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.PrintWriter;
import java.util.Scanner;

public class MaximumSplitting{
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        PrintWriter out=new PrintWriter(System.out);
        int a[]=new int[13];
        a[1]=-1;
        a[2]=-1;
        a[3]=-1;
        a[4]=1;
        a[5]=-1;
        a[6]=1;
        a[7]=-1;
        a[8]=2;
        a[9]=1;
        a[10]=2;
        a[11]=-1;
        a[12]=3;

        int t=sc.nextInt();
        while(t-->0){
           int n=sc.nextInt();
           if(n<13)
               out.println(a[n]);
           else{
               int div=n/4;
               int mod=n%4;
               if(mod==1 || mod==3){
                   out.println(div-1);
               }
               else
                   out.println(div);
           }
        }
        out.close();
    }
}
/*
C. Maximum splitting
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
You are given several queries. In the i-th query you are given a single positive integer n i. You are to represent n i 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 n i (1 ≤ n i ≤ 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
inputCopy
1
12
outputCopy
3
inputCopy
2
6
8
outputCopy
1
2
inputCopy
3
1
2
3
outputCopy
-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.


 */