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.util.*;
import java.lang.*;
import java.io.*;
public class Solution {
	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 ni() { 
			return Integer.parseInt(next());
		}

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

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

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

	// MAIN FUNCTION
//	static long mod = (long)(1e9)+7;
//	static int nn = (int)1e6;
//	static long fact[] = new long[nn+1];
//	static long invFact[] = new long[nn+1];
	public static void main(String[] args) throws java.lang.Exception {
 		FastReader fr = new FastReader();
 		PrintWriter out = new PrintWriter(System.out);
// 		initForNcr();
 		int t = fr.ni();
 		boolean arr [] = new boolean[1000001];
 		SOE(arr , 1000000);
		while(t-->0) {
			int n = fr.ni();
			if((n&1) == 0) {
				out.println((n-3) + " " + 2 + " " + 1);
			}else {
				int num = 0;
				n--;
				for(int i = Math.min(n-2, 1000000) ; i >= 1 ; i--) {
					if(arr[i]) {
						int rem = n-i;
						if(rem > i && rem%i == 0)continue;
						num = i;
						break;
					}
				}
				out.println(num + " " + (n-num) + " " + 1);
			}
		}
		out.close();
	}
	public static void SOE(boolean arr[] ,int n){
	    for(int i = 2 ; i <= n ; i++){
	        arr[i] = true;
	    }
	    for(int i = 2 ; i*i <= n ; i++){
	        if(arr[i]){
	            for(int j = i*i ; j <= n ; j+= i){
	            	if(j < 0)break;
	                arr[j] = false;
	            }
	        }
	    }
	    return;
	}
}