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>
using namespace std;
using Int = long long;
int main()
{
    int N; cin >> N;
    vector<int> D(N); for (auto &d : D) cin >> d;
    vector<int> C(13);
    for (auto d : D) {
        C[d]++;
    }
    vector<bool> X(24);
    X[0] = true;
    auto recur = [&](auto rec, int i) {
        if (i == 13) {
            int j = 0, k = 1, ans = 999;
            while (j < 24) {
                while (k < 24 && X[k] == false) k++;
                ans = min(ans, k - j);
                j = k, k += 1;
            }
            return ans;
        } else if (C[i] == 0) {
            return rec(rec, i+1);
        } else if (C[i] == 1) {
            int ans = 0;
            if (!X[i]) {
                X[i] = true;
                ans = max(ans, rec(rec, i+1));
                X[i] = false;
            }
            if (i != 0 && !X[24-i]) {
                X[24-i] = true;
                ans = max(ans, rec(rec, i+1));
                X[24-i] = false;
            }
            return ans;
        } else if (C[i] == 2) {
            if (X[i] || X[24-i]) {
                return 0;
            }
            X[i] = X[24-i] = true;
            int ans = rec(rec, i+1);
            X[i] = X[24-i] = false;
            return ans;
        } else {
            return 0;
        }
    };
    cout << recur(recur, 0) << '\n';
    return 0;
}