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 Ruby (2.3.3) (judge verdict: Accepted)

N = gets.to_i+1
d_array=gets.chomp.split(" ").map(&:to_i).push(0)

# 0か12が2つあったら0
if d_array.count(0) >= 2 || d_array.count(12) >= 2
    puts 0
    exit
end

# 同じのが3つあったら0
if !d_array.group_by{ |e| e }.select { |k, v| v.size >=3 }.empty?
    puts 0
    exit
end

# 要素が24あったら1
if d_array.size == 24
    puts 1
    exit
end

# その他
def calc_s(array)
    size = array.length
    sorted = array.sort
    diffs = sorted.map.with_index.map do |e, i|
        if i == size - 1
            24 + sorted[0] - sorted[i]
        else
            sorted[i+1] - sorted[i]
        end
    end
    return diffs.min
end

ret = 0
[1, -1].repeated_permutation(N) do |permu|
    target_array = d_array.map.with_index { |e, i| e*permu[i] }
    s = calc_s(target_array)
    if s > ret
        ret = s
    end
end
puts ret