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:
from collections import defaultdict

N=int(input())
S=input()
S1=S[:N]
S2=S[N:][::-1]

bit=1<<N

firstList=[]
secondList=defaultdict(int)
for i in range(bit):
  blue=""
  red=""
  blue2=""
  red2=""
  for j in range(N):
    if (i>>j)%2:
      blue+=S1[j]
      blue2+=S2[j]
    else:
      red+=S1[j]
      red2+=S2[j]
  firstList.append(blue + "-" + red)
  secondList[blue2 + "-" + red2]+=1

ans=0
for s in firstList:
  ans+=secondList[s]
print(ans)