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: Accepted)

#include <bits/stdc++.h>
using namespace std;
using Int = int_fast64_t;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	Int n; cin >> n;
	vector<Int> a(13);
	a[0] = 1;
	for(Int i=0; i<n; ++i){
		Int d; cin >> d;
		++a[d];
	}
	if(a[0] >= 2 || a[12] >= 2 || [a](){
		Int res = 0;
		for(Int i=1; i<=11; ++i) res = max(res, a[i]);
		return res;
	}() >= 3){
		cout << 0 << "\n";
	}else{
		Int ans = 0;
		vector<Int> b(25);
		b[0] = b[24] = 1;
		if(a[12]) b[12] = 1;
		vector<Int> c;
		for(Int i=1; i<=11; ++i){
			if(a[i] == 1) c.push_back(i);
			if(a[i] == 2) b[i] = b[24-i] = 1;
		}
		for(Int i=0; i<(1<<c.size()); ++i){
			for(size_t j=0; j<c.size(); ++j){
				if((i>>j)&1) b[c[j]] = 1;
				else b[24-c[j]] = 1;
			}
			Int dif = 1e9;
			for(Int j=0; j<24; ++j)
				for(Int k=j+1; k<=24; ++k)
					if(b[j] & b[k])
						dif = min(dif, k-j);
			ans = max(ans, dif);
			for(size_t j=0; j<c.size(); ++j) b[c[j]] = b[24-c[j]] = 0;
		}
		cout << ans << "\n";
	}
}