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()
SL = S[:N]
SR = S[N:][::-1]

ans = 0
memo = defaultdict(int)

for bit in range(1 << N):
    red = ""
    blue = ""
    for i in range(N):
        if bit & (1 << i):
            red += SL[i]
        else:
            blue += SL[i]
    memo[(red, blue)] += 1

for bit in range(1 << N):
    red = ""
    blue = ""
    for i in range(N):
        if bit & (1 << i):
            red += SR[i]
        else:
            blue += SR[i]
    ans += memo[(red, blue)]

print(ans)