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()

left, right = S[:N], S[N:][::-1]
a, b = Counter(), Counter()

for i in range(2 ** N):
    t = u = v = w = ""
    for j in range(N):
        if (i >> j) & 1:
            t += left[j]
            u += right[j]
        else:
            v += left[j]
            w += right[j]
    a[t, v] += 1
    b[u, w] += 1

print(sum(a[t] * b[t] for t in a.keys()))