Problem:
Prime Factorization

Factorize a given integer n.

Input

n

An integer n is given in a line.

Output

Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prime factor should be printed according to the number of times. Print a space before each prime factor.

Constraints

2 ≤ n ≤ 109

Sample Input 1

12

Sample Output 1

12: 2 2 3

Sample Input 2

126

Sample Output 2

126: 2 3 3 7

Solution in Python3 (judge verdict: Accepted)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import collections
import itertools


def prime_factorization(n):

    assert n > 0
    if n == 1:
        return collections.deque([1])
    else:
        result = collections.deque()
        for i in itertools.count(2):
            if i * i > n:
                break
            else:
                while n % i == 0:
                    n //= i
                    result.append(i)
        if n > 1:
            result.append(n)
        return result

if __name__ == "__main__":
    n = int(input())
    factors = prime_factorization(n)
    print("{n}: {factors}".format(n=n, factors=" ".join(map(str, factors))))