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 Counter
from itertools import product
N = int(input())
S = input()
Left = Counter()
Right = Counter()
S_left = S[:N]
S_right = S[2*N-1:N-1:-1]
for B in product(range(2),repeat = N):
    red_left = ''
    blue_left = ''
    red_right = ''
    blue_right = ''
    for i in range(N):
        if B[i]:
            red_left += S_left[i]
            red_right += S_right[i]
        else:
            blue_left += S_left[i]
            blue_right += S_right[i]
    Left[red_left + '|' + blue_left] += 1
    Right[blue_right + '|' + red_right] += 1
ans = 0
for i in Left.keys():
    ans += Left[i]*Right[i]
print(ans)