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.*;
import java.util.*;

public class Main {
    static long dp[];

    private static long helper(long n){
        if(n<=15){
            return dp[(int)n];
        }
        else{
            long t=(long)Math.ceil((double)(n-15)/4);
            int x=(int)(n-4*t);
            long k=dp[x];
            if(k==-1){
                return k;
            }
            else{
                return k+t;
            }
        }
    }

	public static void main (String[] args) throws Exception {
    dp=new long[16];
    for(int i=0;i<dp.length;i++){
        dp[i]=-2;
    }
    dp[0]=-1;
    dp[1]=-1;
    dp[2]=-1;
    dp[3]=-1;
    dp[4]=1;
    dp[5]=-1;
    dp[6]=1;
    dp[7]=-1;
    dp[8]=2;
    dp[9]=1;
    dp[10]=2;
    dp[11]=-1;
    dp[12]=3;
    dp[13]=2;
    dp[14]=3;
    dp[15]=2;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String st[] = br.readLine().split(" ");
    int n=Integer.parseInt(st[0]);
    for(int i=0;i<n;i++){
        st=br.readLine().split(" ");
        long a=Long.parseLong(st[0]);
        System.out.println(helper(a));   
    }
    }
}