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:
from itertools import product
from collections import defaultdict
n = int(input())
s = input()
sa,sb = s[:n],s[n:][::-1]
a,b,ans = defaultdict(int),defaultdict(int),0
for i in product(range(2),repeat=n):
	wa,wb,wa2,wb2 = "","","",""
	for j in range(n):
		if i[j]: wa,wb = wa+sa[j],wb+sb[j]
		else: wa2,wb2 = wa2+sa[j],wb2+sb[j]
	a[(wa,wa2)]+=1
	b[(wb,wb2)]+=1
while a:
	p,q = a.popitem()
	ans+=q*b[p]
print(ans)