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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
int main(){
  int N;
  cin >> N;
  vector<int> vec(N);
  for(int i=0; i<N; i++){
    cin >> vec.at(i);
  }
  if(N >= 24){
    cout << 0 << endl;
  }
  else{
    int ans = 0;
    for(int bit = 0; bit < (1 << N); bit++){
      map<int,bool> mp;
      vector<int> time(2);
      time.at(0) = 0;
      time.at(1) = 24;
      for(int i=0; i<N; i++){
        if(bit & (1 << i)){
          mp[i] = true;
        }
      }
      for(int i=0; i<N; i++){
        if(mp.count(i)){
          time.emplace_back(24 - vec.at(i));
        }
        else{
          time.emplace_back(vec.at(i));
        }
      }
      sort(time.begin(),time.end());
      int pre_ans = 100;
      for(int i=0; i<time.size()-1; i++){
        pre_ans = min(pre_ans,time.at(i+1) - time.at(i));
        if(pre_ans <= ans){
          break;
        }
      }
      ans = max(ans,pre_ans);
    }
    cout << ans << endl;
  }
}