Given a positive integer n. Find three distinct positive integers a, b, c such that a + b + c = n and \operatorname{gcd}(a, b) = c, where \operatorname{gcd}(x, y) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers x and y.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Description of the test cases follows.

The first and only line of each test case contains a single integer n (10 ≤ n ≤ 10^9).

Output

For each test case, output three distinct positive integers a, b, c satisfying the requirements. If there are multiple solutions, you can print any. We can show that an answer always exists.

Example

Input


6
18
63
73
91
438
122690412


Output


6 9 3
21 39 3
29 43 1
49 35 7
146 219 73
28622 122661788 2

Note

In the first test case, 6 + 9 + 3 = 18 and \operatorname{gcd}(6, 9) = 3.

In the second test case, 21 + 39 + 3 = 63 and \operatorname{gcd}(21, 39) = 3.

In the third test case, 29 + 43 + 1 = 73 and \operatorname{gcd}(29, 43) = 1.
1
669278611
 10
10
52
91
23
44
99
28
54
99
51

334639303 334639307 1
 4 5 1
25 26 1
43 47 1
9 13 1
21 22 1
47 51 1
13 14 1
26 27 1
47 51 1
23 27 1

/* package codechef; // don't place package name! */
 
import java.util.*;
import java.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner(System.in);
		
        int t=in.nextInt();
        while(t-- > 0){
         
         int n=in.nextInt();
         int m=n-1;
         
         if(m%2!=0){
            int a=m/2;
            out.println(a+" "+(a+1)+" 1");
         }
         else{
             int z=m/2;
             if(z%2==0){
                 out.println((z-1)+" "+(z+1)+" 1");
             }
             else{
                 out.println((z-2)+" "+(z+2)+" 1");
             }
         }
        }
        out.flush();
	}
	
	public static long GCD(long a, long b)
    {
      if (b == 0)
        return a;
      return GCD(b, a % b);
    }
    
}
