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())
string = input()
ans = 0
if string[:n] == string[2*n-1:n-1:-1]:
  ans += 2
for b in range(1,2**n-1):
  s = []
  t = []
  for c in range(n):
    if b & 2**c:
      s.append(string[c])
    else:
      t.append(string[c])
  s = s[::-1]
  t = t[::-1]
  ltr = string[n:]
  l = len(s)
  DP = [[0 for i in range(l+1)] for j in range(n+1)]
  DP[0][0] = 1
  for i in range(1,n+1):
    x = ltr[i-1]
    for j in range(0,min(i+1,l+1)):
      if j>=1 and s[j-1] == x:
        DP[i][j] += DP[i-1][j-1]
      if i-j<=len(t) and t[i-j-1] == x:
        DP[i][j] += DP[i-1][j]
  ans += DP[-1][-1]
print(ans)