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 PYTHON):

Solution:
import sys

if sys.version[0] == '2':
    range, input = xrange, raw_input

from collections import defaultdict
N = int(input())
S = input()
first, second = S[:N], S[N:]

s_set = defaultdict(int)

def make_str(bit, s):
    red = []
    blue = []
    for i in range(N):
        if bit >> i & 1:
            red.append(s[i])
        else:
            blue.append(s[i])
    return ''.join(red), ''.join(blue[::-1])

for bit in range(1 << N):
    s_set[make_str(bit, second)] += 1

ans = 0
for bit in range(1 << N):
    red, blue = make_str(bit, first)
    ans += s_set[blue, red]
print(ans)