Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {

    fun calc(h: Int, n: Int, w: Int, N: Int): Double {
        var ans: Double = 1.0
        ans *= N
        ans *= n * w + h * w + h * n
        ans /= h.toDouble() * n * w
        return ans
    }

    val N = readLine()!!.toInt()
    for (h in 1..3500) {
        for (n in 1..3500) {
            var l = 1
            var r = 3500
            while (l + 1 < r) {
                val w = (l + r) / 2
                val ans = calc(h, n, w, N)
                if (4.0 == ans) {
                    print("$h $n $w")
                    return
                }
                if (4.0 < ans) {
                    l = w
                } else {
                    r = w
                }
            }
        }
    }

}