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 codeforces;
import java.io.*;
import java.util.*;
	
public class practice {
	
	static FastScanner fs = new FastScanner();
		
	public static void main(String[] args) {
		int t = 1;
		t = fs.nextInt();   
		for(int i=1;i<=t;i++) {
			solve(t);
		}
	}
	
	public static void solve(int tt) {
		int n = fs.nextInt();
		if (n % 2 == 0) {
			System.out.println(n/2 + " " + (n / 2 - 1) + " " + 1);
		} else {
			int z = (n - 1) / 2;
			if (z % 2 == 0) {
				System.out.println((z - 1) + " " + (z + 1) + " " + 1);
			} else {
				System.out.println((z - 2) + " " + (z + 2) + " " + 1);
			}
		}
		return;
	}
		
	public static int [] sortarray(int a[]) {
		ArrayList<Integer> L = new ArrayList<Integer>();
		for(int i:a) {
			L.add(i);
		}
		Collections.sort(L);
		for(int i=0;i<L.size();i++)a[i]=L.get(i);
		return a;
	}
	
	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());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		ArrayList<Integer> readList(int n) {
			ArrayList<Integer> a = new ArrayList<Integer>();
			int x;
			for(int i=0;i<n;i++) {
				x=fs.nextInt();
				a.add(x);
			}
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}
