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.io.*;

public class test {

    static long mod = 1000000007;
    static long inf = Long.MAX_VALUE;
    static final int maxSizeSeive = 1000001;
    static Vector<Boolean>isprime = new Vector<>(maxSizeSeive);
    static Vector<Integer>prime = new Vector<>();
    static Vector<Integer>SPF = new Vector<>(maxSizeSeive);

    public static void solve(long n) {
        long a, b, c;
        if(n % 2 == 0) {
            a = (n - 2) / 2;
            b = a + 1;
            c = 1;
        }
        else {
            a = (n) /2;
            b = a - 1;
            c = 2;
        }
        System.out.println(a + " " + b + " " + c);
    }
    
/*
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

*/

    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while(t-- > 0) {
            long n = sc.nextLong();
            // solve
            solve(n);
        }
    }

    public static ArrayList<Integer> seivePrime(int n) {
        ArrayList<Integer> primes = new ArrayList<>();
        for (int i = 0; i < maxSizeSeive; i++){
            isprime.add(true);
            SPF.add(2);
        }

        manipulated_seive(n);

        for (int i=0; i<prime.size() && prime.get(i) <= n; i++) {
            primes.add(prime.get(i));
        }
        return primes;
    }

    public static void manipulated_seive(int N) {
        isprime.set(0, false);
        isprime.set(1, false);
         
        for (int i=2; i<N ; i++) {
            if (isprime.get(i)) {
                prime.add(i);
                SPF.set(i,i);
            }

            for (int j=0;j < prime.size() && i*prime.get(j) < N && prime.get(j) <= SPF.get(i);j++) {
                isprime.set(i*prime.get(j),false);
                SPF.set(i*prime.get(j),prime.get(j));
            }
        }
    }    
     
	public static void sort(long[] a) {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

    public static int maxIndex(long[] arr) {
        long max = Long.MIN_VALUE;
        int index = 0;
        int n = arr.length;
        for(int i = 0; i < n; i++) {
            if(arr[i] > max) {
                index = i;
                max = arr[i];
            }
        }
        return index;
    }

    public static int minIndex(long[] arr) {
        long min = Long.MAX_VALUE;
        int index = 0;
        int n = arr.length;
        for(int i = 0; i < n; i++) {
            if(arr[i] < min) {
                index = i;
                min = arr[i];
            }
        }
        return index;
    }

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

    public static void debugArrayList(ArrayList<Long> arr) {
        for(Long i : arr) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    public static long gcd(long a, long b) {
        if(b == 0) {
            return a;
        }
        else {
            return gcd(b, a % b);
        }
    }
 
    public static long LCM(long a, long b) {
        return Math.abs(a*b) / gcd(a, b);
    }

    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();
        }

        String nextLine() {
            String str="";
            try {
                str=br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        long[] readArray(int n) {
            long[] a = new long[n];
            for(int i = 0; i < n ; i++) {
                a[i] = nextLong();
            }
            return a;
        }
    }
}