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
N=int(input())
S=input()
A=S[:N]
B=S[N:]
B=B[::-1]
def f(A):
    dd=defaultdict(int)
    for i in range(1<<N):
        a=[]
        b=[]
        for j in range(N):
            if i&(1<<j):
                a.append(A[j])
            else:
                b.append(A[j])
        s=''.join(a)
        t=''.join(b)
        dd[(s,t)]+=1
    return dd
dd1=f(A)
dd2=f(B)
ans=0
for t,c in dd1.items():
    ans+=dd2[t]*c
print(ans)