message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
n = int(input())
nums = [int(input()) for _ in range(n)]
standard = nums[:]
standard.sort()
ans = 0
for i in range(n):
p = nums[i]
x = standard.index(p)
if abs(x - i) % 2 == 1:
ans += 1
print(ans)
``` | instruction | 0 | 24,651 | 16 | 49,302 |
No | output | 1 | 24,651 | 16 | 49,303 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
n = int(input())
a = [int(input()) for _ in range(n)]
b = sorted(a)
aa = []
bb = []
for i in range(0,n,2):
aa.append(a[i])
bb.append(b[i])
cnt = 0
for k in aa:
if k not in bb:
cnt += 1
print(cnt)
``` | instruction | 0 | 24,652 | 16 | 49,304 |
No | output | 1 | 24,652 | 16 | 49,305 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,341 | 16 | 52,682 |
"Correct Solution:
```
x,a,b = map(int,input().split(' '))
if abs(x-a) > abs(x-b):
print('B')
else:
print('A')
``` | output | 1 | 26,341 | 16 | 52,683 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,342 | 16 | 52,684 |
"Correct Solution:
```
a,b,c=map(int,input().split(' '))
if abs(a-b)<abs(c-a):
print('A')
else:
print('B')
``` | output | 1 | 26,342 | 16 | 52,685 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,343 | 16 | 52,686 |
"Correct Solution:
```
n,a,b=map(int,input().split())
if(abs(a-n) < abs(b-n)):print("A")
else:print("B")
``` | output | 1 | 26,343 | 16 | 52,687 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,344 | 16 | 52,688 |
"Correct Solution:
```
x, a, b = map(int, input().split())
if abs(b-x)<abs(a-x):
print('B')
else:
print('A')
``` | output | 1 | 26,344 | 16 | 52,689 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,345 | 16 | 52,690 |
"Correct Solution:
```
x,a,b = map(int,input().split())
ansa = (abs(x-a)< abs(x-b))
print("A" if ansa else "B")
``` | output | 1 | 26,345 | 16 | 52,691 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,346 | 16 | 52,692 |
"Correct Solution:
```
a,b,c=map(int,input().split())
if abs(b-a)>abs(c-a):
print("B")
else:
print("A")
``` | output | 1 | 26,346 | 16 | 52,693 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,347 | 16 | 52,694 |
"Correct Solution:
```
x,y,z=map(int,input().split())
if abs(y-x) < abs(z-x):
print("A")
else:
print("B")
``` | output | 1 | 26,347 | 16 | 52,695 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A | instruction | 0 | 26,348 | 16 | 52,696 |
"Correct Solution:
```
x, a, b = map(int, input().split())
if abs(a-x) < abs(x-b):
print("A")
else:
print("B")
``` | output | 1 | 26,348 | 16 | 52,697 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
x,a,b=map(int,input().split());print('AB'[(2*x>a+b)^(a>b)])
``` | instruction | 0 | 26,349 | 16 | 52,698 |
Yes | output | 1 | 26,349 | 16 | 52,699 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
x, a, b = map(int, input().split())
print("A" if (abs(x - a) < abs(x - b)) else "B")
``` | instruction | 0 | 26,350 | 16 | 52,700 |
Yes | output | 1 | 26,350 | 16 | 52,701 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
x,a,b = map(int,input().split())
print('AB'[abs(a-x)>abs(b-x)])
``` | instruction | 0 | 26,351 | 16 | 52,702 |
Yes | output | 1 | 26,351 | 16 | 52,703 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
x,a,b=map(int,input().split());print("AB"[abs(a-x)>abs(b-x)])
``` | instruction | 0 | 26,352 | 16 | 52,704 |
Yes | output | 1 | 26,352 | 16 | 52,705 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
#ABC71
x, a, b = map(int, input().split())
if(abs(x-a)>(abs(x-b))):
print("A")
else:
print("B")
``` | instruction | 0 | 26,353 | 16 | 52,706 |
No | output | 1 | 26,353 | 16 | 52,707 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
x,a,b = map(int ,input().split())
if(abs(x-a) > abs(x-b) ):
print('A')
else:
print('B')
``` | instruction | 0 | 26,354 | 16 | 52,708 |
No | output | 1 | 26,354 | 16 | 52,709 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
tmp=map(int, raw_input().split(" "))
a=abs(tmp[0]-tmp[1])
b=abs(tmp[0]-tmp[2])
if a<b:
print("A")
else:
print("B")
``` | instruction | 0 | 26,355 | 16 | 52,710 |
No | output | 1 | 26,355 | 16 | 52,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives at position x on a number line. On this line, there are two stores A and B, respectively at position a and b, that offer food for delivery.
Snuke decided to get food delivery from the closer of stores A and B. Find out which store is closer to Snuke's residence.
Here, the distance between two points s and t on a number line is represented by |s-t|.
Constraints
* 1 \leq x \leq 1000
* 1 \leq a \leq 1000
* 1 \leq b \leq 1000
* x, a and b are pairwise distinct.
* The distances between Snuke's residence and stores A and B are different.
Input
Input is given from Standard Input in the following format:
x a b
Output
If store A is closer, print `A`; if store B is closer, print `B`.
