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:
n=int(input())
s=input()
from collections import defaultdict
l,r=s[:n],s[-1:-n-1:-1]
d=defaultdict(int)
for i in range(2**n):
    a={j for j in range(n)if (i>>j)%2}
    d[("".join(l[p] for p in sorted(list(a))),"".join(l[o] for o in range(n)if o not in a))]+=1
ans=0
for i in range(2**n):
    a={j for j in range(n)if (i>>j)%2}
    ans+=d[("".join(r[p] for p in sorted(list(a))),"".join(r[o] for o in range(n)if o not in a))]

print(ans)