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 defaultdict

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


def solve(s):
    d = defaultdict(int)
    for i in range(2**n):
        blue = red = ""
        for k in range(n):
            if 1 << k & i:
                blue += s[k]
            else:
                red += s[k]
        d[(blue, red)] += 1
    return d


left = solve(s[:n])
right = solve(s[::-1][:n])


ans = 0
for (b, r), v in left.items():
    ans += v * right[(r, b)]

print(ans)