Examples
Input
5 2 7
Output
B
Input
1 999 1000
Output
A
Submitted Solution:
```
x, a, b = map(int, input().split())
if min(abs(x-a) > abs(x-b)):
print('B')
else:
print('A')
``` | instruction | 0 | 26,356 | 16 | 52,712 |
No | output | 1 | 26,356 | 16 | 52,713 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,367 | 16 | 52,734 |
"Correct Solution:
```
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")
n, x = map(int, input().split())
if x==1 or x==2*n-1:
print("No")
else:
if n==2:
ans = [1,2,3]
else:
s = set(range(1,2*n))
ans = [None]*(2*n-1)
if x>2:
ans[n-2] = x-1
ans[n-1] = x
ans[n] = x+1
ans[n+1] = x-2
else:
ans[n-2] = x+1
ans[n-1] = x
ans[n] = x-1
ans[n+1] = x+2
for i in range(n-2, n+2):
s.remove(ans[i])
for i in range(2*n-1):
if ans[i] is None:
ans[i] = s.pop()
print("Yes")
print("\n".join(map(str, ans)))
``` | output | 1 | 26,367 | 16 | 52,735 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,368 | 16 | 52,736 |
"Correct Solution:
```
a,b=map(int,input().split())
if b<2 or b>2*a-2:print("No")
else:
print("Yes")
d=[i for i in range(1,b-1)]+[i for i in range(b+1,a+1)]+[b-1,b]+[i for i in range(a+1,2*a)]if 1<=b<a+1else[i for i in range(1,a)]+[b,b+1]+[i for i in range(a,b)]+[i for i in range(b+2,2*a)]
for i in d:print(i)
``` | output | 1 | 26,368 | 16 | 52,737 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,369 | 16 | 52,738 |
"Correct Solution:
```
n,x = map(int,input().split())
if x==n*2-1 or x==1:
print('No')
else:
print('Yes')
ans = []
if n==2:
print(1,2,3)
exit()
elif x==2:
ans = [x+1,x,x-1,x+2]
else:
ans = [x-1, x, x+1, x-2]
cnt = 0
i = 1
while cnt<n-2:
if i in ans:
i+=1
continue
else:
print(i,end=' ')
cnt+=1
i+=1
for j in ans:
print(j,end=' ')
while i<2*n:
if i in ans:
i+=1
continue
print(i,end=' ')
i+=1
``` | output | 1 | 26,369 | 16 | 52,739 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,370 | 16 | 52,740 |
"Correct Solution:
```
import sys
#import numpy as np
stdin = sys.stdin
ri = lambda: int(rs())
rl = lambda: list(map(int, stdin.readline().split())) # applies to numbers only
rs = lambda: stdin.readline().rstrip() # ignore trailing spaces
N, x = rl()
if x == 1 or x == 2 * N - 1:
print('No')
exit()
answer = [0] * (2*N-1)
mid = N-1
if x <= N:
answer[mid] = x
answer[mid-1] = x - 1
cur = 0
for y in range(2*N-1, 0, -1):
while cur == mid or cur == mid-1:
cur += 1
if y == x or y == x-1:
continue
answer[cur] = y
cur += 1
else:
answer[mid] = x
answer[mid-1] = x + 1
cur = 0
for y in range(1, 2*N):
while cur == mid or cur == mid-1:
cur += 1
if y == x or y == x+1:
continue
answer[cur] = y
cur += 1
print('Yes')
print(*answer)
#44
``` | output | 1 | 26,370 | 16 | 52,741 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,371 | 16 | 52,742 |
"Correct Solution:
```
n,x=map(int,input().split())
if x==1 or x==2*n-1:
print('No')
else:
print('Yes')
m=[x-1,x,x+1]
i=1
for _ in range(n-2):
while i in m:
i+=1
print(i)
i+=1
for mi in m:
print(mi)
for _ in range(n-2):
while i in m:
i+=1
print(i)
i+=1
``` | output | 1 | 26,371 | 16 | 52,743 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,372 | 16 | 52,744 |
"Correct Solution:
```
N,x = map(int,input().split())
if x == 1 or x == 2*N-1:
print("No")
else:
lis = [0 for _ in range(2*N-1)]
lis[N-1] = x
lis[N] = x-1
lis[N-2] = x+1
count = 1
for i in range(2*N -1):
if count == x-1:
count = x+2
if abs(N-i-1) <= 1:
None
else:
lis[i] = count
count+=1
print("Yes")
for j in lis:
print(j)
``` | output | 1 | 26,372 | 16 | 52,745 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,373 | 16 | 52,746 |
"Correct Solution:
```
import sys
from statistics import median
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7
res = 0
def resolve():
def dfs(S):
""" デバッグ用 """
global res
if len(S) == 1:
res = S[0]
return
tmp = []
for i in range(1, len(S) - 1):
t = median([S[i - 1], S[i], S[i + 1]])
tmp.append(t)
dfs(tmp)
n, x = map(int, input().split())
if x == 1 or x == 2 * n - 1:
print("No")
exit()
n = 2 * n - 1
ans = [0] * n
num = x
for i in range(n // 2, n):
ans[i] = num
num += 1
if num > n:
num = 1
for i in range(n // 2):
ans[i] = num
num += 1
if num > n:
num = 1
print("Yes")
print(*ans, sep="\n")
# dfs(ans)
# print(res == x)
if __name__ == '__main__':
resolve()
