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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.TreeSet;
import java.util.TreeMap;
import java.util.PriorityQueue;
import java.util.Collections;

import java.util.LinkedList;
import java.util.Iterator;

public class First {

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int T = fs.nextInt();
        for (int tt = 0; tt < T; tt++) {

            solve(fs);
        }
        
    }
    static void solve(FastScanner fs)
    {
        int n=fs.nextInt();
        int i=2;
        boolean done=false;
        // while(i*i <= n)
        // {
        //     if(n%i==0)
        //     {
        //         done=true;
        //         break;
        //     }
        //     i++;
        // }

        // if(!done)
        // {
        //     i=1;
        // }
        
        if((n-1)%2==0)
        {
            int x=n-1;
            if(x/2%2==0)
            {
                pn((x/2-1)+" "+(x/2+1)+" 1");
            }
            else
            {

                pn((x/2-2)+" "+(x/2+2)+" 1");
            }
        }
        else
        {
            int x=n-1;
            pn((x/2)+" "+(x/2+1)+" 1");
        }



    }
    static int MOD=(int)(1e9+7);
    
    static long gcd(long a, long b) 
    {
        if (a == 0)
            return b;    
        return gcd(b%a, a);
    }
    static void pn(Object o) { System.out.println(o); } 
    static void p(Object o) { System.out.print(o); }
    static void flush() { System.out.flush(); }

    static void debugInt(int[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debugIntInt(int[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        {
            for(int j=0;j<arr[0].length;++j)
                System.out.print(arr[i][j]+" ");
            System.out.println();
        }
        System.out.println();
    }
    static void debugLong(long[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debugLongLong(long[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        {
            for(int j=0;j<arr[0].length;++j)
                System.out.print(arr[i][j]+" ");
            System.out.println();
        }
        System.out.println();
    }
    static long[] takeLong(int n, FastScanner fs)
    {
        long[] arr=new long[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextLong();
        return arr;
    } 
    static long[][] takeLongLong(int m, int n, FastScanner fs)
    {
        long[][] arr=new long[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextLong();
        return arr;
    } 
    static int[] takeInt(int n, FastScanner fs)
    {
        int[] arr=new int[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextInt();
        return arr;
    } 
    static int[][] takeIntInt(int m, int n, FastScanner fs)
    {
        int[][] arr=new int[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextInt();
        return arr;
    } 
    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    static boolean[] sieve()
    {
        int size=(int)(1e5+5);
        boolean[] isPrime=new boolean[size];
        Arrays.fill(isPrime, true);
        for(int i=2;i<size;++i)
            for(int j=2*i;isPrime[i]==true && j<size;j+=i)
                isPrime[j]=false;

        return isPrime;
    }
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                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());
        }
    }


}
class Pair
{
    
}