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 Ruby (2.7.1) (judge verdict: Wrong Answer)

N=gets.to_i
r = Rational(4,N)

if N.even?
    puts [N/2,N,N].join(' ')
else
    h = (1..10**9).bsearch {|n| 0 < (r - Rational(1,n)).numerator}
    r -= Rational(1,h)
    n = (1..10**18).bsearch {|n| 0 < (r - Rational(1,n)).numerator}
    w = (r - Rational(1,n)).denominator
    puts [h,n,w].join(' ')
end