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()
s1=s[:n]
s2=s[n:][::-1]
dic1={}
dic2={}
for i in range(2**n):
  r1=''
  r2=''
  b1=''
  b2=''
  flag=format(i,'b')
  l=len(flag)
  if l!=n:
    flag='0'*(n-l)+flag
  for j in range(n):
    if flag[j]=='0':
      r1+=s1[j]
      r2+=s2[j]
    else:
      b1+=s1[j]
      b2+=s2[j]
  if (r1,b1) not in dic1:
    dic1[(r1,b1)]=1
  else:
    dic1[(r1,b1)]+=1
  if (r2,b2) not in dic2:
    dic2[(r2,b2)]=1
  else:
    dic2[(r2,b2)]+=1
ans=0
for i in dic1.keys():
  if i in dic2:
    ans+=dic1[i]*dic2[i]
print(ans)