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=input()
S,T=S[:N],S[N:][::-1]
A=dict()
B=dict()
X1,Y1,X2,Y2,Z=0,0,0,0,0
for i in range(1<<N):
  X1,Y1,X2,Y2,Z='','','','',1
  for j in range(N):
    if i&Z:
      X1+=S[j]
      X2+=T[j]
    else:
      Y1+=S[j]
      Y2+=T[j]
    Z<<=1
  A[(X1,Y1)]=A.get((X1,Y1),0)+1
  B[(X2,Y2)]=B.get((X2,Y2),0)+1
P=0
Z=list(A.keys())
for i in range(len(Z)):
  P+=A[Z[i]]*B.get(Z[i],0)
print(P)