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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
    val N = readLine()!!.toInt()
    val D = readLine()!!.split(" ").map { it.toInt() }

    val d = IntArray(13) { 0 }
    d[0] = 1

    D.forEach {
        d[it]++
    }

    var res = 0

    val st = TreeSet<Int>()
    val solo = TreeSet<Int>()

    for (s in 0 until (1 shl 13)) {
        var list = ArrayList<Int>()
        list.addAll(Array(d[0]) {0})
        list.addAll(Array(d[12]) {12})

        for (i in 1..11) {
            if (d[i] == 0) continue

            if (d[i] > 1) {
                list.add(i)
                list.addAll(Array(d[i] - 1) { 24 - i })
            } else if ((s shr i) and 1 == 1) {
                list.add(i)
            } else {
                list.add(24 - i)
            }
        }
        var h = 24
        for (i in list.indices) for (j in (i + 1) until list.size) {
            val d = Math.abs(list[i] - list[j])
            h = Math.min(h, Math.min(d, 24 - d))
        }
        res = Math.max(res, h)
    }

    println(res)
}