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)

def g(a, b):
	if a == b:
		return 1e9
	a, b = max(a, b), min(a, b)
	b += 24 - a
	return min(b, 24 - b)
N = int(input())
D = input().split()
for i in range(N):
	D[i] = int(D[i])
answer = 0
if N == 1:
	answer = D[0]
else:
	for i in range(N - 1):
		for j in range(i + 1, N):
			A = D[i]
			AA = 24 - D[i]
			B = D[j]
			BB = 24 - D[j]
			a = g(A, B)
			b = g(AA, B)
			c = g(A, BB)
			d = g(AA, BB)
			s = min(min(a, b), min(c, d))
		answer = max(answer, s)
print(answer)