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:
N = int(input())
S = input()
S = S[:N] + S[N:][::-1]

import collections

def count(S):
    n = len(S)
    T = []
    for i in range(2**n):
        r, b = '', ''
        for j in range(n):
            if i >> j & 1:
                r += S[j]
            else:
                b += S[j]
        T.append((r, b))
    return collections.Counter(T)

A = count(S[:N])    
B = count(S[N:])

ans  = 0
for a in A:
    if a in B:
        ans += A[a]*B[a]

print(ans)