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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php

$N = trim(fgets(STDIN));

$D = explode(' ', trim(fgets(STDIN)));

$minimum_by_takahashi = min($D);

$check_list = [];
$result_list = [];
foreach ($D as $key1 => $time1)
{
	foreach ($D as $key2 => $time2)
	{
		if ($key1 === $key2)
		{
			continue;
		}

		$self_pos = $time1;
		$self_neg = 24 - $time1;
		$target_pos = $time2;
		$target_neg = 24 - $time2;

		$check_list[] = max([abs($self_pos - $target_pos), abs($self_pos - $target_neg), abs($self_neg - $target_pos), abs($self_neg - $target_neg)]);
	}
	if (count($check_list) === 0)
	{
		continue;
	}
	$result_list[$key1] = min($check_list);
}
$result_list[] = $minimum_by_takahashi;

echo min($result_list);