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())
S = input()
S_l = S[:N]
S_r = S[N:][::-1]
dict_l = {}
dict_r = {}
ans = 0
for num in range(2**N):
  tmpl_1 = ""
  tmpl_2 = ""
  tmpr_1 = ""
  tmpr_2 = ""
  for n in range(N):
    if (num >> (N-1-n) & 1):
      tmpl_1 += S_l[n]
      tmpr_1 += S_r[n]
    else:
      tmpl_2 += S_l[n]
      tmpr_2 += S_r[n]
  dict_l[tmpl_1+"_"+tmpl_2] = dict_l.get(tmpl_1+"_"+tmpl_2, 0) + 1
  dict_r[tmpr_1+"_"+tmpr_2] = dict_r.get(tmpr_1+"_"+tmpr_2, 0) + 1
for k, v in dict_l.items():
  ans += v*dict_r.get(k,0)
print(ans)