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())
print("{}:".format(n), end='')
x = int(pow(n, 0.5))+1
for i in range(2, x):
    while n % i == 0:
        print(" {}".format(i), end='')
        n //= i
print(' {}'.format(n) if n != 1 else '')