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 itertools import product
from collections import defaultdict
N = int(input())
S = input()

ans = 0
D = defaultdict(int)
for pattern in product([0, 1], repeat=N):
    red = ''.join([s for s, p in zip(S[:N], pattern) if p == 0])
    blue = ''.join([s for s, p in zip(S[:N], pattern) if p == 1])
    D[(red, blue)] += 1

for pattern in product([0, 1], repeat=N):
    red = ''.join([s for s, p in zip(S[N:], pattern) if p == 0])
    blue = ''.join([s for s, p in zip(S[N:], pattern) if p == 1])
    ans += D[(blue[::-1], red[::-1])]
print(ans)