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)

N = int(input())
D = list(map(int,input().split()))

T = [0]*13
T[0] = 1
for d in D:
    T[d] += 1


Times = [0]*24
ones =[]
for i,t in enumerate(T):
    if t>=3 or (t==2 and (i==0 or i==12)):
        print(0)
        exit()
    elif t==2:
        Times[i] = 1
        Times[24-i] = 1
    elif t==1:
        ones.append(i)

ans = 0
L = len(ones)
for i in range(2**L):
    stats = [False]*L
    temp = i
    for j in range(L):
        stats[j] = temp&1
        temp >>= 1
    
    newTime = [t for t in Times]
    res = 10**9
    for j,t in enumerate(ones):
        nt = t if stats[j] else (24-t)%24
        newTime[nt] = 1
    
    gaps = []
    for j,t in enumerate(newTime):
        if t==1:
            gaps.append(j)
    for j in range(len(gaps)-1):
        res = min(res,min(gaps[j+1]-gaps[j],gaps[j]+24-gaps[j+1]))
    if len(gaps)>=2:
        res = min(res, gaps[0]+24-gaps[1])
    ans = max(ans, res)
print(ans)