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())
left=s[:n]
right=s[n:]
right.reverse()

from itertools import *
from collections import defaultdict
d = defaultdict(int)

for pro in product([0,1], repeat=n):
    s1=s2=""
    for i,p in enumerate(pro):
        if p==0:
            s1+=left[i]
        else:
            s2+=left[i]
    d[(s1,s2)]+=1

ans=0
for pro in product([0,1], repeat=n):
    s1=s2=""
    for i,p in enumerate(pro):
        if p==0:
            s1+=right[i]
        else:
            s2+=right[i]
    ans+=d[(s1,s2)]
print(ans)