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=int(input())
    s=input()
    d1=dict()
    d2=dict()
    temp1=[None]*n
    temp2=[None]*n
    for ii in range(2**n):
        i=("0"*n+bin(ii)[2:])[-n:]
        cnt1=0
        cnt2=n-1
        for k,j in enumerate(i):
            if j=="1":
                temp1[cnt1]=s[k]
                temp2[cnt1]=s[2*n-k-1]
                cnt1+=1
            else:
                temp1[cnt2]=s[k]
                temp2[cnt2]=s[2*n-k-1]
                cnt2-=1
        t1="".join(temp1)
        t2="".join(temp2)
        if (t1,cnt1) not in d1.keys():
            d1[(t1,cnt1)]=1
        else:
            d1[(t1,cnt1)]+=1
        if (t2,cnt1) not in d2.keys():
            d2[(t2,cnt1)]=1
        else:
            d2[(t2,cnt1)]+=1
    ans=0
    for i,j in d1.items():
        if i in d2.keys():
            ans+=j*d2[i]
    print(ans)
main()