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: Wrong Answer)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.util.*

fun main(args: Array<String>) {
    val sc = FastScanner(System.`in`)

    val n = sc.nextInt()

    val d = Array(n) { sc.nextInt() }

    val clock = mutableSetOf<Int>()
    clock.add(0)
    val unp = mutableListOf<Int>()
    for (x in d) {
        if (x == 0) {
            println(0)
            return
        }
        val count = d.filter { it == x }.count()

        if (x == 12) {
            if (count >= 2) {
                println(0)
                return
            }
            else {
                clock.add(12)
                continue
            }
        }
        when {
            count == 3 -> {
                println(0)
                return
            }
            count == 2 -> {
                clock.add(x)
                clock.add(24 - x)
            }
            count == 1 -> {
                unp.add(x)
            }
        }
    }


    var best = 0
    val s = 1 shl unp.size
    set@
    for (x in 0 until s) {
        val nClock = mutableListOf<Int>()
        nClock.addAll(clock)
        for (k in 0 until unp.size) {
            val y = if (x shr k and 1 == 1) {
                unp[k]
            }
            else {
                24 - unp[k]
            }

            if (nClock.contains(y)) {
                continue@set
            }
            nClock.add(y)
        }
        best = Math.max(best, solve(nClock))
    }

    println(best)

}

fun solve(nClock: List<Int>): Int {
    var min = 24
    for (i in 0 until nClock.size) {
        for (j in i + 1 until nClock.size){
            val y = Math.abs(nClock[i]- nClock[j])
            val z = Math.min(y, 24 - y)
            min = Math.min(min, z)
        }
    }
    return min
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}