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 defaultdict
n=int(input())
s=list(input())
left=s[:n]
right=list(reversed(s[n:]))

DL=defaultdict(int)
for i in range(2**n):
    red=[]
    blue=[]
    for j in range(n):
        if (i>>j)&1:
            red.append(left[j])
        else:
            blue.append(left[j])
    DL["".join(red),"".join(blue)]+=1

DR=defaultdict(int)
for i in range(2**n):
    red=[]
    blue=[]
    for j in range(n):
        if (i>>j)&1:
            red.append(right[j])
        else:
            blue.append(right[j])
    DR["".join(blue),"".join(red)]+=1

ans=0
for k,v in DL.items():
    if k in DR:
        ans+=v*DR[k]
print(ans)