``` | output | 1 | 26,373 | 16 | 52,747 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No | instruction | 0 | 26,374 | 16 | 52,748 |
"Correct Solution:
```
N,x=map(int,input().split())
if x==1 or x==2*N-1:
print("No")
else:
print("Yes")
ans=[int(x+1) for x in range(2*N-1)]
if N-x > 0:
cnt=abs(N-x)
ans=ans[(2*N-1)-cnt:]+ans[:(2*N-1)-cnt]
elif N-x < 0:
cnt=abs(N-x)
ans=ans[cnt:]+ans[:cnt]
for i in range(2*N-1):
print(ans[i])
``` | output | 1 | 26,374 | 16 | 52,749 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
N, X = [int(_) for _ in input().split()]
from itertools import permutations
def calc(x):
def sub(y, debug=0):
if debug:
print("D", y)
while len(y) > 1:
y = [sorted(y[i:i+3])[1] for i in range(len(y) - 2)]
if debug:
print("D", y)
return y
y = sub(x)
return y[0]
if X == 1 or X == N * 2 - 1:
print("No")
else:
print("Yes")
if X == N * 2 - 2:
xs = list(range(N - 1, X + 2)) + list(range(1, N - 1))
else:
ys = list(range(1, X - 1)) + list(range(X + 3, N * 2))
xs = ys[:N-3] + [X + 2, X - 1, X, X + 1] + ys[N-3:]
for x in xs:
print(x)
``` | instruction | 0 | 26,375 | 16 | 52,750 |
Yes | output | 1 | 26,375 | 16 | 52,751 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
import sys
readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)
def main():
n, x = map(int, readline().split())
ans = [0] * (2 * n - 1)
if x == 1 or x == (2 * n - 1):
print("No")
return
for i in range(1, n + 1):
if i % 2 == 1:
ans[i - 1] = (x - 1 + abs(n - i)) % (2 * n - 1) + 1
else:
ans[i - 1] = (x - 1 - abs(n - i)) % (2 * n - 1) + 1
ans[n] = x
for i in range(n + 1, 2 * n):
if i % 2 == 0:
ans[i - 1] = (x - 1 + abs(n - i)) % (2 * n - 1) + 1
else:
ans[i - 1] = (x - 1 - abs(n - i)) % (2 * n - 1) + 1
print("Yes")
print(*ans, sep="\n")
if __name__ == '__main__':
main()
``` | instruction | 0 | 26,376 | 16 | 52,752 |
Yes | output | 1 | 26,376 | 16 | 52,753 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
N, x = map(int, input().split())
if x == 1 or x == 2 * N - 1:
print('No')
exit()
if N == 2:
print('Yes')
for i in [1, 2, 3]:
print(i)
exit()
ans = [0] * (2 * N - 1)
ans[N - 2], ans[N - 1], ans[N] = x - 1, x, x + 1
d = 1
for i in range(2 * N - 1):
if i in [N - 2, N - 1, N]:
continue
if d == x - 1:
d = x + 2
ans[i] = d
d += 1
print('Yes')
for i in ans:
print(i)
``` | instruction | 0 | 26,377 | 16 | 52,754 |
Yes | output | 1 | 26,377 | 16 | 52,755 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
def main():
N, x = map(int, input().split())
if 2 <= x < 2*N-1:
print("Yes")
ans = [0] * (N*2-1)
for i in range(1, N):
if i == x:
ans[i*(-1)**i+N-1] = N
else:
ans[i*(-1)**i+N-1] = i
for i in range(1, N):
if N*2-i == x:
ans[i*(-1)**(i+1)+N-1] = N
else:
ans[i*(-1)**(i+1)+N-1] = N*2-i
ans[N-1] = x
for i in range(0, N*2-1):
print(ans[i])
else:
print("No")
if __name__ == "__main__":
main()
``` | instruction | 0 | 26,378 | 16 | 52,756 |
Yes | output | 1 | 26,378 | 16 | 52,757 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
n,x = map(int, input().split())
if n == x:
print("Yes")
for i in range(1,n*2):
print(i)
else:
print("No")
``` | instruction | 0 | 26,379 | 16 | 52,758 |
No | output | 1 | 26,379 | 16 | 52,759 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
import sys
N, x = map(int, input().split())
if x == 1 or x == 2 * N - 1:
print("Impossible")
sys.exit()
print("Possible")
n = 2 * N - 1
ans = [None] * n
tmp = ans[n//2-1:n//2+3]
# print(tmp)
if x != 2 * N - 2:
tmp[0] = x + 1
tmp[1] = x
tmp[2] = x - 1
tmp[3] = x + 2
else:
tmp[0] = x - 1
tmp[1] = x
tmp[2] = x + 1
tmp[3] = x - 2
cnt = 1
for i in range(n):
if cnt == x-1:
cnt += 4
if ans[i] is None:
ans[i] = cnt
cnt += 1
ans[n//2-1:n//2+3] = tmp
for i in ans:
print(i)
``` | instruction | 0 | 26,380 | 16 | 52,760 |
No | output | 1 | 26,380 | 16 | 52,761 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
N, x = map(int,input().split())
if x == 1 or x == 2*N+1:
print("No")
exit(0)
if N == 2:
print("Yes")
print(*[1,2,3], sep="\n")
exit(0)
A = [0 for k in range(2*N-1)]
A[N-2], A[N-1], A[N] = x-1, x, x+1
t = 1
for k in range(N-2):
while x-1 <= t <= x+1:
t += 1
A[k] = t
t += 1
for k in range(N+1,2*N-1):
while x-1 <= t <= x+1:
t += 1
A[k] = t
t += 1
print("Yes")
print(*A, sep="\n")
``` | instruction | 0 | 26,381 | 16 | 52,762 |
No | output | 1 | 26,381 | 16 | 52,763 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.
Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.
Constraints
* 2≤N≤10^5
* 1≤x≤2N-1
Input
The input is given from Standard Input in the following format:
N x
Output
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.
Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
Examples
Input
4 4
Output
Yes
1
6
3
7
4
5
2
Input
2 1
Output
No
Submitted Solution:
```
import sys
N, x = map(int, sys.stdin.readline().split())
if N == x:
print('Yes')
for i in range(N*2-1):
print(i+1)
else:
print('No')
``` | instruction | 0 | 26,382 | 16 | 52,764 |
No | output | 1 | 26,382 | 16 | 52,765 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,186 | 16 | 54,372 |
"Correct Solution:
```
###############################################################################
from sys import stdout
from bisect import bisect_left as binl
from copy import copy, deepcopy
mod = 1
def intin():
input_tuple = input().split()
if len(input_tuple) <= 1:
return int(input_tuple[0])
return tuple(map(int, input_tuple))
def intina():
return [int(i) for i in input().split()]
def intinl(count):
return [intin() for _ in range(count)]
def modadd(x, y):
global mod
return (x + y) % mod
def modmlt(x, y):
global mod
return (x * y) % mod
def lcm(x, y):
while y != 0:
z = x % y
x = y
y = z
return x
def combination(x, y):
assert(x >= y)
if y > x // 2:
y = x - y
ret = 1
for i in range(0, y):
j = x - i
i = i + 1
ret = ret * j
ret = ret // i
return ret
def get_divisors(x):
retlist = []
for i in range(1, int(x**0.5) + 3):
if x % i == 0:
retlist.append(i)
retlist.append(x // i)
return retlist
def get_factors(x):
retlist = []
for i in range(2, int(x**0.5) + 3):
while x % i == 0:
retlist.append(i)
x = x // i
retlist.append(x)
return retlist
def make_linklist(xylist):
linklist = {}
for a, b in xylist:
linklist.setdefault(a, [])
linklist.setdefault(b, [])
linklist[a].append(b)
linklist[b].append(a)
return linklist
def calc_longest_distance(linklist, v=1):
distance_list = {}
distance_count = 0
distance = 0
vlist_previous = []
vlist = [v]
nodecount = len(linklist)
while distance_count < nodecount:
vlist_next = []
for v in vlist:
distance_list[v] = distance
distance_count += 1
vlist_next.extend(linklist[v])
distance += 1
vlist_to_del = vlist_previous
vlist_previous = vlist
vlist = list(set(vlist_next) - set(vlist_to_del))
max_distance = -1
max_v = None
for v, distance in distance_list.items():
if distance > max_distance:
max_distance = distance
max_v = v
return (max_distance, max_v)
def calc_tree_diameter(linklist, v=1):
_, u = calc_longest_distance(linklist, v)
distance, _ = calc_longest_distance(linklist, u)
return distance
###############################################################################
mod = 10**9 + 7
class Counter:
def __init__(self, zerocount):
self.incr = 1
self.prev_zerocount = zerocount
self.count = 1
def main():
n = intin()
alist = intina()
xorlist = []
xor = 0
for a in alist:
xor = a ^ xor
xorlist.append(xor)
zerocount = 0
counters = {}
for xor in xorlist:
if xor == 0:
zerocount += 1
continue
if xor not in counters:
counters[xor] = Counter(zerocount)
continue
prev_incr = counters[xor].incr
prev_zerocount = counters[xor].prev_zerocount
prev_count = counters[xor].count
incr = modmlt(zerocount - prev_zerocount, prev_count)
incr = modadd(incr, prev_incr)
counters[xor].incr = incr
counters[xor].prev_zerocount = zerocount
counters[xor].count = modadd(prev_count, incr)
if xorlist[-1]:
print(counters[xorlist[-1]].incr)
else:
zerosum = pow(2, zerocount - 1, mod)
xorsum = sum([counter.count for counter in counters.values()]) % mod
print(modadd(zerosum, xorsum))
