==True and point not in V:
compteur+=1
compteur+=len(V)-1
print(compteur)
```
No
| 98,160 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It's a beautiful April day and Wallace is playing football with his friends. But his friends do not know that Wallace actually stayed home with Gromit and sent them his robotic self instead. Robo-Wallace has several advantages over the other guys. For example, he can hit the ball directly to the specified point. And yet, the notion of a giveaway is foreign to him. The combination of these features makes the Robo-Wallace the perfect footballer β as soon as the ball gets to him, he can just aim and hit the goal. He followed this tactics in the first half of the match, but he hit the goal rarely. The opposing team has a very good goalkeeper who catches most of the balls that fly directly into the goal. But Robo-Wallace is a quick thinker, he realized that he can cheat the goalkeeper. After all, they are playing in a football box with solid walls. Robo-Wallace can kick the ball to the other side, then the goalkeeper will not try to catch the ball. Then, if the ball bounces off the wall and flies into the goal, the goal will at last be scored.
Your task is to help Robo-Wallace to detect a spot on the wall of the football box, to which the robot should kick the ball, so that the ball bounces once and only once off this wall and goes straight to the goal. In the first half of the match Robo-Wallace got a ball in the head and was severely hit. As a result, some of the schemes have been damaged. Because of the damage, Robo-Wallace can only aim to his right wall (Robo-Wallace is standing with his face to the opposing team's goal).
The football box is rectangular. Let's introduce a two-dimensional coordinate system so that point (0, 0) lies in the lower left corner of the field, if you look at the box above. Robo-Wallace is playing for the team, whose goal is to the right. It is an improvised football field, so the gate of Robo-Wallace's rivals may be not in the middle of the left wall.
<image>
In the given coordinate system you are given:
* y1, y2 β the y-coordinates of the side pillars of the goalposts of robo-Wallace's opponents;
* yw β the y-coordinate of the wall to which Robo-Wallace is aiming;
* xb, yb β the coordinates of the ball's position when it is hit;
* r β the radius of the ball.
A goal is scored when the center of the ball crosses the OY axis in the given coordinate system between (0, y1) and (0, y2). The ball moves along a straight line. The ball's hit on the wall is perfectly elastic (the ball does not shrink from the hit), the angle of incidence equals the angle of reflection. If the ball bounces off the wall not to the goal, that is, if it hits the other wall or the goal post, then the opposing team catches the ball and Robo-Wallace starts looking for miscalculation and gets dysfunctional. Such an outcome, if possible, should be avoided. We assume that the ball touches an object, if the distance from the center of the ball to the object is no greater than the ball radius r.
Input
The first and the single line contains integers y1, y2, yw, xb, yb, r (1 β€ y1, y2, yw, xb, yb β€ 106; y1 < y2 < yw; yb + r < yw; 2Β·r < y2 - y1).
It is guaranteed that the ball is positioned correctly in the field, doesn't cross any wall, doesn't touch the wall that Robo-Wallace is aiming at. The goal posts can't be located in the field corners.
Output
If Robo-Wallace can't score a goal in the described manner, print "-1" (without the quotes). Otherwise, print a single number xw β the abscissa of his point of aiming.
If there are multiple points of aiming, print the abscissa of any of them. When checking the correctness of the answer, all comparisons are made with the permissible absolute error, equal to 10 - 8.
It is recommended to print as many characters after the decimal point as possible.
Examples
Input
4 10 13 10 3 1
Output
4.3750000000
Input
1 4 6 2 2 1
Output
-1
Input
3 10 15 17 9 2
Output
11.3333333333
Note
Note that in the first and third samples other correct values of abscissa xw are also possible.
