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)

n = int(input())
ans = [str(n) + ":"]
i = 2
while i * i <= n:
    while n % i == 0:
        n //= i
        ans.append(i)
    i += 1
if n != 1:
    ans.append(n)
print(*ans)