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


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

    X = S[:N]
    Y = S[N:]
    Y = Y[::-1]

    dx = defaultdict(int)
    dy = defaultdict(int)

    for bit in range(1 << N):
        red = ""
        blue = ""
        for i in range(N):
            if bit & (1 << i):
                red += X[i]
            else:
                blue += X[i]

        dx[(red, blue)] += 1

    for bit in range(1 << N):
        red = ""
        blue = ""
        for i in range(N):
            if bit & (1 << i):
                red += Y[i]
            else:
                blue += Y[i]

        dy[(red, blue)] += 1

    # 前後が同じになる組がいくつできるか。
    ans = 0
    for k,v in dx.items():
        ans += dy[k] * v

    print(ans)


if __name__ == "__main__":
    main()