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
sys.setrecursionlimit(4100000)
import math
import itertools
INF = float('inf')
from heapq import heapify, heappop, heappush

def main():
    n = int(input())
    S = input()

    l_dict = {}
    r_dict = {}
    L = S[:n]
    R = S[n:]
    for i in range(2**n):
        lr, lb, rr, rb = '', '', '', ''
        for j in range(n):
            if (i>>j) & 1:
                lr += L[j]
                rr += R[j]
            else:
                lb += L[j]
                rb += R[j]
        rr = rr[::-1]
        rb = rb[::-1]

        if l_dict.get((lr,lb)):
            l_dict[(lr,lb)] += 1
        else:
            l_dict[(lr,lb)] = 1
        if r_dict.get((rb,rr)):
            r_dict[(rb,rr)] += 1
        else:
            r_dict[(rb,rr)] = 1
    ans = 0
    for k, v in l_dict.items():
        if k in r_dict:
            ans += v*r_dict[k]
    print(ans)


if __name__ == '__main__':
    main()