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.*;
import java.util.*;
public class Main  {
  static BufferedReader br;
  static void Judge() throws Exception{
    boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    if(oj){
      br=new BufferedReader(new FileReader(new File("input.txt")));
      PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
      System.setOut(out);
    }
    else
      br=new BufferedReader(new InputStreamReader(System.in));
 }
  public static void main(String[] args) throws Exception
    {
         //Judge();
         br= new BufferedReader(new InputStreamReader(System.in));
         PrintWriter pw = new PrintWriter(System.out);  
         int t=Integer.parseInt(br.readLine());
        StringBuilder Ans=new StringBuilder();
        while(t-->0){
         long n=Long.parseLong(br.readLine());
         if(n%2==0){
            long n1=(n-1)/2;
            Ans.append(n1+" "+(n1+1)+" 1\n");
         }
         else{
             long n1=(n-1)/2;
             if((n1)%2==0){
                Ans.append((n1+1)+" "+(n1-1)+" 1\n");
             }
            else Ans.append((n1+2)+" "+(n1-2)+" 1\n");
         }
        }
        pw.println(Ans);
        pw.flush();
}
}