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 void daunism1(long k,long ans) {

    }
    static long nod(long a, long b) {
        while (Math.min(a, b)!=0){
            if (a>b){
                a=a%b;
            }
            else b=b%a;
        }
        return a+b;
    }
    public static void main(String[] args) throws IOException {
        //   br = new BufferedReader(new FileReader("input.txt"));
        //  out = new PrintWriter("output.txt");
        int t=nextInt();
        for (int i = 0; i < t; i++) {
          int n=nextInt();
          int pr=0;
            for (int c = 1; c <= n; c++) {
                for (int j =2 ; j*c <n ; j++) {
int a=c*j;
int b=n-a-c;
if (a>=b)break;
if (b%c==0){
    int k= (int) nod(a,b);
    if (k==c){
        out.println(a+" "+b+" "+c);
        pr=1;
        break;
    }
}
                }
                if (pr==1)break;
            }

        }

        out.close();
    }

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer in = new StringTokenizer("");


    public static boolean hasNext() throws IOException {
        if (in.hasMoreTokens()) return true;
        String s;
        while ((s = br.readLine()) != null) {
            in = new StringTokenizer(s);
            if (in.hasMoreTokens()) return true;
        }
        return false;
    }

    public static String nextToken() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}

class Maincraft implements Comparable<Maincraft> {
    String x;

    public Maincraft(String x) {
        this.x = x;
    }

    @Override
    public int compareTo(Maincraft o) {
       if (Long.parseLong(x+o.x+"")>Long.parseLong(o.x+x+""))return -1;
       else if (Long.parseLong(x+o.x+"")<Long.parseLong(o.x+x+""))return +1;
       else return 0;
    }
}