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()

S1,S2 = S[:N],S[N:][::-1]

dic = {}
Ans = 0
keys = []

for i in range(2**N):
    red,blue = "",""
    red2,blue2 = "",""
    bits = bin(2**N+i)[3:]
    for j in range(N):
        if bits[j]=="0":
            red   += S1[j]
            red2 += S2[j]
        else:
            blue += S1[j]
            blue2 += S2[j]
    keys.append(red2+"-"+blue2)
    key = red+"-"+blue
    if key not in dic.keys():
        dic[key] = 1
    else:
        dic[key] += 1

for k in keys:
    Ans += dic.get(k,0)

print(Ans)