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 <iostream>
#include <vector>
#include <cassert>
#include <algorithm>
#include <functional>

using namespace std;
int main(){
    int n;
    cin >> n;
    vector<int> vec;
    vec.push_back(0);
    vec.push_back(24);
    for(int i=0;i<n;i++){
        int x;
        cin >> x;
        if(x==0){
            cout<<0<<endl;
            return 0;
        }
        if(find(vec.begin(),vec.end(),x)!=vec.end()){
            if(find(vec.begin(),vec.end(),24-x)!=vec.end()){
                cout<<0<<endl;
                return 0;
            }
            vec.push_back(24-x);
        }else{
            vec.push_back(x);
        }
    }
  //  cout<<vec[2]<<endl;
   // cout<<vec.size()<<endl;
    int Min=1e9;
    for(int i=0;i<n+1;i++){
        for(int j=0;j<n+1;j++){
            if(i==j)continue;
            if(vec[i]==0&&vec[j]==24)continue;
            int x = max(abs(vec[i]-vec[j]),abs(24-vec[i]-vec[j]));
            Min = min(x,Min);
        }
    }
    cout<<Min<<endl;
}