Tags: binary search, geometry
Correct Solution:
```
from math import hypot
y1, y2, yw, xb, yb, r = map(int, input().split())
yw -= r
y1, y2 = yw * 2 - y2, yw * 2 - y1
def xww(y):
return (y - yw) * xb / (y - yb)
def dd(y):
xw = xww(y)
return (y - y1) / hypot(1, (yw - y) / xw)
def binary_search():
a, b = y1 + r, 1e10
for i in range(200):
m = (a + b) / 2
if dd(m) < r:
a = m
else:
b= m
return (a + b) / 2
m = binary_search()
if m + r > y2:
print("-1")
else:
m = (m + y2 - r) / 2
print(xww(m))
```
| 98,161 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Tags: combinatorics, math, sortings
Correct Solution:
```
n = input()
c_n = {}
d_n = {}
for a_i, b_i in zip(input().split(), input().split()):
if a_i == b_i:
d_n[a_i] = d_n.get(a_i,0) + 2
c_n[a_i] = c_n.get(a_i,0) + 1
c_n[b_i] = c_n.get(b_i,0) + 1
result = 1
k = int(input())
for a_i, cant in c_n.items():
cant_rep = d_n.get(a_i,0)
for i in range(cant - cant_rep + 1, cant, 2): result = (result * i * (i + 1) // 2) % k
for i in range(1, cant - cant_rep + 1): result = (result * i) % k
print(result)
```
| 98,162 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Tags: combinatorics, math, sortings
Correct Solution:
```
n = int(input())
c, d = {}, {}
for x, y in zip(input().split(), input().split()):
c[x] = c.get(x, 1) + 1
c[y] = c.get(y, 1) + 1
if x == y: d[x] = d.get(x, 0) + 2
s, m = 1, int(input())
for k, v in c.items():
u = d.get(k, 0)
for i in range(v - u, v, 2): s = s * (i * i + i) // 2 % m
for i in range(1, v - u): s = s * i % m
print(s)
```
| 98,163 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Tags: combinatorics, math, sortings
Correct Solution:
```
from collections import defaultdict
def factorial(n, m, rep):
r = 1
for i in range(2, n + 1):
j = i
while j % 2 == 0 and rep > 0:
j = j// 2
rep -= 1
r *= j
r %= m
return r
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
m=int(input())
ans=1
d=defaultdict(lambda:0)
e=defaultdict(lambda:0)
i=0
while(i<n):
d[a[i]]+=1
d[b[i]]+=1
if a[i]==b[i]:
e[a[i]]+=1
i+=1
ans=1
for j in d:
k=d[j]
rep=e[j]
ans=(ans*factorial(k,m,rep))
ans=ans%m
print(int(ans))
```
| 98,164 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Tags: combinatorics, math, sortings
Correct Solution:
```
n=int(input())
y=list(map(int,input().split()))
z=list(map(int,input().split()))
a=sorted([[y[i],i] for i in range(n)]+[[z[i],i] for i in range(n)])
f=0
for i in range(n):
if y[i]==z[i]:
f+=1
m=int(input())
d=0
e=1
for i in range(1,2*n):
if a[i][0]!=a[i-1][0]:
for j in range(1,i-d+1):
while f>0 and j%2==0:
j//=2
f-=1
e*=j
e%=m
d=i
for j in range(1,2*n-d+1):
while f>0 and j%2==0:
j//=2
f-=1
e*=j
e%=m
print(e%m)
```
| 98,165 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Tags: combinatorics, math, sortings
Correct Solution:
```
from math import sqrt,ceil,gcd
from collections import defaultdict
def modInverse(b,m):
g = gcd(b, m)
if (g != 1):
# print("Inverse doesn't exist")
return -1
else:
# If b and m are relatively prime,
# then modulo inverse is b^(m-2) mode m
return pow(b, m - 2, m)
def sol(n,m,rep):
r = 1
for i in range(2,n+1):
j = i
while j%2 == 0 and rep>0:
j//=2
rep-=1
r*=j
r%=m
return r
def solve():
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
m = int(input())
