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:
def main(n,a):
    a1,a2=a[:n],a[n:]
    a2.reverse()
    d1={}
    d2={}
    for i in range(2**n):
        r1=[]
        r2=[]
        l1=[]
        l2=[]
        for j in range(n):
            if (i>>j)&1:
                r1.append(a1[j])
                r2.append(a2[j])
            else:
                l1.append(a1[j])
                l2.append(a2[j])
        s1=''.join(r1)+'-'+''.join(l1)
        s2=''.join(r2)+'-'+''.join(l2)
        if s1 in d1:d1[s1]+=1
        else:d1[s1]=1
        if s2 in d2:d2[s2]+=1
        else:d2[s2]=1
    ans=0
    for k in d1:
        if k in d2:
            ans+=d1[k]*d2[k]
    return ans

n=int(input())
a=list(input())
#a=list(map(int,input().split()))
#b=list(map(int,input().split()))
#ab=[list(map(int,input().split())) for _ in range(n)]
print(main(n,a))