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.Scanner;

public class MaximumSplitting { 
  
	static int maxn = 16;    
  
	public static int[] PreCompute() {  // Function to generate the dp array  
		int dp[] = new int[maxn];
		int arr[]={ 4, 6, 9 }; 
  
		for (int i = 0; i < maxn; i++) dp[i] = -1; 
		dp[0] = 0;  
		for (int i = 1; i < maxn; ++i) {    
			for (int k = 0; k < 3; k++) {  // combination of three integers
				int j = arr[k];   
				// take the maximum number of summands:
				if (i >= j && dp[i - j] != -1) dp[i] = Math.max(dp[i], dp[i - j] + 1);  
			 }  
		}    
		return dp;  
	}  
    
	public static int Maximum_Summands(int[] dp, int n) { // Function to find the maximum number of summands 
		if (n < maxn) return dp[n]; // If n is a smaller number, less than 16, return dp[n] 
		else {  // Else, find a minimal number t  
		    int t = (n - maxn) / 4 + 1;  
		    return t + dp[n - 4 * t];  
		}  
	}  
		  
	public static void main(String args[]) { 
		Scanner sc = new Scanner(System.in);
		int numQueries = sc.nextInt();

		int[] N = new int[numQueries];
		for (int i = 0; i < numQueries; i++) N[i] = sc.nextInt();

		for (int j = 0; j < numQueries; j++) { 
			int n = N[j];  
			int[] dp = PreCompute();    
			System.out.println(Maximum_Summands(dp, n));
		}  
	} 
} 