Problem: 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

Examples

Input

2


Output

1 2 2


Input

3485


Output

872 1012974 1539173474040


Input

4664


Output

3498 3498 3498

Solution (in PYTHON):

Solution:
# coding: utf-8
from itertools import combinations


def prime_decomposition(n):
    i = 2
    table = []
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
    return table


def find_result(primes, cond, total):
    combi = {}
    for i in range(len(primes)):
        for c in combinations(primes, i+1):
            s = reduce(lambda x, y: x * y, c)
            if s <= cond - 2 and total / s < 3500:
                combi[tuple(c)] = s

    keys = sorted(combi.keys())
    for h in keys:
        for n in keys:
            for w in keys:
                s = combi[h] + combi[n] + combi[w]
                if s == cond:
                    return combi[h], combi[n], combi[w]
    return None


N = int(raw_input())
primes = [
    1,
] + prime_decomposition(N)

i = 2
while True:
    cond = i * 4
    all_primes = primes + prime_decomposition(i)
    total = reduce(lambda x, y: x * y, all_primes)
    candi_primes = [p for p in all_primes if p <= cond - 2]

    r = find_result(candi_primes, cond, total)
    if r is not None:
        h, n, w = r
        print '{} {} {}'.format(int(total/h), int(total/n), int(total/w))
        break
    i += 1