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()
#半分全列挙+bit全探索だ！！！！！！天才！！！！！！！！！
left={}
right={}
sl=s[:n]
sr=s[n:]
for i in range(1<<(n)):
  lr=lb=""
  rr=rb=""
  for j in range(n):
    if i&(1<<j):
      lr+=sl[j]
      rr+=sr[j]
    else:
      lb+=sl[j]
      rb+=sr[j]
  l=lr+","+lb
  r=(rr+","+rb)[::-1]
  if l in left:left[l]+=1
  else:left[l]=1
  if r in right:right[r]+=1
  else:right[r]=1
ans=0
for i in left:
  if i in right:ans+=left[i]*right[i]
print(ans)