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.

Examples

Input

3
7 12 8


Output

4


Input

2
11 11


Output

2


Input

1
0


Output

0
#include <iostream>
#include <iomanip>
#include <vector>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <queue>
#include <deque>
#include <stack>
#include <algorithm>
#include <numeric>
#include <string>
#include <sstream>
#include <cmath>
#include <cstring>
#include <assert.h>
#include <utility>
#include <tuple>
#include <array>
#include <bitset>
#include <cstdlib>

using int64 = long long;

int dfs(int dfs_i, const std::vector<int>& ds, std::vector<int>& xs) {
    if (dfs_i == ds.size()) {
        int res = 24,
            l = 0;
        for (int i = 1; i < 24; i++) {
            if (xs[i]) {
                res = std::min({res, 24 - i, i - l});
                l = i;
            }
        }
        return res;
    }

    int d = ds[dfs_i],
        res = 0;

    for (int i = 0; i < 2; i++) {
        if (xs[d] == 0) {
            xs[d]++;
            res = std::max(res, dfs(dfs_i + 1, ds, xs));
            xs[d]--;
        }
        d = (24 - d) % 24;
    }
    return res;
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    int n;
    std::cin >> n;

    std::vector<int> ds(n);
    for (int i = 0; i < n; i++) {
        std::cin >> ds[i];
    }

    std::vector<int> xs(24, 0);
    xs[0] = 1;

    std::cout << dfs(0, ds, xs) << std::endl;

    return 0;
}
