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=list(input())
l=[s[i] for i in range(n)]
r=[s[i] for i in range(n,2*n)]
r=r[::-1]
from collections import defaultdict
ld=defaultdict(int)
rd=defaultdict(int)
for i in range(2**n):
    ls=['', '']
    rs=['', '']
    for j in range(n):
        if (i>>j)%2==0:
            ls[0]+=l[j]
            rs[0]+=r[j]
        elif (i>>j)%2==1:
            ls[1]+=l[j]
            rs[1]+=r[j]
    ls=tuple(ls)
    rs=tuple(rs)
    ld[ls]+=1
    rd[rs]+=1

cnt=0
for k in ld.keys():
    a=ld[k]
    b=rd[k]
    cnt+=a*b
print(cnt)