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)

fun Int.bit(i: Int) = 1 shl i and this > 0

fun main(A: Array<String>) {
    val n = readLine()!!.toInt()
    if (n > 24) {
        println(0)
        return
    }

    val a = readLine()!!.split(" ").map { it.toInt() }
    val b = java.util.BitSet(25)
    b[0] = true
    b[24] = true

    (0 until (1 shl n)).asSequence().map { bit ->
        b.clear(1, 24)
        for (i in a.indices) {
            val j = if (bit.bit(i)) 24 - a[i] else a[i]
            if (b[j])
                return@map 0
            b[j] = true
        }

        (1..24).asSequence().filter { b.get(it) }
                .map { it - b.previousSetBit(it - 1) }
                .min() ?: 0
    }.max().let(::println)
}