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.Scanner;

/**
 *
 * @author Acer
 */
public class GCD_Problem {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        while(T-- > 0){
            int n = sc.nextInt();
            if(n%2 == 0){
                int c = 1;
                n--;
                int b = n/2;
                int a = b+1;
                System.out.println(a+" "+b+" "+c);
            }
            else{
                int c = 1;
                n--;
                int b = 0;
                int a = 0;
                if((n-2)%2 != 0){
                    b = 2;
                    a = n-2;
                }
                else if((n-3)%3 != 0){
                    b = 3;
                    a = n-3;
                }
                else if((n-5)%5 != 0){
                    b = 5;
                    a = n-5;
                }
                else if((n-7)%7 != 0){
                    b = 7;
                    a = n-7;
                }
                else if((n-11)%11 != 0){
                    b = 11;
                    a = n-11;
                }
                else if((n-13)%13 != 0){
                    b = 13;
                    a = n-13;
                }
                else if((n-17)%17 != 0){
                    b = 17;
                    a = n-17;
                }
                else if((n-19)%19 != 0){
                    b = 19;
                    a = n-19;
                }
                System.out.println(a+" "+b+" "+c);
            }
        }
    }
    
}