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=input()
print(n+': ',end='')
n=int(n)
x = 2
ans = []
while x * x <= n:
    while n % x == 0:
        n //= x
        ans.append(x)
    x = x + 1
if n > 1:
    ans.append(n)
print(" ".join(list(map(str, ans))))