hash = defaultdict(int)
e = defaultdict(int)
for i in range(n):
hash[a[i]]+=1
hash[b[i]]+=1
if a[i] == b[i]:
e[a[i]]+=1
ans = 1
for i in hash:
z1 = hash[i]
z2 = e[i]
ans*=sol(z1,m,z2)
ans%=m
print(ans)
# t = int(input())
# for _ in range(t):
solve()
```
| 98,166 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Submitted Solution:
```
from math import sqrt,ceil,gcd
from collections import defaultdict
def modInverse(b,m):
g = gcd(b, m)
if (g != 1):
# print("Inverse doesn't exist")
return -1
else:
# If b and m are relatively prime,
# then modulo inverse is b^(m-2) mode m
return pow(b, m - 2, m)
def solve():
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
m = int(input())
dp = [1]*(10**5+1000)
for i in range(1,10**5+1000):
dp[i] = dp[i-1]*i
dp[i]%=m
l1 = []
l2 = []
for i in range(n):
l1.append([a[i],i+1])
l2.append([b[i],i+1])
z = l1+l2
z = sorted(z, key=lambda x: (x[0], x[1]))
hash = defaultdict(list)
for a,b in z:
hash[a].append(b)
ans = 1
print(z)
for i in hash:
z1 = dp[len(hash[i])]
j = 0
z2 = 1
while j<len(hash[i]):
k = hash[i][j]
cnt = 0
while j<len(hash[i]) and hash[i][j] == k:
cnt+=1
j+=1
# print(i,cnt)
z2 *= modInverse(dp[cnt],m)
# print(i,z2)
ans*=z1*z2
ans%=m
print(ans)
# print(z)
# t = int(input())
# for _ in range(t):
solve()
```
No
| 98,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Submitted Solution:
```
from math import sqrt,ceil
from collections import defaultdict
def solve():
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
m = int(input())
l1 = []
l2 = []
for i in range(n):
l1.append([a[i],i+1])
l2.append([b[i],i+1])
z = l1+l2
z.sort()
hash = defaultdict(list)
for a,b in z:
hash[a].append(b)
ans = 1
for i in hash:
ans*=len(hash[i])
ans%=m
print(ans)
# t = int(input())
# for _ in range(t):
solve()
```
No
| 98,168 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Submitted Solution:
```
f = lambda: map(int, input().split())
n = int(input())
c, d = {}, {}
for x, y in zip(f(), f()):
c[x] = c.get(x, 0) + 1
c[y] = c.get(y, 0) + 1
if x == y: d[x] = d.get(x, 0) + 2
s, m = 1, int(input())
for k, v in c.items():
u = d.get(k, 0)
for i in range(v - u, v, 2): s = s * (i * i + i) // 2 % m
for i in range(v - u): s = s * (i + 1) % m
print(s)
```
No
| 98,169 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).
Now Dima wants to count the number of distinct sequences of points of length 2Β·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.
Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2Β·n, q2Β·n) and (x1, y1), (x2, y2), ..., (x2Β·n, y2Β·n) distinct, if there is such i (1 β€ i β€ 2Β·n), that (pi, qi) β (xi, yi).
As the answer can be rather large, print the remainder from dividing the answer by number m.
Input
The first line contains integer n (1 β€ n β€ 105). The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109). The third line contains n integers b1, b2, ..., bn (1 β€ bi β€ 109). The numbers in the lines are separated by spaces.
The last line contains integer m (2 β€ m β€ 109 + 7).
Output
In the single line print the remainder after dividing the answer to the problem by number m.
Examples
Input
1
1
2
7
Output
1
Input
2
1 2
2 3
11
Output
2
Note
In the first sample you can get only one sequence: (1, 1), (2, 1).
