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 collections
d=collections.defaultdict(int)
n=int(input())
s=input()
def f(s,r,b,t):
    if t==n:
        d[(r,b)]+=1
        return
    f(s,r+s[t],b,t+1)
    f(s,r,b+s[t],t+1)
f(s[:n],"","",0)
d1=d
d=collections.defaultdict(int)
f(s[-1:n-1:-1],"","",0)
ans=0
for i,j in d.items():
    ans+=j*d1[i]
print(ans)