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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n int
	fmt.Scan(&n)
	ds := make([]int, n+1)
	ds[0] = 0
	for i := 1; i < len(ds); i++ {
		fmt.Scan(&ds[i])
	}
	sort.Ints(ds)

	ans := max(calc(ds, 0), calc(ds, 1))
	fmt.Println(ans)
}

func calc(ds []int, x int) int {
	n := len(ds)
	ts := make([]int, n)
	copy(ts, ds)

	for i := 0; i < len(ts); i++ {
		if i%2 == x && ts[i] > 0 {
			ts[i] = 24 - ts[i]
		}
	}
	ts = append(ts, 24)
	sort.Ints(ts)

	t := int(1e9)
	for i := 1; i < len(ts); i++ {
		t = min(t, abs(ts[i]-ts[i-1]))
	}

	return t
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}