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 sys
input = sys.stdin.readline
from collections import defaultdict
from itertools import compress 
N = int(input())
S = input().strip()
#N = 18
#S = 'abc' * 12
S1 = S[:N]
S2 = S[N:][::-1]

Ls = defaultdict(lambda : defaultdict(int))

def int2bin(x,N): 
    res = [0]*N
    for i in range(N):
        res[N-1-i] = x % 2
        x >>= 1
    return res

for i in range(2**N):
    bs = int2bin(i,N)
    n = sum(bs)
    R = ""
    B = ""
    for s,b in zip(S1,bs):
        if b == 1:
            R += s
        else:
            B += s
    Ls[n][(R,B[::-1])] += 1

ans = 0
for i in range(2**N):
    bs = int2bin(i,N)
    n = sum(bs)
    R = ""
    B = ""
    for s,b in zip(S2,bs):
        if b == 1:
            B += s
        else:
            R += s
    R = R[::-1]
    ans += Ls[n][(B,R)]

print(ans)