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:
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda:sys.stdin.readline().rstrip()
from collections import defaultdict
def resolve():
    n=int(input())
    S=input()
    S,T=S[:n],S[2*n-1:n-1:-1]
    C=defaultdict(int)

    for V in range(1<<n):
        s=''.join([s if((V>>i)&1) else '' for i,s in enumerate(S)])
        t=''.join([s if(not (V>>i)&1) else '' for i,s in enumerate(S)])
        C[(s,t)]+=1

    ans=0
    for V in range(1<<n):
        s=''.join([t if((V>>i)&1) else '' for i,t in enumerate(T)])
        t=''.join([t if(not (V>>i)&1) else '' for i,t in enumerate(T)])
        ans+=C[(s,t)]

    print(ans)
resolve()