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
	//	FastReader sc = new FastReader();
	   // PrintWriter out = new PrintWriter(System.out, true);
		FastReader sc = new FastReader();
	    PrintWriter out = new PrintWriter(System.out, true);
	    int t=sc.nextInt();
	    while(t-->0) {
	    long n =sc.nextLong();
	    if(n%2==0) {
	    	System.out.println(n-3+" 2"+" 1");
	    }else {
	    	System.out.println(n-4+" 3"+" 1");
	    }
	    }
		
		
	}
		static class FastReader {
	    BufferedReader in;
	    StringTokenizer st;
	    
	    public FastReader() {
	        in = new BufferedReader(new InputStreamReader(System.in));
	    }
	    
	    String next() {
	        while (st == null || !st.hasMoreElements()) {
	            try {
	                st = new StringTokenizer(in.readLine());
	            }
	            catch (Exception IO) {
	                IO.printStackTrace();
	            }
	        }
	        
	        return st.nextToken();
	    }
	    
	    long nextLong() {
	        return Long.parseLong(next());
	    }
	    
	    int nextInt() {
	        return Integer.parseInt(next());
	    }
	    
	    Double nextDouble() {
	        return Double.parseDouble(next());
	    }
	    
	    String nextLine() {
	        String str = "";
	        try {
	            str = in.readLine();
	        } catch(Exception IO) {
	            IO.printStackTrace();
	        }
	        
	        return str;
	    }
	    
	    long[] nextLongArray(int size) {
	        long[] arr = new long[size];
	        
	        for (int i = 0; i < size; i++) {
	            arr[i] = this.nextLong();
	        }
	        
	        return arr;
	    }
	    
	    int[] nextIntegerArray(int size) {
	        int[] arr = new int[size];
	        
	        for (int i = 0; i < size; i++) {
	            arr[i] = this.nextInt();
	        }
	        
	        return arr;
	    }
	    
	    double[] nextDoubleArray(int size) {
	        double[] arr = new double[size];
	        
	        for (int i = 0; i < size; i++) {
	            arr[i] = this.nextDouble();
	        }
	        
	        return arr;
	    }
	    
	    void printArray(Object[] arr) {
	        for (int i = 0; i < arr.length; i++) {
	            System.out.println(arr[i] + " ");
	        }
	        System.out.println();
	    }
	}
}