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.*;
import java.lang.Math;
import java.io.* ;


public class Account {
	
	public static class Pair<Object1 ,Object2> {
	    Object1 key ;
	    Object2 val ;
	    
	    Pair(Object1 key ,Object2 val) {
	        this.key = key ;
	        this.val = val ;
	    }
	    
	    Pair() {}
	    
	}
	
	public static void main (String[] args) {
		
//		Scanner sc = new Scanner(System.in) ;
		FastReader sc = new FastReader() ;
//		StringBuilder res = new StringBuilder() ;
		int t= 1 ;  
		t = sc.nextInt() ;
		while(t-- > 0) {
			long n = sc.nextLong() ;
			if(n%2 == 0) {
				System.out.println((n/2)+" "+(n/2 - 1)+" 1");
			}else {
				n = n/2 ;
				if(n%2 != 0) {
					System.out.println((n + 2)+" "+(n - 2)+" 1");
				}else {
					System.out.println((n + 1)+" "+(n - 1)+" 1");
				}
					
			}
  		}
	}
	
	
	/*
	 *   1--> a   3b   2c
	 *   2--> 2a  b    3c
	 *   3--> 3a  2b   c
	 */
		
	
	public static long gcd(long a, long b)
	{
	    if (b == 0)
	        return a;
	    return gcd(b, a % b);
	     
	}
	
	
//	_xor from 1 to n
	public static int xor(int n)
    {
        if (n % 4 == 0)
            return n;
      
        if (n % 4 == 1)
            return 1;
      
        if (n % 4 == 2)
            return n + 1;
      
        return 0;
    }

	
	public static class FastReader {
        
		BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
 
        int [] readintarray(int n) {
            int res [] = new int [n];
            for(int i = 0; i<n; i++)res[i] = nextInt();
            return res;
        }
        long [] readlongarray(int n) {
            long res [] = new long [n];
            for(int i = 0; i<n; i++)res[i] = nextLong();
            return res;
        }
    }	
	
}