if __name__ == '__main__':
main()
``` | output | 1 | 27,186 | 16 | 54,373 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,187 | 16 | 54,374 |
"Correct Solution:
```
N=int(input())
A=[int(i) for i in input().split()]
B=[0]*N
mod=10**9+7
B[0]=A[0]
for i in range(1,N):
B[i]=A[i]^B[i-1]
F=[0]*(1<<20)
dp=[1]*(1<<20)
dp1=[0]*(1<<20)
x=1
#print(B)
for i in range(N):
if B[i]==0:
x+=1
dp[B[i]]+=dp1[B[i]]*(x-F[B[i]])
dp[B[i]]%=mod
dp1[B[i]]+=dp[B[i]]
dp1[B[i]]%=mod
F[B[i]]=x
#print(dp[:16],dp1[:16])
#print(dp[:10],B,x)
if B[-1]!=0:
print(dp[B[-1]])
else:
ans=pow(2,x-2,mod)
for i in range(1,1<<20):
ans+=dp1[i]
ans%=mod
print(ans)
``` | output | 1 | 27,187 | 16 | 54,375 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,188 | 16 | 54,376 |
"Correct Solution:
```
from collections import defaultdict
import sys
import bisect
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
mod = 10**9+7
acc = [0]
acc0 = [0]*(n+1)
for i in range(n):
acc.append(acc[-1]^a[i])
if i:
acc0[i+1] += acc0[i]
if acc[-1] == 0:
acc0[i+1] += 1
if acc[-1] != 0:
s = acc[-1]
ansls = []
cnt0 = 0
cnts = 0
flg = 0
dp = [0,0]
for i in range(1,n+1):
if acc[i] == s:
dp = [dp[0]+dp[1]+1,dp[1]]
elif acc[i] == 0:
dp = [dp[0],dp[0]+dp[1]]
dp[0] %= mod
dp[1] %= mod
print((dp[1]+1)%mod)
else:
dcn = defaultdict(list)
dp = defaultdict(list)
c0 = 0
for i in range(1,n+1):
if acc[i]:
dcn[acc[i]].append(i)
else:
c0 += 1
ans = pow(2,c0-1,mod)
for i in range(1,n+1):
t = acc[i]
if t:
if not dp[t]:
dp[t] = [1,0]
else:
idx = bisect.bisect_left(dcn[t],i)
n0 = acc0[i]-acc0[dcn[t][idx-1]]
dp[t][1] += n0*dp[t][0]
dp[t][0] += dp[t][1]+1
dp[t][0] %= mod
dp[t][1] %= mod
for t,ls in dp.items():
ans += ls[0]
ans %= mod
print(ans)
``` | output | 1 | 27,188 | 16 | 54,377 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,189 | 16 | 54,378 |
"Correct Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]
def main():
md=10**9+7
n=II()
aa=LI()
cs=[0]
for a in aa:cs.append(cs[-1]^a)
#print(cs)
cnt={}
cnt0=[1]*len(cs)
for i,s in enumerate(cs[1:],1):
if s==0:
cnt0[i]=cnt0[i-1]+1
elif s in cnt:
cnt0[i]=cnt0[i-1]
c0=cnt0[i]-cnt0[cnt[s][2]]
cnt[s][0]=(cnt[s][0]+cnt[s][1]*c0)%md
cnt[s][1]=(cnt[s][1]+cnt[s][0])%md
cnt[s][2]=i
else:
cnt0[i]=cnt0[i-1]
cnt[s]=[1,1,i]
#print(cnt)
#print(cnt0)
if cs[-1]==0:ans=sum(v[1] for v in cnt.values())+pow(2,cnt0[-1]-2,md)
else:ans=cnt[cs[-1]][0]
print(ans%md)
main()
``` | output | 1 | 27,189 | 16 | 54,379 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,190 | 16 | 54,380 |
"Correct Solution:
```
N=int(input())
A=list(map(int,input().split()))
mod=10**9+7
data=[0]
for i in range(N):
data.append(data[-1]^A[i])
if data[-1]==0:
ans=0
zero=[int(data[i]==0) for i in range(N+1)]
for i in range(1,N+1):
zero[i]+=zero[i-1]
val={}
for i in range(N+1):
if data[i]!=0:
if data[i] not in val:
val[data[i]]=[]
val[data[i]].append(i)
for v in val:
B=0
W=1
for i in range(len(val[v])):
j=val[v][i]
if i!=len(val[v])-1:
B+=W
W+=B*(zero[val[v][i+1]]-zero[j])
B%=mod;W%=mod
else:
B+=W
B%=mod
ans+=B
ans%=mod
n=data.count(0)
ans+=pow(2,n-2,mod)
ans%=mod
print(ans)
else:
val=data[-1]
que=[0]*2**20
dp=[0]*(N+1)
dp[0]=1
que[0]=1
for i in range(1,N+1):
j=data[i]
dp[i]=que[j^val]
que[data[i]]+=dp[i]
que[data[i]]%=mod
print(dp[N]%mod)
``` | output | 1 | 27,190 | 16 | 54,381 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,191 | 16 | 54,382 |
"Correct Solution:
```
def mod_pow(a: int, n: int, mod: int)->int:
'''a の n 乗を計算します。
'''
res = 1
while n > 0:
if n & 1:
res = (res * a) % mod
a = (a * a) % mod
n >>= 1
return res
def xor_partitioning(N: int, A: list)->int:
MOD = 10**9 + 7
# dp[i][0] = i マス目まで処理した時に現在こまが置かれているますに 0 が書かれている
# dp[i][1] = i マス目まで処理した時に現在こまが置かれているマスに X が書かれている。
dp = [[0, 1] for _ in range(1 << 20)]
memo = [0] * (1 << 20)
b = 0
num_zero = 0
for a in A:
b ^= a
if b == 0:
num_zero += 1
else:
dp[b][1] += dp[b][0] * (num_zero-memo[b])
dp[b][1] %= MOD
dp[b][0] += dp[b][1]
dp[b][0] %= MOD
memo[b] = num_zero
if b > 0:
return dp[b][1]
return (sum(_dp[0] for _dp in dp) + mod_pow(2, num_zero-1, MOD)) % MOD
if __name__ == "__main__":
N = int(input())
A = [int(s) for s in input().split()]
ans = xor_partitioning(N, A)
print(ans)
``` | output | 1 | 27,191 | 16 | 54,383 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,192 | 16 | 54,384 |
"Correct Solution:
```
from collections import defaultdict
from math import sqrt
def inpl(): return list(map(int, input().split()))
MOD = 10**9 + 7
N = int(input())
S = []
x = 0
for a in map(int, input().split()):
x ^= a
S.append(x)
A = defaultdict(int)
B = defaultdict(int)
L = defaultdict(int)
Z = 0
if S[-1] != 0:
sr = S[-1]
a, b = 0, 0
for s in S:
if s == sr:
b = (b + a + 1)%MOD
elif s == 0:
a = (a + b)%MOD
print(a+1)
else:
for s in S:
if s == 0:
Z += 1
else:
A[s] = (A[s] + (Z - L[s])*B[s])%MOD
B[s] = (A[s] + B[s] + 1)%MOD
L[s] = Z
print((sum(B.values()) + pow(2, Z-1, MOD))%MOD)
``` | output | 1 | 27,192 | 16 | 54,385 |
Provide a correct Python 3 solution for this coding contest problem.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292 | instruction | 0 | 27,193 | 16 | 54,386 |
"Correct Solution:
```
def pow(n,k,m):#n^k mod m
ans = 1
while k>0:
if(k & 1):ans = (ans*n) % m
n = (n*n)%m
k >>= 1
return ans
MOD = 10**9 + 7
n = int(input())
a = list(map(int,input().split()))
for i in range(1,n):
a[i] = a[i]^a[i-1] #累積和
zero = [0 for i in range(n)] #zero[i] = i番目までの0の個数
if a[0] == 0: zero[0] = 1
for i in range(1,n):
if a[i] == 0:zero[i] = zero[i-1]+1
else : zero[i] = zero[i-1]
dp = [0 for i in range(n)]
pre,dpsum = {},{}
for i in range(n):
if a[i] == 0:continue
if pre.get(a[i]) is None:
dp[i] = 1
pre[a[i]] = i
dpsum[a[i]] = 1
else:
j = pre[a[i]]
z = zero[i]-zero[j]
dp[i] = (dpsum[a[i]]*z + dp[j]) % MOD
pre[a[i]] = i
dpsum[a[i]] = (dp[i]+dpsum[a[i]]) % MOD
if a[-1] != 0:
print(dp[-1])
else:
print((pow(2,zero[-1]-1,MOD)+sum(dp)) % MOD)
``` | output | 1 | 27,193 | 16 | 54,387 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
import sys
from collections import defaultdict
from itertools import accumulate
from operator import xor
def solve_0(acc):
MOD = 10 ** 9 + 7
cnt_0 = 0
counts = defaultdict(list)
last_0 = {}
for a in acc:
if a == 0:
cnt_0 += 1
else:
cnt = counts[a]
if len(cnt) == 0:
cnt.append(1)
last_0[a] = cnt_0
else:
btw_0 = cnt_0 - last_0[a]
if btw_0 > 0:
cnt.append(btw_0)
cnt.append(1)
last_0[a] = cnt_0
else:
cnt[-1] += 1
ans = pow(2, cnt_0 - 1, MOD)
for i, cnt in counts.items():
dp0 = 1
dp1 = cnt[0]
for c0, c1 in zip(cnt[1::2], cnt[2::2]):
dp0 = (dp0 + dp1 * c0) % MOD
dp1 = (dp1 + dp0 * c1) % MOD
ans = (ans + dp1) % MOD
return ans
def solve_1(acc):
MOD = 10 ** 9 + 7
common = acc[-1]
dp0 = 1
dp1 = 0
for a in acc:
if a == 0:
dp0 = (dp0 + dp1) % MOD
elif a == common:
dp1 = (dp1 + dp0) % MOD
return dp0
n = int(input())
aaa = list(map(int, input().split()))
if 'PyPy' in sys.version:
acc = [0] * n
t = 0
for i in range(n):
t = acc[i] = t ^ aaa[i]
else:
acc = list(accumulate(aaa, func=xor))
# print(acc)
if acc[-1] == 0:
print(solve_0(acc))
else:
print(solve_1(acc))
``` | instruction | 0 | 27,194 | 16 | 54,388 |
Yes | output | 1 | 27,194 | 16 | 54,389 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
max_a = 2 ** 20