In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
Submitted Solution:
```
n=int(input())
a=sorted(list(map(int,input().split()))+list(map(int,input().split())))
m=int(input())
b=[]
c=1
for i in range(1,n+1):
c*=i
c%=m
b.append(c)
d=0
e=1
for i in range(n):
if a[i]!=a[i-1]:
e*=b[i-d-1]
e%=m
d=i
e*=b[n-d-1]
print(e%m)
```
No
| 98,170 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
import math
n = int(input())
arr = list(map(int, input().split()))
req = 0
if n == 1:
print("YES")
else:
for k in set(arr):
req = max(req, arr.count(k))
if n - req >= req - 1:
print("YES")
else:
print("NO")
```
| 98,171 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
a = int(input())
l = list(map(int, input().split()))
d = dict()
s = set()
for i in l:
if i not in d:
d[i] = 1
else:
d[i] += 1
s.add(i)
flag = False
for i in s:
sum = 0
for j in d:
sum += d[j]
sum -= d[i]
if d[i] - sum > 1:
flag = True
if flag:
print('NO')
else:
print('YES')
```
| 98,172 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
import math
import collections
n=int(input())
A=[int(x) for x in input().split()]
D=collections.Counter(A)
m=math.ceil(n/2)
for v in D.values():
if v>m:
print("NO")
exit()
print("YES")
```
| 98,173 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
import sys,math
from collections import deque,defaultdict
import operator as op
from functools import reduce
from itertools import permutations
#sys.setrecursionlimit(10**6)
I=sys.stdin.readline
#s="abcdefghijklmnopqrstuvwxyz"
"""
x_move=[-1,0,1,0,-1,1,1,-1]
y_move=[0,1,0,-1,1,1,-1,-1]
"""
def ii():
return int(I().strip())
def li():
return list(map(int,I().strip().split()))
def mi():
return map(int,I().strip().split())
"""def ncr(n, r):
r = min(r, n-r)
numer = (reduce(op.mul, range(n, n-r, -1), 1))%(10**9+7)
denom = (reduce(op.mul, range(1, r+1), 1))%(10**9+7)
return (numer // denom)%(10**9+7)"""
def ncr(n, r, p):
# initialize numerator
# and denominator
num = den = 1
for i in range(r):
num = (num * (n - i)) % p
den = (den * (i + 1)) % p
return (num * pow(den,
p - 2, p)) % p
def gcd(x, y):
while y:
x, y = y, x % y
return x
def valid(row,col,rows,cols,rcross,lcross):
return rows[row]==0 and cols[col]==0 and rcross[col+row]==0 and lcross[col-row]==0
def div(n):
tmp=[]
for i in range(2,int(n**.5)+1):
if n%i==0:
cnt=0
while(n%i==0):
n=n//i
cnt+=1
tmp.append((i,cnt))
if n>1:
tmp.append((n,1))
return tmp
def isPrime(n):
if n<=1:
return False
elif n<=2:
return True
else:
flag=True
for i in range(2,int(n**.5)+1):
if n%i==0:
flag=False
break
return flag
def s(b):
ans=[]
while b>0:
tmp=b%10
ans.append(tmp)
b=b//10
return ans
def main():
n=ii()
arr=li()
if n==1:
print("YES")
else:
sett=set(arr)
d=defaultdict(int)
for i in range(n):
d[arr[i]]+=1
flag=1
for i in sett:
if n-d[i]<d[i]-1:
flag=0
break
if flag:
print("YES")
else:
print("NO")
if __name__ == '__main__':
main()
```
| 98,174 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
import sys
def input(): return sys.stdin.readline().strip()
def iinput(): return int(input())
def rinput(): return map(int, sys.stdin.readline().strip().split())
def get_list(): return list(map(int, sys.stdin.readline().strip().split()))
n=iinput()
h=((n+1)/2)
a=list(map(int,input().split()))
l=list(set(a))
s=len(l)
r=[]
for i in range(s):
r.append(a.count(l[i]))
m=max(r)
if(m<=h):
print("YES")
else:
print("NO")
```
| 98,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
import math
N = int(input())
numbers = list(map(int, input().split()))
set_of_numbers = list(set(numbers))
countr = [None] * len(set_of_numbers)
for i in range(len(set_of_numbers)):
countr[i] = numbers.count(set_of_numbers[i])
if max(countr) > math.ceil(N/2):
print('NO')
else:
print('YES')
```
| 98,176 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
# Author : nitish420 --------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
# sys.setrecursionlimit(10**6)
from collections import Counter
def check(l):
prev=l[0]
for i in range(1,len(l)):
if l[i]==prev:
return 0
prev=l[i]
return 1
def main():
n=int(input())
a=list(map(int,input().split()))
d=Counter(a)
k=(n+1)//2
ans=1
for item in d.keys():
if d[item]<=k:
pass
else:
ans=0
break
if ans:
print("YES")
else:
print("NO")
#----------------------------------------------------------------------------------------
def nouse0():
