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)

def main():
    N = int(input())
    D = [int(i) for i in input().split()]
    ans = 0
    cnt = [0]*24
    from collections import Counter
    c = Counter(D)
    cnt[0] = 1
    s = [0]*13
    for k, v in c.items():
        if v >= 3 or k == 0:
            ans = 0
            return print(ans)
        elif v >= 2:
            cnt[k] += 1
            cnt[24 - k] += 1
        elif k == 12:
            cnt[12] += 1
        else:
            s[k] += 1
    if any(c >= 2 for c in cnt):
        return print(0)
    for bit in range(1 << 11):
        cur = cnt[:]
        for i in range(11):
            if s[i+1]:
                if bit & (1 << i):
                    cur[24 - (i+1)] += 1
                else:
                    cur[i+1] += 1
        if any(c >= 2 for c in cnt):
            continue
        pre = 0
        mi = 24
        for i, ne in enumerate(cur[1:] + [1], start=1):
            if ne and i - pre < mi:
                mi = i - pre
                pre = i
        if mi != 24:
            ans = max(ans, mi)
    print(ans)


if __name__ == '__main__':
    main()