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:
def main():
    from collections import defaultdict

    N = int(input())
    S = str(input())

    dic = defaultdict(int)

    for i in range(2 ** N):
        a = str()
        b = str()
        for j in range(N):
            if (i >> j) & 1:
                a += S[j + N]
            else:
                b += S[j + N]
        
        dic[(a, b)] += 1

    count = 0
    for i in range(2 ** N):
        a = str()
        b = str()
        for j in range(N):
            if (i >> j) & 1:
                a += S[j]
            else:
                b += S[j]
        count += dic[b[::-1], a[::-1]]

    print (count)

if __name__ == '__main__':
    main()