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
from itertools import combinations


def get_pair(s, cmb):
    g, h = 0, 0
    for i in range(n):
        if i in cmb:
            g <<= 5
            g += s[i]
        else:
            h <<= 5
            h += s[i]
    return g, h


def patterns(k, d, e):
    ret = 0
    f = defaultdict(int)
    for cmb in combinations(range(n), k):
        f[get_pair(d, cmb)] += 1
    for cmb in combinations(range(n), k):
        ret += f[get_pair(e, cmb)]
    return ret


def solve(n, b):
    d = b[:n]
    e = b[2 * n - 1:n - 1:-1]
    ans = 0

    if n % 2 == 0:
        for k in range(n // 2):
            ans += 2 * patterns(k, d, e)
        ans += patterns(n // 2, d, e)
    else:
        for k in range(n // 2 + 1):
            ans += 2 * patterns(k, d, e)
    return ans


n = int(input())
s = input()
a = ord('a') - 1
b = [ord(c) - a for c in s]
print(solve(n, b))