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=list(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
a=0
for i in d.keys():
  a+=d[i]*e.get(i,0)
print(a)