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

// Generated by Code Flattener.
// https://plugins.jetbrains.com/plugin/9979-idea-code-flattener

import java.io.*;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        Solution solution = new ASolution();

        boolean local = System.getProperty("ONLINE_JUDGE") == null && !solution.isInteractive();
        String input = local ? "input.txt" : null;

        solution.in = new MyScanner(input);
        solution.out = MyWriter.of(null);
        solution.bm = new Benchmark();
        solution.al = new Algorithm();
        solution.run();
        solution.close();
    }

    private abstract static class Solution {
        public MyScanner in;
        public MyWriter out;
        public Benchmark bm;
        public Algorithm al;

        public void init() {
        }

        public abstract void solve();

        protected boolean isMultiTest() {
            return true;
        }

        public void run() {
            init();
            if (isMultiTest()) {
                int t = in.nextInt();
                for (int i = 0; i < t; i++) {
                    solve();
                }
            } else {
                solve();
            }
        }

        public void close() {
            out.close();
        }

        public boolean isInteractive() {
            return false;
        }
    }

    private static class ASolution extends Solution {
        public void solve() {
            int n = in.nextInt();
            if (n % 2 == 0) {
                out.println((n - 3) + " 2 1");
            } else {
                int x = (n + 1) / 2;
                out.println(x + " " + (x - 2) + " 1");
            }
        }
    }

    private static class MyScanner {
        private final BufferedReader br;
        private StringTokenizer st;

        public MyScanner(String fileName) {
            if (fileName != null) {
                try {
                    File file = new File(getClass().getClassLoader().getResource(fileName).getFile());
                    br = new BufferedReader(new FileReader(file));
                } catch (FileNotFoundException e) {
                    throw new RuntimeException(e);
                }
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

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

        public String nextLine() {
            try {
                String line = br.readLine();
                if (line == null) {
                    throw new RuntimeException("empty line");
                }
                st = null;
                return line;
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }

    private static class Benchmark {
    }

    private static class Algorithm {
    }

    private static class MyWriter extends PrintWriter {
        public static MyWriter of(String fileName) {
            if (fileName != null) {
                try {
                    return new MyWriter(new FileWriter(fileName));
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            } else {
                return new MyWriter(new BufferedOutputStream(System.out));
            }
        }

        public MyWriter(Writer writer) {
            super(writer);
        }

        public MyWriter(OutputStream out) {
            super(out);
        }
    }
}