404640: GYM101597 C Candy division

Your older sister has three kids. Whenever you go to visit her, you bring along a bag of candies for the kids. There are n candies in the bag. You want to give all the candies to the kids, but you also want to teach them a little math along the way. Therefore, you gave them not just the bag of candies but also one simple rule: each of the kids must take an integer fraction of candies in the bag. In other words, the amount of candies each kid takes must be a divisor of n.

Formally, in order to divide all the candies the kids have to find three positive integers a₁, a₂, a₃ such that n = a₁ + a₂ + a₃ and each a_i divides n.

The first line of the input contains a single integer t – the number of test cases to follow. Each of the following t lines of the input contains the integer n. You may assume that 1 ≤ t ≤ 100 and 1 ≤ n ≤ 10¹⁸.

Output t lines. The k-th line will solve the k-th test case and will contain three integers a_i as specified above. If there are multiple solutions you may select an arbitrary one. If there are no solutions, output the word 'IMPOSSIBLE' instead (quotes only for clarity).

3
1
3
12

IMPOSSIBLE
1 1 1
4 6 2