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
n = int(input())
s = input().rstrip()
front = s[:n]
back = s[n:]
back = list(reversed(back))
front_cnt = Counter()
back_cnt = Counter()
for i in range(2**n):
    fred = fblue = bred = bblue = "" 
    for j in range(n):
        if(i & 1 << j):
            fred += front[j]
            bred += back[j]
        else:
            fblue += front[j]
            bblue += back[j]
    front_cnt[fred + "_" + fblue] += 1
    back_cnt[bred + "_" + bblue] += 1

ans = 0
for key in front_cnt.keys():
    ans += front_cnt[key] * back_cnt[key]
print(ans)