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
from collections import Counter

n=int(input())
s=input()

t=s[:n][::-1]
u=s[n:]
tc=Counter()
uc=Counter()
for i in itertools.product(range(2),repeat=n):
	t0=""
	t1=""
	u0=""
	u1=""
	for j in range(n):
		if not i[j]:
			t0+=t[j]
			u0+=u[j]
		else:
			t1+=t[j]
			u1+=u[j]
	tc[t0+"-"+t1]+=1
	uc[u0+"-"+u1]+=1

ans=0
for i in tc.keys():
	ans+=tc[i]*uc[i]
print(ans)