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 f():
    n,s=int(input()),input()
    a,b=s[n-1::-1],s[n:]
    ad={}
    bd={}
    for i in range(2**n):
        sa,ta,sb,tb="","","",""
        for j in range(n):
            if i%2:
                sa+=a[j]
                sb+=b[j]
            else:
                ta+=a[j]
                tb+=b[j]
            i//=2
        ad[(sa,ta)]=(1 if (sa,ta)not in ad else ad[(sa,ta)]+1)
        bd[(sb,tb)]=(1 if (sb,tb)not in bd else bd[(sb,tb)]+1) 
    ans=0
    for k in ad:
        if k in bd:ans+=bd[k]*ad[k]
    print(ans)
if __name__ == "__main__":
    f()