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,n) for(int i=0;i<int(n);++i)
typedef long long ll;
map<int, int> mp;

int rec(int k,ll mask){
    if(k == 12){
        int ans = 12;
        mask |= mask<<24;
        rep(i,48)rep(j,i){
            if((mask&(1LL<<i)) && (mask&(1LL<<j))){
                ans = min(ans,i-j);
            }
        }
        return ans;
    }
    if(mp[k]==1){
        return max(rec(k+1,mask|(1<<k)),rec(k+1,mask|(1<<(24-k))));
    }else{
        return rec(k+1,mask);
    }
}

int solve(){
    int n;
    cin>>n;
    mp[0]++;
    rep(i,n){
        int d;
        cin>>d;
        mp[d]++;
        if(mp[d] >= 3) return 0;
    }
    if(mp[0] >= 2 || mp[12] >= 2) return 0;
    ll mask = 1;
    if(mp[12]==1) mask |= 1<<12;
    rep(i,12) if(mp[i]==2) mask |= (1<<i)|(1<<(24-i));
    return rec(1,mask);
}

int main(void){
    cout<<solve()<<endl;
    return 0;
}
