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)

//ヘッダー
#include<bits/stdc++.h>
using namespace std;

//型定義
typedef long long ll;

//定数
const int INF=1e+9;
const int MOD=1e+9+7;

//REPマクロ
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define REP2(i,a,b) for(ll i=a;i<(ll)(b);i++)
#define REPD2(i,a,b) for(ll i=a;i>(ll)(b);i--)

// 多次元 vector 生成
template<class T>
vector<T> make_vec(size_t a){
    return vector<T>(a);
}
template<class T, class... Ts>
auto make_vec(size_t a, Ts... ts){
  return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

//vectorの扱い
#define ALL(x) (x).begin(),(x).end() //sortなどの引数省略
#define SIZE(x) ((ll)(x).size()) //size
#define MAX(x) *max_element(ALL(x)) //最大値
#define MIN(x) *min_element(ALL(x)) //最小値

int main(){
    int N;
    cin>>N;
    vector<int> D(N);
    REP(i,N) cin>>D[i];
    vector<ll> t;
    t.emplace_back(0);
    ll ans=INF;
    REP(i,N){
        ll tmp1=INF;
        ll tmp2=INF;
        REP(j,t.size()){
            tmp1=min(tmp1,min(abs(t[j]-D[i]+24LL),abs(t[j]-D[i])));
            tmp2=min(tmp2,min(abs(t[j]-(24LL-D[i])%24LL+24LL),abs(t[j]-(24LL-D[i])%24LL)));
        }
        if(tmp1<tmp2){
            t.push_back((24LL-D[i])%24LL);
        }else{
            t.push_back(D[i]);
        }
    }
    REP(i,t.size()-1){
        REP2(j,i+1,t.size()){
            ans=min(ans,min(abs(t[i]-t[j]+24LL),abs(t[i]-t[j])));
        }
    }
    cout<<ans<<endl;

       
}