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()

sleft = S[:N]
sright = S[2*N:N-1:-1]
ldict,rchoise = {},[]
count = 0
for i in range(2**N):
    red = bin(i)[2:].zfill(N)
    leftred, rightred, leftblue, rightblue = "","","",""
    for j in range(N):
        if red[j] == "1":
            leftred += sleft[j]
            rightred += sright[j]
        else:
            leftblue += sleft[j]
            rightblue += sright[j]
    if leftred + "-" + leftblue in ldict.keys():
        ldict[leftred + "-" + leftblue] += 1
    else:
        ldict[leftred + "-" + leftblue] = 1
    rchoise.append(rightred + "-" + rightblue)
    
for i in rchoise:
    count += ldict.get(i, 0)
print(count)