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()
ans=0

first={}
last={}

def dfs(r,b,num):
    if num==N:
        if (r,b) not in first:
            first[(r,b)]=0
        first[(r,b)]+=1
        return 0

    if len(r)<N:
        dfs(r+S[num],b,num+1)

    if len(b)<N:
        dfs(r,S[num]+b,num+1)

dfs("","",0)

def dfs2(r,b,num):
    if num==2*N:
        if (r,b) not in last:
            last[(r,b)]=0
        last[(r,b)]+=1
        return 0

    if len(r)<N:
        dfs2(r+S[num],b,num+1)

    if len(b)<N:
        dfs2(r,S[num]+b,num+1)

dfs2("","",N)

for r,b in first:
    if (b,r) in last:
        ans+=first[(r,b)]*last[(b,r)]
        
print(ans)