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()

a = s[:n]
b = s[n:][::-1]
d = defaultdict(int)
e = defaultdict(int)

for bit in range(1 << n):
    x = ""
    y = ""
    z = ""
    w = ""
    for i in range(n):
        if bit >> i & 1:
            x += a[i]
            z += b[i]
        else:
            y += a[i]
            w += b[i]
    d[x+'ω'+y] += 1
    e[z+'ω'+w] += 1

print(sum([e[k] * v for k, v in d.items()]))