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 *

N = int(input())
s = list(input())
cnt = defaultdict(lambda : defaultdict(int))

for S in range(2**N):
    red, blue = [], []
    
    for i in range(N):
        if (S>>i)&1:
            red.append(s[i])
        else:
            blue.append(s[i])
    
    cnt[''.join(red)][''.join(blue)] += 1

s.reverse()
ans = 0

for S in range(2**N):
    red, blue = [], []
    
    for i in range(N):
        if (S>>i)&1:
            red.append(s[i])
        else:
            blue.append(s[i])
    
    ans += cnt[''.join(blue)][''.join(red)]

print(ans)