GCD Problem

Description:

Input:

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases. Description of the test cases follows.

The first and only line of each test case contains a single integer $$$n$$$ ($$$10 \le n \le 10^9$$$).

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.

Sample Input:

6
18
63
73
91
438
122690412

Sample 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 $$$\operatorname{gcd}(29, 43) = 1$$$.