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 (7.3.0) (judge verdict: Accepted)

from collections import Counter
from itertools import product

n = int(input())
d = Counter(list(map(int, input().split())) + [0])

ans, cnt = [], []
for num in d:
    if d[num] > (2 - (num in {0, 12})):
        print(0)
        exit()
    elif ((num in {0, 12}) and d[num] == 1) or d[num] == 2:
        ans += list(set([num, (24 - num) % 24]))
    elif d[num] == 1:
        cnt.append(num)

s = 0
if len(cnt) == 0:
    s = min(ans[i] - ans[i - 1] for i in range(1, len(ans)))
for bit in product([1, -1], repeat=len(cnt)):
    tmp = ans[:]
    tmp += [(ci - 12) * bi + 12 for bi, ci in zip(bit, cnt)]
    tmp = sorted(tmp + [i + 24 for i in tmp])
    stmp = min(tmp[i] - tmp[i - 1] for i in range(1, len(tmp)))
    s = max(s, stmp)
print(s)