Problem:
Score : 500 points

Problem Statement

In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.

Takahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.
The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours.
Here, we are using 24-hour notation.
That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.

Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.

Find the maximum possible value of s.

Constraints

1 \leq N \leq 50

0 \leq D_i \leq 12

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N

Output

Print the maximum possible value of s.

Sample Input 1

3
7 12 8

Sample Output 1

4

For example, consider the situation where it is 7, 12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.

Sample Input 2

2
11 11

Sample Output 2

2

Sample Input 3

1
0

Sample Output 3

0

Note that Takahashi himself is also a participant.

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import Counter

N = int(input())
D = [int(i) for i in input().split()]

cnt = Counter(D)

ret = 0
for i in range(pow(3, len(cnt))) :
  L = []
  tmp = float('inf')
  for j, (k, v) in enumerate(cnt.items()) :
    if i % 3 == 0 :
      if v < 2 :
        break
      L.append(k)
      L.append(24 - k)
    elif i % 3 == 1 :
      L.append(k)
    elif i % 3 == 2 :
      L.append(24 - k)
    i //= 3
  else :
    L.sort()
    for i in range(1, len(L)) :
      tmp = min(tmp, L[i] -  L[i-1])
    if tmp != float('inf') :
      ret = max(ret, tmp)

print(ret)