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 (3.4.3) (judge verdict: Runtime Error)

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

data = Counter(d).most_common()
if data[0][1] >= 3:
    print(0)
    exit()
ans = 0
#print(data)
for bit in range(2**11):
    this_time = []
    for x,c in data:
        if c == 2:
            if x == 0 or x == 12:
                print(0)
                exit()
            this_time.append(x)
            this_time.append(24-x)
        else:
            if bit>>(x-1) & 1 or x == 0 or x == 12:
                this_time.append(x)
            else:
                this_time.append(24-x)
    #print(this_time)
    ans_now = 20
    m = len(this_time)
    for  i in range(m):
        for j in range(i+1,m):
            ans_now = min(ans_now,abs(this_time[i]-this_time[j]))
    ans = max(ans,ans_now)

print(ans)