p03298 AtCoder Grand Contest 026 - String Coloring
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
```python
def f():
    n=int(input())
    s=list(input())
    a,b=s[n-1::-1],s[n:]
    from collections import defaultdict

    ad=defaultdict(int)
    bd=defaultdict(int)
    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
        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()
```