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 = input()

    L, R = S[:N], S[N * 2 - 1:N - 1:-1]

    def make_counter(s: str) -> defaultdict(int):
        ret = defaultdict(int)
        for bit in range(1 << N):
            red, blue = '', ''
            for j in range(N):
                if (bit >> j) & 1:
                    red += s[j]
                else:
                    blue += s[j]

            ret[red + '_' + blue] += 1
        return ret

    ld = make_counter(L)
    rd = make_counter(R)

    print(sum(ld[key] * rd[key] for key in ld))


if __name__ == '__main__':
    main()