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]

def get_s(s, i):
  s1 = s2 = ''
  for j in range(N):
    if i>>j & 1:
      s1 += s[j]
    else:
      s2 += s[j]
  return (s1, s2)

d1 = defaultdict(int)
d2 = defaultdict(int)
for i in range(2**N):
  s1 = get_s(S1, i)
  d1[s1] += 1
  s2 = get_s(S2, i)
  d2[s2] += 1

ans = 0
for k in d1:
  ans += d1[k] * d2[k]

print(ans)