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[::-1][:n]
d=defaultdict(int)
ans=0
def paint(str,ptn):
  p=['','']
  for i in range(n):
    p[int(2**i&ptn>0)]+=str[i]
  return tuple(p)
for i in range(2**n):
  d[paint(s1,i)]+=1
for i in range(2**n):
  ans+=d[paint(s2,i)]
print(ans)