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:
def i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]
n=i1()
s=input()
from collections import defaultdict
ad1 = defaultdict(int)
ad2 = defaultdict(int)

for i in range(1<<n):
 a=""
 b=""
 for j in range(n):
  if i & (1<<j) ==0:
     a+=s[j]
  else:
     b+=s[j]
 ad1[a+"_"+b[::-1]]+=1
 a=""
 b=""
 for j in range(n):
  if i & (1<<j):
     a+=s[j+n]
  else:
     b+=s[j+n]
 ad2[b[::-1]+"_"+a]+=1
 
cc=0
for i in ad1.keys():
 cc+=ad1[i]*ad2[i]

print(cc)