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: Runtime Error)

N = int(input())

# a >= b >= c を仮定できる
# a,b,c <= 3500
# 4/N <= 3/a  a <= 0.75N
# 4/N >= 3/c  c >= 0.75N

amax = int(0.75 * N) + 2
bmin = int(0.75 * N) - 1
max = 3501
for b in range(bmin,max):
  for a in range(1,amax):
    res = 4/N - 1/a - 1/b
    if res<=0:
      continue
    candc = int(1/res)
    for c in range(candc-1,candc+2):
      if 4*a*b*c == N*(a*b + b*c + c*a):
        print(a,b,c)
        exit(0)