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;
#define ll long long
#define REP(i,m,n) for(int i=(int)(m); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define RREP(i,m,n) for(int i=(int)(m); i>=(int)(n); i--)
#define rrep(i,n) RREP(i,n-1,0)
#define REPL(i,m,n) for(ll i=(ll)(m); i<(ll)(n); i++)
#define repl(i,n) REPL(i,0,n)
#define all(v) v.begin(), v.end()
const int inf = 1e9+7;
const ll longinf = 1LL<<60;
const ll mod = 1e9+7;
int main() {
  int N;
  cin >> N;
  vector<int> D(N+1);
  D[0] = 0;
  rep(i, N) cin >> D[i+1];
  sort(all(D));
  vector<int> cnt(24);
  int flag = 0;
  rep(i, N+1) {
    if(flag) {
      cnt[D[i]%24]++;
    } else {
      cnt[(24-D[i])%24]++;
    }
    flag = 1-flag;
  }
  int ans = 24;
  int tmp = 0;
  rep(i, 25) {
    if(cnt[i] > 1) ans = 0;
    if(i) {
      tmp++;
      if(cnt[i%24]) {
	ans = min(tmp, ans);
	tmp = 0;
      }
    }
  }
  cout << ans << endl;
  return 0;
}