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.buffer.readline
from collections import defaultdict

def main():
    N = int(input())
    S = input()
    mae,usi = S[:N],S[N:][::-1]
    md,ud = defaultdict(int),defaultdict(int)
    
    for i in range(1<<N):
        mr,mb,ur,ub = "","","",""
        for j in range(N):
            if (i>>j)&1:
                mr += mae[j]
                ur += usi[j]
            else:
                mb += mae[j]
                ub += usi[j]
        md[(mr,mb)] += 1
        ud[(ur,ub)] += 1
    
    ans = 0
    for key,val in md.items():
        ans += ud[key]*val
        
    print(ans)

if __name__ == "__main__":
    main()