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 Counter

N = int(input())
S = input()

S1 = S[:N]
S2 = S[N:]
S2 = S2[::-1]
rb1 = Counter()
rb2 = Counter()
for i in range(2 ** N):
    flag = bin(i)[2:].zfill(N)
    r1 = ''
    b1 = ''
    r2 = ''
    b2 = ''
    for j in range(N):
        if flag[j] == '0':
            r1 += S1[j]
            r2 += S2[j]
        else:
            b1 = S1[j] + b1
            b2 = S2[j] + b2
    key1 = r1 + '&' + b1
    key2  =r2 + '&' + b2
    rb1[key1] += 1
    rb2[key2] += 1

ans = 0
for key in rb1.keys():
    ans += rb1[key] * rb2[key]

print(ans)