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 Python (3.8.2) (judge verdict: Wrong Answer)

import itertools
n = int(input())
d = list(map(int,input().split()))
time = [0 for i in range(13)]
for i in range(n):
    time[d[i]] += 1

if n == 1:
    print(min(d[0],24-d[0]))
    exit()
kouho = [0]
doti = []
for i in range(13):
    if time[i] >= 3:
        print(0)
        exit()
    elif time[i] == 2:
        kouho.append(i)
        kouho.append(24-i)
    elif time[i] == 1:
        doti.append((i,24-i))


ans = 0
for i in range(2**len(doti)):
    kar = []
    for j in range(len(doti)):
        kar.append(doti[j][i>>j&1])
    c = kouho[:] + kar[:]
    c.sort()
    now = 24
    for k in range(len(c)-1):
        now = min(now,c[k+1]-c[k])
    ans = max(ans,now)
if ans == 24:
    print(0)
else:
    print(ans)