MOD = 10 ** 9 + 7
ru = [0] * (n + 1)
for i in range(n):
ru[i + 1] = ru[i] ^ a[i]
if ru[-1] != 0:
# 0, ru[-1], 0, ru[-1], 0, ..., ru[-1]
dp = [0] * (max_a)
dp[0] = 1
tot_ex0 = 0
for i in range(n):
if i == n - 1:
print(dp[0])
exit()
if ru[i + 1] == 0:
dp[0] += tot_ex0
dp[0] %= MOD
elif ru[i + 1] == ru[-1]:
dp[ru[i + 1]] += dp[0]
dp[ru[i + 1]] %= MOD
tot_ex0 += dp[0]
tot_ex0 %= MOD
else:
# 0, x, 0, x, 0, x, ..., 0 (x != 0)
dp = [0] * max_a
dq = [1] * max_a
set_evaled = [0] * max_a
times = 0
ans = 0
for i in range(n):
if i == n - 1:
ans = sum(dp)
break
elif ru[i + 1] == 0:
# これを遅延評価する
# for j in range(max_a):
# dq[j] += dp[j]
times += 1
else:
dq[ru[i + 1]] += (times - set_evaled[ru[i + 1]]) * dp[ru[i + 1]]
dq[ru[i + 1]] %= MOD
set_evaled[ru[i + 1]] = times
dp[ru[i + 1]] += dq[ru[i + 1]]
dp[ru[i + 1]] %= MOD
# 0, 0, 0, 0, 0, 0, ..., 0
cnt_0 = sum([1 for i in range(n) if ru[i + 1] == 0])
ans = (ans + pow(2, cnt_0 - 1, MOD)) % MOD
print(ans)
``` | instruction | 0 | 27,195 | 16 | 54,390 |
Yes | output | 1 | 27,195 | 16 | 54,391 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
from collections import defaultdict
MOD = 10**9 + 7
N = int(input())
S = []
x = 0
for a in map(int, input().split()):
x ^= a
S.append(x)
A = defaultdict(int)
B = defaultdict(int)
L = defaultdict(int)
Z = 0
for s in S:
if s == 0:
Z += 1
else:
A[s] = (A[s] + (Z - L[s])*B[s])%MOD
B[s] = (A[s] + B[s] + 1)%MOD
L[s] = Z
if S[-1] != 0:
print((A[S[-1]] + 1)%MOD)
else:
print((sum(B.values()) + pow(2, Z-1, MOD))%MOD)
``` | instruction | 0 | 27,196 | 16 | 54,392 |
Yes | output | 1 | 27,196 | 16 | 54,393 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
N = int(input())
A = [int(i) for i in input().split()]
mod = 10**9 + 7
b = [0]*N #
b[0] = A[0]
for n in range(1,N):
b[n] = A[n] ^ b[n-1]
#print('累積論理和',b)
m = max(b)
dp = [[0]*(m+1) for j in range(2)]
dp[0] = [True]*(m+1)
dp[1] = [False]*(m+1)
cnt = [0]*(m+1)
z = 0
for i in range(N):
if b[i] == 0:
z +=1
dp[0][b[i]] += dp[1][b[i]]*(z-cnt[b[i]])
dp[0][b[i]] %= mod
dp[1][b[i]] += dp[0][b[i]]
dp[1][b[i]] %= mod
cnt[b[i]] = z
if b[N-1]:
print(dp[0][b[N-1]])
else:
ans = pow(2, z-1, mod)
for i in range(1,m+1):
ans += dp[1][i]
ans %= mod
print(ans)
``` | instruction | 0 | 27,197 | 16 | 54,394 |
Yes | output | 1 | 27,197 | 16 | 54,395 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
N = int(input())
a_list = list(map(int, input().split()))
LARGE = 10**9 + 7
bins = [0] * 20
zeros = 0
v_dict = dict()
v_dict[0] = dict()
v_all_dict = dict()
for i in range(N):
a = a_list[i]
b = 0
for k in range(20):
r = (a // (2**k)) % 2
bins[k] = (bins[k] + r) % 2
b += bins[k]*(2**k)
if b in v_dict[zeros].keys():
v_dict[zeros][b] += 1
else:
v_dict[zeros][b] = 1
if b == 0:
for v in v_dict[zeros].keys():
if v not in v_all_dict.keys():
v_all_dict[v] = [zeros, v_dict[zeros][v] % LARGE, 1]
else:
z, c1, c2 = v_all_dict[v]
v_all_dict[v][1] = (v_all_dict[v][1] + v_all_dict[v][1] * (zeros - z) * v_dict[zeros][v] + v_all_dict[v][2] * v_dict[zeros][v]) % LARGE
zeros += 1
v_dict[zeros] = dict()
# print(zeros)
# print(v_all_dict)
if b == 0:
res = 0
for v in v_all_dict.keys():
if v != 0:
res = (res + v_all_dict[v][1]) % LARGE
else:
res = (res + 2 ** (zeros - 1) - 1) % LARGE
res += 1
else:
if b in v_all_dict.keys():
z, c1, c2 = v_all_dict[b]
res = (v_all_dict[b][1] + v_all_dict[b][1] * (zeros - z) + v_all_dict[v][2]) % LARGE
else:
res = 1
print(res)
``` | instruction | 0 | 27,198 | 16 | 54,396 |
No | output | 1 | 27,198 | 16 | 54,397 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
N=int(input())
mod=10**9+7
X=[-1]*N
