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

// हर हर महादेव
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;
import java.text.DecimalFormat;

public final class Solution {

    static int inf = Integer.MAX_VALUE;
    static long mod = 1000000000 + 7;

 static void ne(Scanner sc, BufferedWriter op) throws Exception { 
   long n=sc.nextLong();
    long a=n-2;
    long b=1;
    long c=1;
    op.write(a+" "+b+" "+c+"\n");
    
  
         
 }

    public static void main(String[] args) throws Exception {
        BufferedWriter op = new BufferedWriter(new OutputStreamWriter(System.out));
        // Reader sc = new Reader();
        Scanner sc= new Scanner(System.in);
        int t = sc.nextInt();
        while (t-->0){ ne(sc, op); }
        
        // ne(sc,op);
           
                   
        op.flush();
    }

    static void print(Object o) {
        System.out.println(String.valueOf(o));
    }
    static int[] toIntArr(String s){
        int[] val= new int[s.length()];
        for(int i=0;i<s.length();i++){
            val[i]=s.charAt(i)-'a';
        }
        return val;
    }

    static void  sort(int[] arr){
        ArrayList<Integer> list= new ArrayList<>();
        for(int i=0;i<arr.length;i++){
            list.add(arr[i]);

        }
        Collections.sort(list);
        for(int i=0;i<arr.length;i++){
            arr[i]=list.get(i);
        }
    }
       static void  sort(long[] arr){
        ArrayList<Long> list= new ArrayList<>();
        for(int i=0;i<arr.length;i++){
            list.add(arr[i]);

        }
        Collections.sort(list);
        for(int i=0;i<arr.length;i++){
            arr[i]=list.get(i);
        }
    }

}



// return -1 to put no ahed in array
class pair {
    int  xx;
    int yy;
    pair(int xx, int yy ) {
        this.xx = xx;
        this.yy = yy;
    }
}


class sortY implements Comparator<pair> {
    public int compare(pair p1, pair p2) {
        if (p1.yy > p2.yy) {
            return 1;
        } else if (p1.yy == p2.yy) {
            if (p1.xx > p2.xx) {
                return 1;
            } else if (p1.xx < p2.xx) {
                return -1;
            }
            return 0;

        }
        return -1;
    }
}

class sortX implements Comparator<pair> {
    public int compare(pair p1, pair p2) {
        if (p1.xx > p2.xx) {
            return 1;
        } else if (p1.xx == p2.xx) {
            if (p1.yy > p2.yy) {
                return 1;
            } else if (p1.yy < p2.yy) {
                return -1;
            }
            return 0;

        }
        return -1;
    }
}

class debug {

    static void print1d(long[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + " ");
        }

    }

    static void print1d(int[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.println(i+" = "+arr[i]);
        }

    }

    static void print1d(boolean[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.println(i + "= " + arr[i]);
        }

    }

    static void print2d(int[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }

    static void print2d(long[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }
     static void printPair(ArrayList<pair> list) {
        if(list.size()==0){
            System.out.println("empty list");
            return;
        }
       System.out.println();
       for(int i=0;i<list.size();i++){
          System.out.println(list.get(i).xx+"-"+list.get(i).yy);
       }
    }

}

class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') {
                if (cnt != 0) {
                    break;
                } else {
                    continue;
                }
            }
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null)
            return;
        din.close();
    }
}
 
 