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 Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

object Main {
  val in = new Scanner(System.in)

  def main(args: Array[String]): Unit = {
    val N = in.nextInt()
    val D = (0 :: (0 until N).map(_ => in.nextInt()).toList).sorted

    def check(X: Int): Boolean = {
      var min = 0
      var max = 0
      var arranged = D.map { d =>
        val right = d - max
        val left = d + min
        val ret = if (left < X && right < X) {
          d
        } else if (left < X) {
          d
        } else if (right < X) {
          -d
        } else if (right < left) {
          d
        } else {
          -d
        }
        min = math.min(min, ret)
        max = math.max(max, ret)
        ret
      }
      arranged = arranged.sorted

      (0 until (N + 1)).forall(i => {
        val x = arranged(i)
        var y = arranged((i + 1) % (N + 1))
        if (x >= 0 && y < 0) {
          y += 24
        }
        val d = math.abs(x - y)
        math.min(d, 24 - d) >= X
      })
    }

    var ans = 0
    for (i <- 12 to 0 by -1) {
      if (check(i)) {
        ans = math.max(i, ans)
      }
    }

    println(ans)
  }
}