# This is to save my code from plag due to use of FAST IO template in it.
a=420
b=420
print(f'i am nitish{(a+b)//2}')
def nouse1():
# This is to save my code from plag due to use of FAST IO template in it.
a=420
b=420
print(f'i am nitish{(a+b)//2}')
def nouse2():
# This is to save my code from plag due to use of FAST IO template in it.
a=420
b=420
print(f'i am nitish{(a+b)//2}')
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in file.mode or 'r' not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b'\n') + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode('ascii'))
self.read = lambda: self.buffer.read().decode('ascii')
self.readline = lambda: self.buffer.readline().decode('ascii')
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')
def nouse3():
# This is to save my code from plag due to use of FAST IO template in it.
a=420
b=420
print(f'i am nitish{(a+b)//2}')
def nouse4():
# This is to save my code from plag due to use of FAST IO template in it.
a=420
b=420
print(f'i am nitish{(a+b)//2}')
def nouse5():
# This is to save my code from plag due to use of FAST IO template in it.
a=420
b=420
print(f'i am nitish{(a+b)//2}')
# endregion
if __name__ == '__main__':
main()
```
| 98,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Tags: greedy, math
Correct Solution:
```
n = int(input())
l1 = [int(num) for num in input().split(' ')]
l2 = list(set(l1))
l3 = []
for i in l2:
l3.append(l1.count(i))
if n == 1:
print("YES")
else:
if len(l2) == 1:
print("NO")
else:
if sum(l3) % 2 == 0:
if max(l3) <= sum(l3) // 2:
print("YES")
else:
print("NO")
else:
if max(l3) <= sum(l3) // 2 + 1:
print("YES")
else:
print("NO")
```
| 98,178 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
n = int(input())
arr = list(map(int, input().split()))
max_ = max(arr, key = arr.count)
print("YES" if(arr.count(max_) <= (n + 1) // 2) else "NO")
```
Yes
| 98,179 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
from collections import Counter
n = int(input())
stuff = Counter(input().split())
space = (n-1)//2
print ("YNEOS"[stuff.most_common()[0][1]-1 > space::2])
```
Yes
| 98,180 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
import math
n = int(input())
numbers = [int(i) for i in input().split()]
for item in numbers:
if numbers.count(item)>math.ceil(len(numbers)/2):
print("NO")
break
else:
print("YES")
```
Yes
| 98,181 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
n=int(input())
a=list(map(int, input().split()))
b={}
for i in a:
if i in b:b[i]+=1
else:b[i]=1
t=0
for i in b:
if b[i]>t:t=b[i]
if n-t>=t-1:print('YES')
else:print('NO')
```
Yes
| 98,182 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
n = int(input())
arr = list(map(int, input().split()))
track = {}
for i in arr:
if not (i in track.keys()):
track[i] = 0
track[i] += 1
counts = []
for i in track.keys():
counts.append(track[i])
counts.sort()
counts.reverse()
for i in range(len(counts) - 1):
curr = counts[i]
sep = sum(counts[i + 1: len(counts)])
if(sep < curr - 1):
print("NO")
break
else:
if(len(counts) == 1):
print("NO")
else:
print("YES")
```
No
| 98,183 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
def yaro(n,arr):
if n == 1:
return "YES"
if n == 2:
if arr[0] != arr[1]:
return "YES"
else:
return "NO"
if n == 3:
if arr[0] != arr[1] or arr[1] != arr[2] or arr[0] == arr[2]:
return "YES"
else:
return "NO"
l = [0]*1001
limit = n//2
for i in range(n):
l[arr[i]] += 1
for i in l:
if i > limit:
return "NO"
return "YES"
n = int(input())
arr = map(int,input().split())
yaro(n,arr)
```
No
| 98,184 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
n = int(input())
ls = list(map(int,input().split()))
ans = ""
for i in ls:
if ls.count(i)*2 <= n:
ans = "YES"
else:
ans = "NO"
print(ans)
```
No
| 98,185 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.
