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()

l = Counter()
for i in range(2 ** n):
    r, b = [], []
    for j in range(n):
        if (i >> j) & 1:
            r.append(s[j])
        else:
            b.append(s[j])
    r = ''.join(r)
    b = ''.join(b)
    l[(r[::-1], b[::-1])] += 1

ans = 0
for i in range(2 ** n):
    r, b = [], []
    for j in range(n):
        if (i >> j) & 1:
            r.append(s[n + j])
        else:
            b.append(s[n + j])
    
    r = ''.join(r)
    b = ''.join(b)
    ans += l[(b, r)]

print(ans)