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: Wrong Answer)

import math

def simple_prime_factrize(x):
    pfs = []
    for y in range(2, math.ceil(math.sqrt(x))):
        if x == 1: break
        while True:
            if x%y == 0:
                pfs.append(y)
                x = x/y
            else:
                break
    return pfs

n = int(input())
print(str(n) + ': ' + ' '.join([str(x) for x in simple_prime_factrize(n)]))