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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
//import java.util.*;
public class cp1 {
	
	public long gcd(long a,long b) {
    	if(b==0) {
    		return a;
    	}
    	long m=a%b;
    	return gcd(b,m);
    }
	
	public static void main(String[] args)throws Exception {
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		cp1 cp1=new cp1();
		int t1=Integer.parseInt(br.readLine());
		
		
		while(t1-->0) {
			long n=Long.parseLong(br.readLine());
//			if(n%2==0) {
//				System.out.println((n-1)/2+" "+((n-1)/2+1)+" "+1);
////				System.out.println("even");
//			}
//			else {
				long no=n-1;
				  for (long i = no / 2; i > 0; i--) {
					
			            long x = i, y = no - i;
			            
			            if (cp1.gcd(x,y) == 1 && x < y) {
							System.out.println(x+" "+y+" 1");
			                break;
			            }
			            
//			        }
				
			}
		
		}
			}
	}


