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.*;
public class MyClass {
    public static void main(String args[]) {
      int arr[]=new int[]{4,6,9};
      int dp[]=new int[16];
      dp[0]=0;dp[1]=-1;dp[2]=-1;dp[3]=-1; dp[5]=-1;dp[7]=-1;dp[11]=-1;
      for(int i=4;i<=15;i++)
      {
          for(int j=0;j<3;j++)
          {
              if(arr[j]<=i && dp[i-arr[j]]!=-1)
              {
                  dp[i]=Math.max(dp[i],dp[i-arr[j]]+1);
              }
          }
          //System.out.print(dp[i]+" ");
      }
      System.out.println();
      Scanner sc=new Scanner(System.in);
      int q=sc.nextInt();
      while(q-->0)
      {
          int n=sc.nextInt();
          if(n<16)
          {
              System.out.println(dp[n]);
          }
          else
          {
              int atLst_4=(n-16)/4+1;
              int ans=atLst_4+dp[n-4*atLst_4];
              System.out.println(ans);
          }
      }
    }
}