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

hash = {}
for bit in range(1 << n):
    red, blue = "", ""
    for i in range(n):
        if (bit & (1 << i)) > 0:
            red += s[i]
        else:
            blue += s[i]
    hash[(red, blue)] = hash.get((red, blue), 0)+1

t = s[n:][::-1]
cnt = 0
for bit in range(1 << n):
    red, blue = "", ""
    for i in range(n):
        if (bit & (1 << i)) > 0:
            red += t[i]
        else:
            blue += t[i]
    cnt += hash.get((blue, red), 0)

print(cnt)