for i,a in enumerate(map(int,input().split())):
if i==0:
X[0]=a
else:
X[i]=X[i-1]^a
if X[-1]>0:
x=X[-1]
dp0=1
dp1=0
zero=0
for i in range(N):
if X[i]==x:
dp0=(dp0+dp1*zero)%mod
zero=0
dp1=(dp1+dp0)%mod
elif X[i]==0:
zero+=1
print(dp0)
exit()
from collections import defaultdict
dp0=defaultdict(lambda :1)
dp1=defaultdict(int)
zero=defaultdict(int)
zeronow=0
for i in range(N-1):
x=X[i]
if x>0:
dp0[x]=(dp0[x]+dp1[x]*(zeronow-zero[x]))%mod
zero[x]=zeronow
dp1[x]=(dp1[x]+dp0[x])%mod
elif x==0:
zeronow+=1
print(sum(dp1.values())+pow(2,zeronow,mod))
``` | instruction | 0 | 27,199 | 16 | 54,398 |
No | output | 1 | 27,199 | 16 | 54,399 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
mod = 10**9+7
N = int(input())
A = list(map(int, input().split()))
n = max(A).bit_length()
S = [0]*N
for i, a in enumerate(A):
S[i]=S[i-1]^a
index = [[-1] for _ in range(2<<n)]
cumsum = [0]*(N+1)
for i, s in enumerate(S):
index[s].append(i)
cumsum[i] = cumsum[i-1]
if s == 0:
cumsum[i]+=1
ans = 0
if S[-1] == 0:
print(1/0)
for i in range(1, 1<<n):
l = len(index[i])
if l == 1:
continue
dp = [0]*(l-1)
dp_cum = [0]*(l-1)
for j, k in enumerate(index[i][1:]):
dp[j] = (dp_cum[j-1]*(cumsum[k]-cumsum[index[i][j]])+1)%mod
dp_cum[j] = (dp_cum[j-1]+dp[j])%mod
ans+=dp_cum[-1]
ans%=mod
ans+=pow(2, cumsum[N-1]-1, mod)
ans%=mod
else:
l = len(index[S[-1]])
dp = [0]*(l-1)
dp_cum = [0]*(l-1)
for j in range(l-1):
k = index[S[-1]][j+1]
p = index[S[-1]][j]
dp[j] = dp_cum[j-1]*(cumsum[k]-cumsum[p])%mod+1
dp_cum[j] = (dp_cum[j-1]*(cumsum[k]-cumsum[p])+dp[j])%mod
ans = dp[-1]%mod
print(ans)
``` | instruction | 0 | 27,200 | 16 | 54,400 |
No | output | 1 | 27,200 | 16 | 54,401 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).
You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.
There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_{N}
Output
Print the answer.
Examples
Input
3
1 2 3
Output
3
Input
3
1 2 2
Output
1
Input
32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output
147483634
Input
24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2
Output
292
Submitted Solution:
```
def run_length_encoding(A: list)->list:
'''A をランレングス圧縮します。
'''
res = []
if len(A) == 0:
return res
pre = A[0]
cnt = 0
for a in A:
if a == pre:
cnt += 1
else:
res.append((pre, cnt))
pre = a
cnt = 1
else:
res.append((pre, cnt))
return res
def mod_pow(a: int, n: int, mod: int)->int:
'''a の n 乗を計算します。
'''
res = 1
while n > 0:
if n & 1:
res = (res * a) % mod
a = (a * a) % mod
n >>= 1
return res
def xor_partitioning(N: int, A: list)->int:
MOD = 10**9 + 7
B = [0] * (N+1)
for n, a in enumerate(A):
B[n+1] = a ^ B[n]
if B[-1] == 0:
X = set(B)
else:
X = set([B[-1]])
res = 1
# dp[i][0] = i マス目まで処理した時に現在こまが置かれているますに 0 が書かれている
# dp[i][1] = i マス目まで処理した時に現在こまが置かれているマスに X が書かれている。
dp = [[0, 0] for _ in range(N+1)]
for x in X:
enc = run_length_encoding([b for b in B if b == 0 or b == x])
dp[0] = [1, 0]
for i, (b, v) in enumerate(enc):
coeff = mod_pow(2, v-2, MOD)
if b == 0 and x == 0:
dp[i+1][0] = ((dp[i][0] + dp[i][1]) * coeff) % MOD
dp[i+1][1] = ((dp[i][1] + dp[i][0]) * coeff) % MOD
elif b == 0:
dp[i+1][0] = (dp[i][0] + dp[i][1] * v) % MOD
dp[i+1][1] = dp[i][1]
elif b == x:
dp[i+1][0] = dp[i][0]
dp[i+1][1] = (dp[i][1] + dp[i][0] * v) % MOD
else:
dp[i+1][0] = dp[i][0]
dp[i+1][1] = dp[i][1]
res = (res + dp[len(enc)][0] - 1) % MOD
return res
if __name__ == "__main__":
N = int(input())
A = [int(s) for s in input().split()]
ans = xor_partitioning(N, A)
print(ans)
``` | instruction | 0 | 27,201 | 16 | 54,402 |
No | output | 1 | 27,201 | 16 | 54,403 |
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