Help Yaroslav.
Input
The first line contains integer n (1 β€ n β€ 100) β the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 1000) β the array elements.
Output
In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.
Examples
Input
1
1
Output
YES
Input
3
1 1 2
Output
YES
Input
4
7 7 7 7
Output
NO
Note
In the first sample the initial array fits well.
In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.
In the third sample Yarosav can't get the array he needs.
Submitted Solution:
```
b=int(input())
a={int(s) for s in input().split()}
if len(a)>=b/2:
print('YES')
else:
print('NO')
```
No
| 98,186 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
from sys import stdin, stdout
def readIn():
return ( map(int,input().split()) )
s = input()
sz = len(s)+1
cnt = [ [0]*3 for _ in range(sz) ]
for i in range(sz-1):
for j in range(3):
cnt[i+1][j] = cnt[i][j]
if s[i] == 'x':
cnt[i+1][0] += 1
elif s[i] == 'y':
cnt[i+1][1] += 1
else :
cnt[i+1][2] += 1
n = int(input())
res = []
for _ in range(n):
l,r = readIn()
tmp = [ cnt[r][i]-cnt[l-1][i] for i in range(3) ]
res.append( 'YES' if r-l<2 or max(tmp)-min(tmp)<2 else 'NO' )
print('\n'.join(res))
```
| 98,187 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
#!/usr/bin/python3
def readln(): return tuple(map(int, input().split()))
q = input()
cnt = [[0] * 3 for _ in range(len(q) + 1)]
for i, v in enumerate(list(q)):
for j in range(3):
cnt[i + 1][j] = cnt[i][j]
if v == 'x':
cnt[i + 1][0] += 1
elif v == 'y':
cnt[i + 1][1] += 1
else:
cnt[i + 1][2] += 1
ans = []
for _ in range(readln()[0]):
l, r = readln()
tmp = [cnt[r][i] - cnt[l - 1][i] for i in range(3)]
ans.append('YES' if r - l < 2 or max(tmp) - min(tmp) < 2 else 'NO')
print('\n'.join(ans))
```
| 98,188 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
import sys
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
input = sys.stdin.readline
s = input().strip()
x_c, y_c, z_c = [0], [0], [0]
for el in s:
x_c.append(x_c[-1]+int(el=="x"))
y_c.append(y_c[-1]+int(el=="y"))
z_c.append(z_c[-1]+int(el=="z"))
for _ in range(int(input())):
l, r = map(int, input().split())
if r - l < 2:
print("YES")
continue
#...
x, y, z = x_c[r]-x_c[l-1], y_c[r]-y_c[l-1], z_c[r]-z_c[l-1]
if max(x, y, z) - min(x, y, z) > 1:
print("NO")
else:
print("YES")
```
| 98,189 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
def f(t): return t[2] - t[0] > 1
t = input()
n, m, p = len(t), int(input()), {'x': 0, 'y': 1, 'z': 2}
s = [[0] * (n + 1) for i in range(3)]
for i, c in enumerate(t, 1): s[p[c]][i] = 1
for i in range(3):
for j in range(1, n): s[i][j + 1] += s[i][j]
a, b, c = s
q, d = [map(int, input().split()) for i in range(m)], ['YES'] * m
for i, (l, r) in enumerate(q):
if r - l > 1 and f(sorted([a[r] - a[l - 1], b[r] - b[l - 1], c[r] - c[l - 1]])): d[i] = 'NO'
print('\n'.join(d))
# Made By Mostafa_Khaled
```
| 98,190 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
import sys
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
input = sys.stdin.readline
s = input().strip()
x_c, y_c, z_c = [0], [0], [0]
for el in s:
x_c.append(x_c[-1]+int(el=="x"))
y_c.append(y_c[-1]+int(el=="y"))
z_c.append(z_c[-1]+int(el=="z"))
for _ in range(int(input())):
l, r = map(int, input().split())
if r - l < 2:
print("YES")
continue
x, y, z = x_c[r]-x_c[l-1], y_c[r]-y_c[l-1], z_c[r]-z_c[l-1]
if max(x, y, z) - min(x, y, z) > 1:
print("NO")
else:
print("YES")
```
