A14679. GCD Problem

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 $y$ .

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 $n$ ( $10 \le n \le 10^9$ ).

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.

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