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.Arrays;
import java.util.Scanner;

public class C {

	public static void main(String[] args) {
		new C();
	}

	int dp[];
	int dp_len = 15;
	
	C() {
		
		Scanner in = new Scanner(System.in);

		dp = new int[dp_len+1];
		Arrays.fill(dp, -1);
		dp[0] = 0;
		for(int i=4;i<=dp_len;i++){
			if(!isPrime(i)){
				//System.out.println("i="+i);
				for(int j=i;j<=dp_len;j++){
					if(dp[j-i]!=-1)
						dp[j] = Math.max(dp[j], dp[j-i]+1);
				}
			}
		}
		
//		System.out.println(Arrays.toString(dp));
//		for(int i=0;i<=dp_len;i++){
//			System.out.printf("%d: %d\n",i,dp[i]);
//		}
		
		int Q = in.nextInt();
		querying:
		for(int q=0;q<Q;q++){
			
			int n = in.nextInt();
//			System.out.println("You asked me for "+n);
			if(n<=dp_len){
				System.out.println(dp[n]);
				continue querying;
			}

			for(int i=n-dp_len;i<=n;i++){
				if(i%4==0){
					System.out.println(i/4 + dp[n-i]);
					continue querying;
				}
			}

			System.out.println(-1);
		}
		in.close();

	}
	
	int numFactors(int n){
		ArrayList<Integer> ans = new ArrayList<>();
		for(int i=1;i<Math.sqrt(n);i++){
			if(n%i==0){
				/*if(isPrime(i))*/ ans.add(i);
				/*if(isPrime(n/i))*/ ans.add(n/i);
			}
		}
		if(n%Math.sqrt(n)==0)
			ans.add((int)Math.sqrt(n));
//		System.out.println(ans);
		return ans.size();
	}
	
	boolean isPrime(int n){
		for(int i=2;i<=Math.sqrt(n);i++){
			if(n%i==0)
				return false;
		}
		return true;
	}
	
}
