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<algorithm>
#include<cmath>
#include<iomanip>
#include<iostream>
#include<map>
#include<numeric>
#include<queue>
#include<set>
#include<sstream>
#include<unordered_map>
#include<unordered_set>
#include<vector>
using uint = unsigned int;
using ll = long long;
enum : int { M = (int)1e9 + 7 };
enum : ll { MLL = (ll)1e18L + 9 };
using namespace std;
#ifdef LOCAL
#include"rprint2.hpp"
#include"debug_deque.hpp"
#define vector DebugDeque
#else
#define FUNC(name) template <ostream& out = cout, class... T> void name(T&&...){ }
FUNC(prints) FUNC(printe) FUNC(printw) FUNC(printew) FUNC(printb) FUNC(printd) FUNC(printde);
#endif

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n; cin >> n;
    vector<int> ds(n);
    for(int i = 0; i < n; i++){
        cin >> ds[i];
    }
    vector<char> dp(1 << 24);
    dp[1] = true;
    for(int i = 0; i < n; i++){
        vector<char> next(1 << 24);
        int d = ds[i];
        if(!d){
            cout << 0 << '\n';
            return 0;
        }
        for(int bits = 0; bits < (1 << 24); bits++){
            if(dp[bits]){
                if((bits & (1 << d)) == 0){
                    next[bits | (1 << d)] = true;
                }
                if((bits & (1 << (24 - d))) == 0){
                    next[bits | (1 << (24 - d))] = true;
                }
            }
        }
        dp.swap(next);
    }
    int ans = 0;
    for(int bits = 0; bits < (1 << 24); bits++){
        if(!dp[bits]){ continue; }
        printb(bits);
        vector<int> v;
        for(int i = 0; i < 24; i++){
            if(bits >> i & 1){
                v.push_back(i);
            }
        }
        prints(v);
        int cand = M;
        if(v.size() <= 1){ exit(1); }
        for(size_t i = 0; i < v.size(); i++){
            cand = min(cand, abs(v[i] - v[(i + 1) % v.size()]));
            printd(cand, i);
        }
        ans = max(ans, cand);
    }
    cout << ans << '\n';
}