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()
A = S[:n]
B = S[n:][::-1]
Da = defaultdict(int)
Db = defaultdict(int)
ans = 0
for i in range(2**n):
  a1, a2 = "", ""
  for j in range(n):
    if i>>j & 1:
      a1 += A[j]
    else:
      a2 += A[j]
  Da[(a1, a2)] += 1
for i in range(2**n):
  b1, b2 = "", ""
  for j in range(n):
    if i>>j & 1:
      b1 += B[j]
    else:
      b2 += B[j]
  Db[(b1, b2)] += 1

for k in Da:
  ans += Da[k] * Db[k]
print(ans)