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:
'''
自宅用PCでの解答
'''
import math
#import numpy as np
import itertools
import queue
import bisect
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    n = int(ipt())
    s = input()
    ld = defaultdict(int)
    rd = defaultdict(int)

    for i in range(2**n):
        r = ""
        b = ""
        for j,sj in enumerate(s[:n:]):
            if (i>>j)&1:
                r += sj
            else:
                b += sj
        ld[(r,b)] += 1

    for i in range(2**n):
        r = ""
        b = ""
        for j,sj in enumerate(s[2*n-1:n-1:-1]):
            if (i>>j)&1:
                r += sj
            else:
                b += sj
        rd[(r,b)] += 1

    ans = 0
    for lk,lv in ld.items():
        ans += lv*rd[lk]
    print(ans)
    return None

if __name__ == '__main__':
    main()