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;

public class GCDProblem {
	
	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();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
        
        double nextFloat() { return Float.parseFloat(next()); }
 
        double nextDouble() { return Double.parseDouble(next()); }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
        int[] nextArray(int n)
        {
        	int[] a = new int[n];
        	for (int i=0; i<n; i++) {
        		a[i] = this.nextInt();
        	}
        	return a;
        }
        
        long[] nextArrayLong(int n)
        {
        	long[] a = new long[n];
        	for (int i=0; i<n; i++) {
        		a[i] = this.nextLong();
        	}
        	return a;
        }
        
    }
	
	static StringBuilder ans;
	public static void solve(int n) {
		
		if ((n&1) == 0) {
			int a = (n-2)/2;
			ans.append(a + " " + (a+1) + " " + 1);
		}
		else {
			int a = (n-1)/2;
			if ((a&1) == 0) {
				ans.append((a-1) + " " + (a+1) + " " + 1);
			}
			else {
				ans.append((a-2) + " " + (a+2) + " " + 1);
			}
		}
		ans.append("\n");
		
	}

	public static void main(String[] args) {
		
		FastReader in = new FastReader();
		ans = new StringBuilder();
		int t = in.nextInt();
		while (t-- > 0) {
			solve(in.nextInt());
		}
		System.out.print(ans);

	}

}
