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:
import itertools

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

left = s[:n]
right = s[n:][::-1]

dicleft = {}
for v in itertools.product([0, 1], repeat=n):
    red, blue = '', ''
    for i in range(n):
        if v[i] == 0: red += left[i]
        else: blue += left[i]
    idx = red + '_' + blue
    if idx in dicleft:
        dicleft[idx] += 1
    else:
        dicleft[idx] = 1

dicright = {}
for v in itertools.product([0, 1], repeat=n):
    red, blue = '', ''
    for i in range(n):
        if v[i] == 0: red += right[i]
        else: blue += right[i]
    idx = red + '_' + blue
    if idx in dicright:
        dicright[idx] += 1
    else:
        dicright[idx] = 1

ans = 0
for key, value in dicleft.items():
    if key in dicright:
        ans += value * dicright[key]
print(ans)