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:
N=int(input())
S=list(input())
left=S[:N]
right=S[N:][::-1]
ans=0
for i in range(2**N):
    red=[]
    blue=[]
    for j in range(N):
        if (i>>j)&1==1:
            red.append(S[j])
        else:
            blue.append(S[j])
    L=len(red)
    if L==0 or L==N:
        if right==left:
            ans+=1
        continue
    dp=[[0]*L for _ in range(N)]
    zero=0
    if right[0]==red[0]:
        dp[0][0]=1
    if right[0]==blue[0]:
        zero=1
    for j in range(1,N):
        if right[j]==red[0]:
            dp[j][0]=zero
        if j-1+L<N and right[j]==blue[j-1]:
            dp[j][0]+=dp[j-1][0]
        if j+L<N and right[j]==blue[j]:
            zero*=1
        else:
            zero=0
        for k in range(1,min( j+1,len(red))):
            if right[j]==red[k]:
                dp[j][k]+=dp[j-1][k-1]
            if j-k<=N-L and right[j]==blue[j-k-1]:
                dp[j][k]+=dp[j-1][k]
    ans+=dp[N-1][-1]
print(ans)