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()

T = S[:N]
U = S[N:]
U = U[::-1]

from collections import defaultdict

dd1 =defaultdict(int)
dd2 =defaultdict(int)

for i in range(2**N):
    red1 = ""
    blue1 = ""
    red2 = ""
    blue2 = ""
    for j in range(N):
        if (i//(2**j))%2==0:
            red1 = red1 + T[j]
            red2 = red2 + U[j]
        else:
            blue1 = blue1 + T[j]
            blue2 = blue2 + U[j]
    dd1[red1 + " " + blue1]+=1
    dd2[red2 + " " + blue2]+=1
ans=0
for key in dd1:
    ans+=dd1[key]*dd2[key]
print(ans)