You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.

An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself.

Input

The first line contains single integer q (1 ≤ q ≤ 105) — the number of queries.

q lines follow. The (i + 1)-th line contains single integer ni (1 ≤ ni ≤ 109) — the i-th query.

Output

For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings.

Examples

Input

1
12


Output

3


Input

2
6
8


Output

1
2


Input

3
1
2
3


Output

-1
-1
-1

Note

12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.

8 = 4 + 4, 6 can't be split into several composite summands.

1, 2, 3 are less than any composite number, so they do not have valid splittings.
import java.io.*;

public class Main243743C
{
    static int[] ans = {0, -1,-1,-1,1,-1,1,-1,2,1,2,-1,3,2,3};
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int N = Integer.parseInt(br.readLine());
        while(N-->0)
        {
            int cur = Integer.parseInt(br.readLine());
            if(cur<15)
            {
                bw.write(ans[cur]+"\n");
                continue;
            }
            int r = cur%4;
            switch (r)
            {
                case 0:
                    bw.write((cur/4)+"\n");
                    break;
                case 1:
                    bw.write(((cur-9)/4+1)+"\n");
                    break;
                case 2:
                    bw.write(((cur-6)/4+1)+"\n");
                    break;
                case 3:
                    bw.write(((cur-15)/4+2)+"\n");
                    break;
            }
        }
        bw.close();
    }

}
