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 combinations
from collections import defaultdict

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

d = defaultdict(int)
left = set()

for r in range(n + 1):
	for j in combinations(range(n), r):
		sl = ""
		sr = ""
		for i in range(n):
			if i in j:
				sl += s[i]
			else:
				sr += s[i]
		left.add(sl + "," + sr)
		d[sl + "," + sr] += 1
res = 0
for r in range(n + 1):
	for j in combinations(range(n, 2 * n), r):
		sl = ""
		sr = ""
		for i in range(n, 2 * n):
			if i in j:
				sl = s[i] + sl
			else:
				sr = s[i] + sr
		if sr + "," + sl in left:
			res += d[sr + "," + sl]
print(res)