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 Counter

N = int(input())
S = input()
S_former = S[:N]
S_latter = S[N:][::-1]
ans = 0


def analyzer(St):
    n = len(St)
    A = []
    for i in range(2**n):
        red = ''
        blue = ''
        for j in range(n):
            if (i >> j) & 1 == 1:
                red += St[j]
            else:
                blue += St[j]
        A.append((red, blue))
    return Counter(A)


SC_former = analyzer(S_former)
SC_latter = analyzer(S_latter)
for ke, va in SC_former.items():
    ans += SC_latter[ke] * va

print(ans)