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 Python (3.4.3) (judge verdict: Accepted)

import sys
import math
import itertools

N=int(input())
if(N%4==0):
    x=3*N//4
    print(x,x,x)
    exit()
for x in range(3501):
    if(4*x-2*N>0 and (N*x)%(4*x-2*N)==0):
        h=(N*x)//(4*x-2*N)
        print(h,x,x)
        exit()
if(N>2000):st=-1
else:st=1
for h,n in itertools.product(range(1,3501)[::st],range(1,3501)[::st]):
    x=N*h*n
    y=4*n*h-N*n-N*h
    if(y>0 and x%y==0):
        print(h,n,x//y)
        break
"""
4/N=1/h+1/n+1/w
4/N=(nw+hw+hn)/nhw
4nhw/N=nw+hw+hn
4nhw=Nnw+Nhw+Nhn
(4nh-Nn-Nh)w=Nhn
w=Nhn/(4nh-Nn-Nh)

4/N=3/x
4x/N=3
4x=3N
h,n,w=3N/4  (N%4==0)

4/N=1/h+2/x
4/N-2/x=1/h
(4x-2N)/Nx=1/h
h=Nx/(4x-2N)
"""