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();l=s[:n];r=s[n:][::-1];d={};e={}
for i in range(1<<n):
 s=t=u=v=''
 for j in range(n):
  if i>>j&1:s+=l[j];t+=r[j]
  else:u+=l[j];v+=r[j]
 d[s,u]=d.get((s,u),0)+1
 e[t,v]=e.get((t,v),0)+1
print(sum(d[i]*e.get(i,0)for i in d.keys()))