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()
cnt = defaultdict(dict)

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)
    
    if b not in cnt[r]:
        cnt[r][b] = 1
    else:
        cnt[r][b] += 1

S = S[::-1]
ans = 0

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)
    
    if r in cnt[b]:
        ans += cnt[b][r]

print(ans)