Problem: You are given a string S of length 2N consisting of lowercase English letters.

There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

* The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Constraints

* 1 \leq N \leq 18
* The length of S is 2N.
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the number of ways to paint the string that satisfy the condition.

Examples

Input

4
cabaacba


Output

4


Input

11
mippiisssisssiipsspiim


Output

504


Input

4
abcdefgh


Output

0


Input

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa


Output

9075135300

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(pow(10, 6))

from collections import defaultdict

def main():
    n = int(input())
    s = input().strip()

    tmp = defaultdict(lambda : 0)
    for state in range(1 << n):
        rs, bs = "", ""
        for i in range(n):
            if (state >> i) & 1:
                rs += s[i]
            else:
                bs += s[i]
        tmp[(rs, bs)] += 1
    
    ans = 0
    for state in range(1 << n):
        rs, bs = "", ""
        for i in range(n):
            if (state >> i) & 1:
                rs += s[-i - 1]
            else:
                bs += s[-i - 1]
        ans += tmp[(rs, bs)]
    print(ans)


if __name__ == '__main__':
    main()