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.*;
import java.util.*;

public class Main {
	static int mod=1000000007,max=0;
	static MyScanner sc = new MyScanner();
	static Output out = new Output();
	public static void main(String[] args) {
		int t=sc.nextInt();
		for (int i=0;i<t;i++) {
			solve();
		}
		out.flush();
	}

	public static void solve() {
		int n=sc.nextInt();
		for(int i=2;true;i++) {
			if(gcd(i,n-i-1)!=1)
				continue;
			out.println(i+" "+(n-i-1)+" 1");
			return;
		}
	}
	
	public static int gcd(int a, int b) {   
		if (b == 0)   
			return a;     
		return gcd(b, a % b);   
	}
	
}
























class Array{
	static void sort(int[] arr){
		mergesort(arr,0,arr.length-1);
	}
	static void sort(int[] arr,int startIndex,int endIndex){
		mergesort(arr,startIndex,endIndex);
	}

	static void mergesort(int[] arr,int b,int e) {
		if(b<e) {
			int m=b+(e-b)/2;
			mergesort(arr,b,m);
			mergesort(arr,m+1,e);
			merge(arr,b,m,e);
		}
		return;	
	}
	static void merge(int[] arr,int b,int m,int e) {
		int len1=m-b+1,len2=e-m;
		int[] l=new int[len1];
		int[] r=new int[len2];
		for(int i=0;i<len1;i++)l[i]=arr[b+i];
		for(int i=0;i<len2;i++)r[i]=arr[m+1+i];
		int i=0,j=0,k=b;
		while(i<len1 && j<len2) {
			if(l[i]<r[j])arr[k++]=l[i++];
			else arr[k++]=r[j++];
		}
		while(i<len1)arr[k++]=l[i++];
		while(j<len2)arr[k++]=r[j++];
		return;
	}
	
	public static  void SortColoumn (int[][] array, final int columnIndex){
        Arrays.sort(array, new Comparator<int[]>() {
            @Override
            public int compare(int[] first, int[] second) {
               if(first[columnIndex] > second[columnIndex]) return 1;
               else return -1;
            }
        });
	}
	
//	2d sort
//	static void sort(int[][] arr){
//		mergesort(arr,0,arr.length-1);
//	}
//	static void sort(int[][] arr,int startIndex,int endIndex){
//		mergesort(arr,startIndex,endIndex);
//	}
//
//	static void mergesort(int[][] arr,int b,int e) {
//		if(b<e) {
//			int m=b+(e-b)/2;
//			mergesort(arr,b,m);
//			mergesort(arr,m+1,e);
//			merge(arr,b,m,e);
//		}
//		return;	
//	}
//	static void merge(int[][] arr,int b,int m,int e) {
//		int len1=m-b+1,len2=e-m;
//		int[][] l=new int[len1][2];
//		int[][] r=new int[len2][2];
//		for(int i=0;i<len1;i++) {
//			l[i][0]=arr[b+i][0];
//			l[i][1]=arr[b+i][1];
//		}
//		for(int i=0;i<len2;i++) {
//			r[i][0]=arr[m+1+i][0];
//			r[i][1]=arr[m+1+i][1];
//		}
//		int i=0,j=0,k=b;
//		while(i<len1 && j<len2) {
//			if(l[i][0]<r[j][0]) {
//				arr[k++][0]=l[i++][0];
//				arr[k-1][1]=l[i-1][1];
//			}
//			else {
//				arr[k++][0]=r[j++][0];
//				arr[k-1][1]=r[j-1][1];
//			}
//		}
//		while(i<len1) {
//			arr[k++][0]=l[i++][0];
//			arr[k-1][1]=l[i-1][1];
//		}
//		while(j<len2) {
//			arr[k++][0]=r[j++][0];
//			arr[k-1][1]=r[j-1][1];
//		}
//		return;
//	}
	
}
class MyScanner {

	BufferedReader br;
	StringTokenizer st;

	public MyScanner() {
		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;
	}

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

	public long[] nextLongArr(int n) {
		long a[] = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public double[] nextDoubleArr(int n) {
		double a[] = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public String[] nextArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = next();
		return a;
	}

	public String[] nextLineArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLine();
		return a;
	}
}

class Output {
	BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
	public void print() {}
	public void println() {
		try {
			out.write("\n");
		} catch (Exception e) {}
	}
	public void print(Object s) {
		try {
			out.write(s + "");
		} catch (Exception e) {}
	}
	public void println(Object s) {
		try {
			out.write(s + "\n");
		} catch (Exception e) {}
	}
	public void flush() {
		try {
			out.flush();
		} catch (Exception e) {}
	}
}