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 (2.7.1) (judge verdict: Accepted)

@n = gets.to_i
@d = gets.split.map(&:to_i)

@memo = Array.new(24)
@memo[0] = 1
def calc(i)
    if i == @n
        a = -24
        x = 24
        @memo.each_with_index do |e, j|
            next if !e
            x = [x, j - a].min
            a = j
        end
        [x, 24 - a].min
    else
        x = []
        if !@memo[@d[i]]
            @memo[@d[i]] = 1
            x << calc(i+1)
            @memo[@d[i]] = nil
        end

        if !@memo[24-@d[i]]
            @memo[24-@d[i]] = 1
            x << calc(i+1)
            @memo[24-@d[i]] = nil
        end

        x.empty? ? 0 : x.max
    end
end

p calc(0)