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
N = int(input())
S = input()
r = [0, 1]
ans = 0
d = [{} for i in range(N+1)]
for p in product(r, repeat=N):
    s = []
    for i in range(N):
        if p[i]:
            s.append(S[i])
    for i in range(N-1, -1, -1):
        if p[i] == 0:
            s.append(S[i])
    l = sum(p)
    s = "".join(s)
    d[l][s] = d[l].get(s, 0) + 1
for p in product(r, repeat=N):
    s = []
    for i in range(N-1, -1, -1):
        if p[i]:
            s.append(S[i+N])
    for i in range(N):
        if p[i] == 0:
            s.append(S[i+N])
    l = sum(p)
    s = "".join(s)
    ans += d[l].get(s, 0)
print(ans)