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

n = int(input())
s = input()

d = defaultdict(int)

s1 = s[:n]
s2 = s[n:][::-1]

for i in range(2**n):
    left,right = [],[]
    for j in range(n):
        if(i >> j)&1:
            left.append(s1[j])
        else:
            right.append(s1[j])
    d[ ''.join(left) + '_' + ''.join(right) ] += 1

ans = 0
for i in range(2**n):
    left,right = [],[]
    for j in range(n):
        if(i >> j)&1:
            left.append(s2[j])
        else:
            right.append(s2[j])
    ans += d[ ''.join(left) + '_' + ''.join(right) ]

print(ans)