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 collections import Counter
from itertools import product

n = int(input())
s = list(input())
s_l = list(reversed(s[n:]))

red = Counter(["".join([s[i] for i in range(n) if bit[i] == 1] + ["|"] + [s[i] for i in range(n) if bit[i] == 0]) for bit in product(range(2), repeat=n)])
blue = Counter(["".join([s_l[i] for i in range(n) if bit[i] == 1] + ["|"] + [s_l[i] for i in range(n) if bit[i] == 0]) for bit in product(range(2), repeat=n)])

ans = 0

for key, value in red.items():
	ans += value * blue[key]

print(ans)