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)

def soinnsuubunnkai(n):
  ret = []
  for i in range(2, int(n ** (1 / 2)) + 1):
    if i > n:break
    while n % i == 0:
      n //= i
      ret.append(i)
  if n != 1:
    ret.append(n)
  return ret

n = int(input())
print(str(n)+": ",end="")
print(*soinnsuubunnkai(n))