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.util.*;

import java.io.*;
import java.math.BigInteger;
import java.nio.charset.StandardCharsets;
	
public class Main {
		private static FS sc = new FS();
		
		private static class FS {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			StringTokenizer st = new StringTokenizer("");
			String next() {
				while (!st.hasMoreTokens())
					try {
						st=new StringTokenizer(br.readLine());				               
		            } catch (IOException e) {}
				return st.nextToken();
			}
			
			int nextInt() {
				return Integer.parseInt(next());
			}
			long nextLong() {
				return Long.parseLong(next());
			}
		}
		
		private static class extra {
			
			static int[] intArr(int size) {
				int[] a = new int[size];
				for(int i = 0; i < size; i++) a[i] = sc.nextInt();
				return a;
			}
			
			static long[] longArr(int size) {
				Scanner scc = new Scanner(System.in);
				long[] a = new long[size];
				for(int i = 0; i < size; i++) a[i] = sc.nextLong();
				return a;
			}
			
			static long intSum(int[] a) {
				long sum = 0; 
				for(int i = 0; i < a.length; i++) {
					sum += a[i];
				}
				return sum;
			}
			
			static long longSum(long[] a) {
				long sum = 0; 
				for(int i = 0; i < a.length; i++) {
					sum += a[i];
				}
				return sum;
			}
			
			static LinkedList[] graphD(int vertices, int edges) {
				LinkedList<Integer>[] temp = new LinkedList[vertices+1];
				for(int i = 0; i <= vertices; i++) temp[i] = new LinkedList<>();
				for(int i = 0; i < edges; i++) {
					int x = sc.nextInt();
					int y = sc.nextInt();
					temp[x].add(y);
				}
				return temp;
			}
			
			static LinkedList[] graphUD(int vertices, int edges) {
				LinkedList<Integer>[] temp = new LinkedList[vertices+1];
				for(int i = 0; i <= vertices; i++) temp[i] = new LinkedList<>();
				for(int i = 0; i < edges; i++) {
					int x = sc.nextInt();
					int y = sc.nextInt();
					temp[x].add(y);
					temp[y].add(x);
				}
				return temp;
			}
			
			static void printG(LinkedList[] temp) {
				for(LinkedList<Integer> aa:temp) System.out.println(aa);
			}
			
			static long cal(long val, long pow, long mod) {
				if(pow == 0) return 1;
				long res = cal(val, pow/2, mod);
				
				long ret = (res*res)%mod;
				if(pow%2 == 0) return ret;
				return (val*ret)%mod;
			}
			
			static long gcd(long a, long b) { return b == 0 ? a:gcd(b, a%b); }
			
		}
		
		static int mod = (int) 1e9 + 7;
		
		static LinkedList<Integer>[] temp, idx;
		static long inf = (long) Long.MAX_VALUE;
//		static long inf = Long.MAX_VALUE;
//		static int max;
		
		public static void main(String[] args) { 
			int t = sc.nextInt();
//			int t = 1;
			StringBuilder ret = new StringBuilder();
			while(t-- > 0) {
				int n = sc.nextInt();
				if(n%2 == 0) {
					ret.append((n - 3) + " " + 2 + " " + 1 + "\n");
				} else {
					int half = (n-1)/2;
					if(extra.gcd(half+1, half-1) == 1) ret.append((half+1) + " " + (half-1) + " " + 1 + "\n");
					else ret.append((half+2) + " " + (half-2) + " " + 1 + "\n");
				}
			}
			System.out.println(ret);
		}

	}

	
	


	
	
	
