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.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(br.readLine());

        for(int i = 0; i < N; i++) {
            int number = Integer.parseInt(br.readLine());

            int tmp = 1;

            int numberTmp = number - tmp;

            for(int k = 0; k < numberTmp; k++) {
                int n1 = k;
                int n2 = numberTmp - k;
                if(gcd(n1, n2) == tmp && n1 != n2 && n1 != tmp && n2 != tmp) {
                    System.out.println(n1 +" " + n2 +" " +tmp);
                    break;
                }
            }
        }
    }

    static int gcd(int a, int b){
        int tmp, n;

        if(a < b) {
            tmp = a;
            a = b;
            b = tmp;
        }

        while(b != 0) {
            n = a % b;
            a = b;
            b = n;
        }

        return a;
    }
}
