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:
from collections import defaultdict
from itertools import combinations


def solve():
    N = int(input())
    S = input()
    s1, s2 = S[:N], S[N:][::-1]
    
    l_dict = defaultdict(int)
    r_dict = defaultdict(int)
    for i in range(N+1):
        for red_idx in combinations(range(N), i):
            red, blue = '', ''
            for j in range(N):
                if j in red_idx:
                    red += s1[j]
                else:
                    blue += s1[j]
            l_dict[red+' '+blue] += 1
    for i in range(N+1):
        for red_idx in combinations(range(N), i):
            red, blue = '', ''
            for j in range(N):
                if j in red_idx:
                    red += s2[j]
                else:
                    blue += s2[j]
            r_dict[red+' '+blue] += 1
    
    ans = sum(l_dict[key] * r_dict[key] for key in l_dict)
    print(ans)


if __name__ == '__main__':
    solve()