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:
# -*- coding: utf-8 -*-
from collections import defaultdict

N = int(input())
S = input()
A, B = S[:N], S[N:]
D = defaultdict(int)
ans = 0

def paint(X, i):
    r = ""
    b = ""
    for j, k in enumerate(format(i, "b").zfill(N)):
        if k == "1":
            r += X[j]
        else:
            b += X[j]
    return r, b

for i in range(2**N):
    r, b = paint(A, i)
    D[(r, b)] += 1

for i in range(2**N):
    r, b = paint(B, i)
    ans += D[(b[::-1], r[::-1])]

print(ans)