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:
ans=0

from collections import defaultdict
n=int(input())
s=input()
a=s[:n]
b=s[n:][::-1]
def coloring(x):
    N=1<<n
    dc=defaultdict(int)
    for i in range(N):
        r=''
        b=''
        for j in range(n):
            if i>>j&1:
                r+=x[j]
            else:
                b+=x[j]
        dc[r+'-'+b]+=1
    return dc    

fd=coloring(a)
ld=coloring(b)

for i,j in fd.items():
    ans+=ld[i]*j

print(ans)