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.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.time.Duration;
import java.time.Instant;
import java.util.ArrayList;
import java.util.Map;
import java.util.NavigableSet;
import java.util.StringTokenizer;
import java.util.TreeSet;

import static java.lang.Math.min;
import static java.lang.Math.max;
import static java.lang.Math.abs;

@SuppressWarnings("unused")
public class A {
	static boolean DEBUG = false;

	public static void main(String[] args) throws IOException {
		Instant start = Instant.now();
		if (args.length == 2) {
			System.setIn(new FileInputStream(new File("D:\\program\\javaCPEclipse\\CodeForces\\src\\input.txt")));
			// System.setOut(new PrintStream(new File("output.txt")));
			System.setErr(new PrintStream(new File("D:\\program\\javaCPEclipse\\CodeForces\\src\\error.txt")));
			DEBUG = true;
		}
		Reader fs = new Reader();
		PrintWriter pw = new PrintWriter(System.out);
//		NavigableSet<Integer>pre = sieve((int)1e9);
		int t = fs.nextInt();
		while (t-- > 0) {
			long n = fs.nextLong();
			if ((n & 1) == 0) {
				long a = n - 1;
				long b = 2;
				long c = 1;
				pw.println(a + " " + b + " " + c);
//				log(__gcd(a, b) == c);
			} else {
				long a = n - 2, b = 2, c = 1;
//				log(__gcd(a, b) == c);
				pw.println(a + " " + b + " " + c);
			}

		}
		Instant end = Instant.now();
		if (DEBUG) {
			pw.println(Duration.between(start, end));
		}
		pw.close();
	}

	public static void print(long a, long b, long c, PrintWriter pw) {
		pw.println(a + " " + b + " " + c);
		return;
	}

	public static long __gcd(long a, long b) {
		if (b != 0) {
			return __gcd(b, a % b);
		} else {
			return a;
		}
	}

	public static int lower_bound(ArrayList<Integer> ar, int k) {
		int s = 0;
		int e = ar.size();
		while (s != e) {
			int mid = s + e >> 1;
			if (ar.get(mid) < k) {
				s = mid + 1;
			} else {
				e = mid;
			}
		}
		if (s == ar.size()) {
			return -1;
		}
		return s;
	}

	public static int upper_bound(ArrayList<Integer> ar, int k) {
		int s = 0;
		int e = ar.size();
		while (s != e) {
			int mid = s + e >> 1;
			if (ar.get(mid) <= k) {
				s = mid + 1;
			} else {
				e = mid;
			}
		}
		if (s == ar.size()) {
			return -1;
		}
		return s;
	}

	static void log(Object o) {
		System.err.println(o);
	}

	static <T> void log(T a[]) {
		if (DEBUG) {
			System.err.print("[");
			for (T x : a)
				System.err.print(x + " ");
			System.err.println("]");
		}
	}

	static <T> void log(ArrayList<T> a) {
		if (DEBUG) {
			System.err.print("[");
			for (T x : a) {
				System.err.print(x + " ");
			}
			System.err.println("]");
		}
	}

	static <T, V> void log(Map<T, V> mp) {
		if (DEBUG) {
			System.err.print(mp);
		}
	}

	static class Reader {
		BufferedReader br;
		StringTokenizer st;

		public Reader() {
			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 nextDouble() {
			return Double.parseDouble(next());
		}

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

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

		int[][] read2Array(int n, int m) {
			int a[][] = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					a[i][j] = nextInt();
				}
			}
			return a;
		}
	}
}