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 = list(input())

    L = s[:n]
    R = s[n:]
    R.reverse()

    br_l = defaultdict(int)
    br_r = defaultdict(int)

    L_map = dict()

    for i in range(2**n):
        al,bl,ar,br = '','','',''
        for j in range(n):
            if (i>>j)%2:
                al += L[j]
                ar += R[j]
            else:
                bl += L[j]
                br += R[j]
        br_l[(al,bl)] += 1
        br_r[(ar,br)] += 1

    ans = 0
    for k in br_l.keys():
        ans+= br_r[k] * br_l[k]
    print(ans)

main()