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 Main
{
    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;
        }
    }
    public static boolean isPrime(int num) {
           if (num <= 1) {
               return false;
           }
           for (int i = 2; i <= Math.sqrt(num); i++) {
               if (num % i == 0) {
                   return false;
               }
           }
           return true;
    }
    static long modPow(long var, long num) {
    long m = 1;
    while (num > 0) {
        m = (m * var) %1000000007;
        --num;
    }
    return m;}
	public static void main (String[] args) throws java.lang.Exception
	{
		FastReader s = new FastReader();
		 BufferedWriter output = new BufferedWriter(
            new OutputStreamWriter(System.out));
		int t=s.nextInt();
		for(int w=0;w<t;w++)
		{
		    int n=s.nextInt();
		    n=n-1;
		    if(n%2!=0)
		    {
		        output.write("1 2 "+String.valueOf(n-2)+"\n" );
		    }
		    else
		    {
		         for(int i = 3;i<= n/2;i++)
                    if (isPrime(i))
                     if (isPrime(n-i))
                       {output.write("1 "+String.valueOf(i)+" "+String.valueOf(n-i)+"\n");
                       break;}
                                    
		    }
		    
		   
		
		}
		output.flush();
	}
}
