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 <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#define MOD 1000000007
typedef long long ll;
using namespace std;

int main(){
  int n;
  cin>>n;
  int d[n+1]={};
  int tim[13]={};
  for(int i=0;i<n;i++){
    cin>>d[i];
    tim[d[i]]++;
  }

  for(int i=0;i<=12;i++){
    if(tim[i]>=3){
      cout<<0<<endl;
      return 0;
    }
  }
  if(tim[0]>=1||tim[12]>=2){
    cout<<0<<endl;
    return 0;
  }

  int ans=0;
  for(int i=0;i<(1<<11);i++){
    vector<int> res;
    res.push_back(0);
    if(tim[12]==1) res.push_back(12);
    for(int j=0;j<11;j++){
      if(tim[j+1]==2){
        res.push_back(j+1);
        res.push_back(24-(j+1));
      }else if(tim[j+1]==1){
        if(i&(1<<j)) res.push_back(j+1);
        else res.push_back(24-(j+1));
      }
    }
    int sub=min(res[res.size()-1],24-res[res.size()-1]);
    sort(res.begin(),res.end());
    for(int j=0;j<res.size()-1;j++){
      sub=min(sub,res[j+1]-res[j]);
    }
    ans=max(ans,sub);
  }

  cout<<ans<<endl;

  return 0;
}