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: Wrong Answer)

import sys
read = sys.stdin.read

N, *D = map(int, read().split())

if N == 1:
    print(0)
    exit()

D_1 = [D.count(i) for i in range(13)]
D_1[0] += D_1.pop()

for i in range(12):
    if i == 0:
        if D_1[i] > 1:
            print(0)
            exit()
    if D_1[i] > 2:
        print(0)
        exit()

d = [False] * (12 + 1 + 12)

# 高橋君
d[12] = True

rl = True
for i in range(12):
    for _ in range(D_1[i]):
        if i == 0:
            i = 12
        if rl:
            d[12 + i] = True
            rl = False
        else:
            d[12 - i] = True
            rl = True

a = [i for i, j in enumerate(d) if j]
a.append(24 + a[0])
s = 24
for i, j in zip(a, a[1:]):
    if j - i < s:
        s = j - i

print(s)