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();
SL=S[:N];SR=S[N:];SR=SR[::-1]
MR={};ans=0
for i in range(2**N):
  R="";B="";
  for j in range(N):
    if(i%2):
      R+=SL[j]
    else:
      B+=SL[j]
    i//=2
  if R+"_"+B in MR: 
    MR[R+"_"+B]+=1
  else:
    MR[R+"_"+B]=1
for i in range(2**N):
  R="";B="";
  for j in range(N):
    if(i%2):
      R+=SR[j]
    else:
      B+=SR[j]
    i//=2
  if R+"_"+B in MR: 
    ans+=MR[R+"_"+B]
print(ans)