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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <cmath>
#include <cstdio>
#include <queue>
#include <deque>
#include <map>
#include <stack>
#include <set>
#include <utility>
#include <functional>
using namespace std;
typedef pair<int, int> pii;
typedef pair<string, int> P;
typedef long long ll;
int dy[] = {1, 0, -1, 0};
int dx[] = {0, 1, 0, -1};
const int MAXN = 100000;
const int MAXE = 100000;
const int MAXV = 10000;
const ll INF = 1e9;
const ll MOD = 1e9 + 7;
int main(){
    int n;cin>>n;
    vector<int> d(n),c(13,0);
    for(int i=0;i<n;++i){
        cin>>d[i];
        c[d[i]]++;
    }
    for(int i=0;i<12;++i){
        if(c[i]>=3){
            cout<<0<<endl;
            return 0;
        }
    }
    for(int i=0;i<12;++i){
        if((c[i]>=1&&c[i+1]==2)||(c[i]==2&&c[i+1]>=1)){
            cout<<1<<endl;
            return 0;
        }
    }
    for(int i=0;i+2<=12;++i){
        if((c[i]>=1&&c[i+2]==2)||(c[i]==2&&c[i+2]>=1)){
            cout<<2<<endl;
            return 0;
        }
    }
    vector<int> t(n);
    int ans=0;
    for(int bit=0;bit<(1<<n);++bit){
        fill(t.begin(),t.end(),0);
        for(int i=0;i<n;++i){
            if(bit&(1<<i)) t[i]=24-d[i];
            else t[i]=d[i];
        }
        int s=24;
        for(int i=0;i<n;++i){
            s=min(s,min(t[i],24-t[i]));
        }
        for(int i=0;i<n;++i){
            for(int j=i+1;j<n;++j){
                s=min(s,min(abs(t[i]-t[j]),24-abs(t[i]-t[j])));
            }
        }
        ans=max(ans,s);
    }
    cout<<ans<<endl;
    return 0;
}