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>
#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;
using ll=long long;
constexpr ll mod=1000000007;
constexpr int inf=1000000000;
constexpr ll linf=1000000000000000000;

int main(){
    int n;
    cin>>n;
    if(n>=24){
        cout<<0<<endl;
        return 0;
    }
    int d[n];
    rep(i,n)cin>>d[i];
    int ans=0;
    rep(s,1<<n){
        int cnt[24]={1};
        bool flag=true;
        rep(i,n){
            if(s&(1<<i)){
                if(cnt[d[i]]){
                    flag=false;
                    break;
                }
                ++cnt[d[i]];
            }
            else{
                if(d[i]==0||cnt[24-d[i]]){
                    flag=false;
                    break;
                }
                ++cnt[24-d[i]];
            }
        }
        if(!flag)continue;
        int mn=inf;
        int mx=0;
        for(int i=1;i<=23;++i){
            if(cnt[i]){
                mn=min(mn,i-mx);
                mx=i;
            }
        }
        mn=min(mn,24-mx);
        ans=max(ans,mn);
    }
    cout<<ans<<endl;
}