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

import java.util.*;

public class gcd {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner (System.in);
		int t=s.nextInt();
		while(t-->0){
			int n= s.nextInt();
			ArrayList<Integer> a=new ArrayList<>();
			for(int i=2;i<=n;i++) {
				if(n%i==0) {
					a.add(i);
				}
				
			}
			int temp;
			int temp2;
			int temp3=1;
			int count=0;
			for(int i=1;i<a.size();i++) {
				temp=a.get(i);
				temp2=n-temp;
				if(temp2%temp==0) {
					temp3=temp;
					break;
				
				}
				else {
					count++;
				}
				if(count==n-1) {
					temp3=1;
				}
				
			}
			int temp5=0;
			int temp6=0;
			int temp4=(n-temp3)/temp3;
			for(int i=2;i<temp4-1;i++) {
				if(temp4-i>1) {
					temp5=i*temp3;
					temp6=(temp4-i)*temp3;
					
				}
			}
			System.out.print(temp5+" ");
			System.out.print(temp6+" ");
			System.out.print(temp3+" ");
			System.out.println();
		}
	}

}
