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.math.*

fun main(args: Array<String>) {
    val cnt = IntArray(13)
    readInputLine()
    readInputLine().split(" ").forEach { cnt[it.toInt()]++ }

    cnt[0]++

    var ans = Int.MAX_VALUE

    for (i in 0..12) {
        if (cnt[i] == 0) {
            continue
        }
        for (j in 0..12) {
            if (cnt[j] == 0 || (i == j && cnt[j] == 1)) {
                continue
            }
            var tmp = 0
            tmp = Math.max(tmp, Math.abs(i - j))
            tmp = Math.max(tmp, Math.abs((24 - i) % 24 - j))
            tmp = Math.max(tmp, Math.abs(i - (24 - j) % 24))
            tmp = Math.max(tmp, Math.abs((24 - i) % 24 - (24 - j) % 24))
            ans = Math.min(ans, tmp)
        }
    }

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}