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 itertools
N=int(input())
S=input()
ans=0
L=dict()
R=dict()
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    T3=""
    for i in range(N):
        if seq[i]==0:
            T0+=S[i]
            T2+=S[-i-1]
        else:
            T1+=S[i]
            T3+=S[-i-1]
    a0=len(T0)
    a1=len(T1)
    a2=len(T2)
    a3=len(T3)
    if (T0,T1) in L:
        L[(T0,T1)]+=1
    else:
        L[(T0,T1)]=1
    if (T2,T3) in R:
        R[(T2,T3)]+=1
    else:
        R[(T2,T3)]=1
for tup in L:
    if tup in R:
        ans+=L[tup]*R[tup]
print(ans)