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 I
from collections import Counter as C
n=int(input());s=input();l=s[:n];r=s[n:][::-1];a=C();b=C()
for i in I.product([0,1],repeat=n):
 t=u=v=w=''
 for j in range(n):
  if i[j]:t+=l[j];u+=r[j]
  else:v+=l[j];w+=r[j]
 a[t,v]+=1
 b[u,w]+=1
print(sum(a[i]*b[i]for i in a.keys()))