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 <bits/stdc++.h>
#define REP(i, a, n) for(ll i = ((ll) a); i < ((ll) n); i++)
using namespace std;
typedef long long ll;

ll N, D[51];

int main(void) {
  cin >> N;
  D[0] = 0;
  REP(i, 1, N + 1) cin >> D[i];
  N++;

  if(N > 24) {
    cout << 0 << endl;
  } else {
    vector<ll> d(N);
    vector<ll> cnt(25);
    ll ans = 0;
    REP(i, 0, 1LL << N) {
      bool f = true;
      REP(j, 0, 25) cnt[j] = 0;
      REP(j, 0, N) {
        d[j] = ((i & (1LL << j)) == 0 ? D[j] : 24 - D[j]);
        if(cnt[d[j]] > 0) {
          f = false;
          break;
        }
        cnt[d[j]]++;
      }
      if(!f) continue;

      sort(d.begin(), d.end());

      ll s = (1LL << 60);
      REP(j, 0, N) s = min(s, min(abs(d[(j + 1) % N] - d[j]), 24 - abs(d[(j + 1) % N] - d[j])));

      ans = max(ans, s);
    }
    cout << ans << endl;
  }
}
