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
import sys
input = sys.stdin.readline

N = int(input())
S = input().rstrip()
ans = 0

cnt = defaultdict(int)
for bit in range(1 << N):
    a = b = ''
    for i in range(N):
        if bit >> i & 1:
            a += S[i]
        else:
            b += S[i]
    cnt[(a, b)] += 1
ans = 0
for bit in range(1 << N):
    a = b = ''
    for i in range(N):
        if bit >> i & 1:
            a += S[N+i]
        else:
            b += S[N+i]
    ans += cnt[(b[::-1], a[::-1])]
print(ans)