| 98,191 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
import sys
input=sys.stdin.readline
s=input().strip()
xc=yc=zc=0
xlis,ylis,zlis=[0],[0],[0]
for i in s:
xlis.append(xlis[-1]+int(i=='x'))
ylis.append(ylis[-1]+int(i=='y'))
zlis.append(zlis[-1]+int(i=='z'))
for __ in range(int(input())):
l,r=map(int,input().split())
if r-l<2:
print('YES')
continue
xc=xlis[r]-xlis[l-1]
yc=ylis[r]-ylis[l-1]
zc=zlis[r]-zlis[l-1]
if max(xc,yc,zc)-min(xc,yc,zc)>1:
print('NO')
else:
print('YES')
```
| 98,192 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
def sum_chr(ch):
tem, cur = [0], 0
for i in range(len(s)):
if s[i] == ch:
cur += 1
tem.append(cur)
return tem
s, m = input(), int(input())
xs, ys, zs, ans = sum_chr('x'), sum_chr('y'), sum_chr('z'), []
for i in range(m):
l, r = map(int, input().split())
if r - l + 1 < 3:
ans.append('YES')
else:
chrs = sorted([xs[r] - xs[l - 1], ys[r] - ys[l - 1], zs[r] - zs[l - 1]])
ans.append('YES' if chrs[-1] - chrs[0] <= 1 else 'NO')
for i in range(m):
print(ans[i])
```
| 98,193 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Tags: data structures, implementation
Correct Solution:
```
def f(x, y, z): return abs(y - x) > 1 or abs(z - x) > 1 or abs(y - z) > 1
t = input()
n, p = len(t), {'x': 0, 'y': 1, 'z': 2}
s = [[0] * (n + 1) for i in range(3)]
for i, c in enumerate(t, 1): s[p[c]][i] = 1
for i in range(3):
for j in range(1, n): s[i][j + 1] += s[i][j]
a, b, c = s
q = [map(int, input().split()) for i in range(int(input()))]
d = ['YES'] * len(q)
for i, (l, r) in enumerate(q):
if r - l > 1 and f(a[r] - a[l - 1], b[r] - b[l - 1], c[r] - c[l - 1]): d[i] = 'NO'
print('\n'.join(d))
```
| 98,194 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Submitted Solution:
```
s=input()
l=len(s)
d={'x':0,'y':1,'z':2}
cnt=[[0]*(l+1) for _ in range(3)]
for i,c in enumerate(s,1):
cnt[d[c]][i]+=1
for j in range(3):
cnt[j][i]+=cnt[j][i-1]
# import sys, io, os
# try:
# input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# except:
# input=lambda:sys.stdin.readline().encode()
ans=[]
m=int(input())
for _ in range(m):
l,r=map(int,input().split())
if r-l+1<3:
ans.append('YES')
continue
t=[]
for i in range(3):
t.append(cnt[i][r]-cnt[i][l-1])
if max(t)-min(t)<=1 and min(t)>=1:
ans.append('YES')
else:
ans.append('NO')
print('\n'.join(ans))
```
Yes
| 98,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Submitted Solution:
```
s=input()
d={'x':0,'y':1,'z':2}
cnt=[[0]*(len(s)+1) for _ in range(3)]
for i,c in enumerate(s,1):
cnt[d[c]][i]+=1
for j in range(3):
cnt[j][i]+=cnt[j][i-1]
ans=[]
m=int(input())
for _ in range(m):
l,r=map(int,input().split())
if r-l+1<3:
ans.append('YES')
continue
t=[]
for i in range(3):
t.append(cnt[i][r]-cnt[i][l-1])
if max(t)-min(t)<=1 and min(t)>=1:
ans.append('YES')
else:
ans.append('NO')
print('\n'.join(ans))
```
Yes
| 98,196 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Submitted Solution:
```
def main():
l, xyz, res = [(0, 0, 0)], [0, 0, 0], []
for c in input():
xyz[ord(c) - 120] += 1
l.append(tuple(xyz))
for _ in range(int(input())):
a, b = map(int, input().split())
if b - a > 1:
xyz = [i - j for i, j in zip(l[b], l[a - 1])]
res.append(("NO", "YES")[max(xyz) - min(xyz) < 2])
else:
res.append("YES")
print('\n'.join(res))
if __name__ == '__main__':
main()
```
Yes
| 98,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Submitted Solution:
```
import sys
from functools import lru_cache, cmp_to_key
