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:
import itertools as it
from collections import Counter as c
n=int(input())
a=c()
b=c()
s=input()
q=s[:n]
r=s[n:][::-1]
for i in it.product([0,1],repeat=n):
    d,e,f,g="","","",""
    for j in range(n):
        if i[j]==1:
            d+=q[j]
            f+=r[j]
        else:
            e+=q[j]
            g+=r[j]
    a[d,e]+=1
    b[f,g]+=1
print(sum(a[i]*b[i] for i in a.keys()))