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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <algorithm>
#include <vector>

std::vector<int> middle;
int r = 0, input[13], maxA = 0;

void dfs(int num) {
	if (num == 13) {
		std::vector<int> ss = middle;

		std::sort(ss.begin(), ss.end());
		int tmp = ss[0] + 24 - ss[ss.size() - 1];

		for (int i = 0; i < ss.size() - 1; i++)
			tmp = std::min(tmp, ss[i + 1] - ss[i]);
		r = std::max(r, tmp);
		return;
	}

	if (input[num] != 0) {
		if (num < maxA || (maxA == num && input[num] == 1)) {
			middle.push_back(num);
			dfs(num + 1);
			middle.pop_back();

			middle.push_back(24 - num);
			dfs(num + 1);
			middle.pop_back();
		}
		else if (maxA == num && input[num] > 1) {
			middle.push_back(num);
			middle.push_back(24 - num);
			dfs(num + 1);
			middle.pop_back();
			middle.pop_back();
		}
	}
	else if (input[num] == 0)
		dfs(num + 1);
}

int main(void) {
	int n;
	scanf("%d", &n);

	for (int i = 1; i <= n; i++) {
		int a;
		scanf("%d", &a);
		input[a]++;
		maxA = std::max(maxA, a);
	}

	dfs(0);

	printf("%d\n", r);
}