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.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class Test4 {

	static boolean []isComposite = new boolean[100001];
	static ArrayList<Integer> composites = new ArrayList<Integer>();
	
	static int[] dp = new int[100001];
	
	public static void main(String[] args) {
		setup();
		dp[4] = 1;
		dp[5] = -1;
		dp[6] = 1;
		dp[7] = -1;
		dp[8] = 2;

		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		
		for(int i = 0; i < n; ++i) {
			System.out.println(solve(in.nextInt()));
		}
		
	}
	
	static int solve(int num) {
		if(num < 4) return -1;
		if(num%4 == 0) return num/4;
		if(num%4 == 1) {
			if(num == 5) return -1;
			return 1 + (num-9)/4;
		}
		if(num%4 == 2) return 1 + (num - 6)/4;
		else {
			if(num == 7 || num == 11) return -1;
			return (num-3)/4 - 1;
		}
	}

	static void setup() {
		for(long i = 2; i <= 100000; ++i) {
			if(!isComposite[(int)i]) {				
				for(long j = i*i; j <= 100000; j+= i) {
					int jj = (int) j;
					isComposite[jj] = true;
				}
			}
		}	
		
		for(int i = 4; i <= 100000; ++i) {
			if(isComposite[i]) composites.add(i);
		}
	}
	
}