from heapq import merge, heapify, heappop, heappush
from math import *
from collections import defaultdict as dd, deque, Counter as C
from itertools import combinations as comb, permutations as perm
from bisect import bisect_left as bl, bisect_right as br, bisect, insort
from time import perf_counter
from fractions import Fraction
import copy
from copy import deepcopy
import time
starttime = time.time()
mod = int(pow(10, 9) + 7)
mod2 = 998244353
def data(): return sys.stdin.readline().strip()
def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
def L(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
try:
# sys.setrecursionlimit(int(pow(10,6)))
sys.stdin = open("input.txt", "r")
# sys.stdout = open("../output.txt", "w")
except:
pass
def pmat(A):
for ele in A:
print(*ele,end="\n")
l, xyz, res = [(0, 0, 0)], [0, 0, 0], []
for c in input():
xyz[ord(c) - 120] += 1
l.append(tuple(xyz))
for _ in range(int(input())):
a, b = map(int, input().split())
if b - a > 1:
xyz = [i - j for i, j in zip(l[b], l[a - 1])]
res.append(("NO", "YES")[max(xyz) - min(xyz) < 2])
else:
res.append("YES")
print('\n'.join(res))
endtime = time.time()
# print(f"Runtime of the program is {endtime - starttime}")
```
Yes
| 98,198 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps:
1. Find any continuous subsequence (substring) of three characters of string q, which doesn't equal to either string "zyx", "xzy", "yxz". If q doesn't contain any such subsequence, terminate the algorithm, otherwise go to step 2.
2. Rearrange the letters of the found subsequence randomly and go to step 1.
Sereja thinks that the algorithm works correctly on string q if there is a non-zero probability that the algorithm will be terminated. But if the algorithm anyway will work for infinitely long on a string, then we consider the algorithm to work incorrectly on this string.
Sereja wants to test his algorithm. For that, he has string s = s1s2... sn, consisting of n characters. The boy conducts a series of m tests. As the i-th test, he sends substring slisli + 1... sri (1 β€ li β€ ri β€ n) to the algorithm input. Unfortunately, the implementation of his algorithm works too long, so Sereja asked you to help. For each test (li, ri) determine if the algorithm works correctly on this test or not.
Input
The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.
The second line contains integer m (1 β€ m β€ 105) β the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 β€ li β€ ri β€ n).
Output
For each test, print "YES" (without the quotes) if the algorithm works correctly on the corresponding test and "NO" (without the quotes) otherwise.
Examples
Input
zyxxxxxxyyz
5
5 5
1 3
1 11
1 4
3 6
Output
YES
YES
NO
YES
NO
Note
In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string "xzyx" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.
Submitted Solution:
```
s = input()
m = int(input())
nX = [0]*len(s)
nY = [0]*len(s)
nZ = [0]*len(s)
for i in range(len(s)):
if i:
nX[i] = nX[i-1]
nY[i] = nY[i-1]
nZ[i] = nZ[i-1]
if s[i]=='x': nX[i] += 1
elif s[i]=='y': nY[i] += 1
else: nZ[i] += 1
for i in range(m):
x, y = map(int, input().split())
x -= 1
y -= 1
numX = nX[y]
numY = nY[y]
numZ = nZ[y]
if x:
numX -= nX[x-1]
numY -= nY[x-1]
numZ -= nZ[x-1]
if abs(numX-numZ)<=1 and abs(numX-numY)<=1 and abs(numY-numZ)<=1:
print("YES")
else:
print("NO")
```
No
| 98,199 |
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