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
N = int(input())
S = input()
Sl = list(S[:N])
Sr = list(reversed(S[N:]))
d_l = defaultdict(int)
d_r = defaultdict(int)
for s in range(1<<N):
    sl1 = ''
    sl2 = ''
    sr1 = ''
    sr2 = ''
    for i in range(N):
        if s&(1<<i):
            sl1+=Sl[i]
            sr1+=Sr[i]
        else:
            sl2+=Sl[i]
            sr2+=Sr[i]
    d_l[sl1+' '+sl2]+=1
    d_r[sr1+' '+sr2]+=1
ans = 0
for k, v in d_l.items():
    ans += d_r[k]*v
print(ans)