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>
using namespace std;

#define REP(i,s,n) for(int i=s; i<n; ++i)
#define rep(i,n) REP(i,0,n)
#define SORT(c) sort((c).begin(),(c).end())
#define IINF INT_MAX
#define LLINF LLONG_MAX
#define DEBUG false

typedef long long ll;
typedef pair<int, int> ii;

vector<int> cnt(13, 0);

int gap(vector<bool> v){
	int ret = IINF;
	rep(i, v.size()){
		REP(j, i+1, v.size()){
			if(v[i] && v[j]){
				int tmp = j - i;
				ret = min(ret, min(tmp, 24 - tmp));
			}
		}
	}
	return ret;
}

int calc(vector<bool> v, int pos){//v 0-23 =>24element
	int ret = 0;
	if(pos == 12){
		if(cnt[pos] == 1) v[12] = true;
		ret = gap(v);
	}
	else{
		if(cnt[pos] == 1){
			v[pos] = true;
			ret = calc(v, pos+1);
			v[pos] = false; v[24-pos] = true;
			ret = max(ret, calc(v, pos+1));
		}
		else if(cnt[pos] == 2){
			v[pos] = v[24-pos] = true;
			ret = calc(v, pos+1);
		}
		else ret = calc(v, pos+1);
	}
	return ret;
}

int main(){
	int n;
	cin >> n;
	vector<int> d(n);

	cnt[0]++;
	rep(i, n) {
		cin >> d[i];
		cnt[d[i]]++;
	}

	bool f = true;
	if(cnt[0] > 1 || cnt[12] > 1) f = false;
	REP(i, 1, 12){
		if(cnt[i] > 2) f = false;
	}

	if(!f) cout << 0 << endl;
	else{
		vector<bool> v(24, false);
		v[0] = true;
		cout << calc(v, 1) << endl;
	}


	return 0;
}
