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)

N = int(input())
n = N
m = N ** 0.5
L = []
i = 3

print(str(N) + ': ', end = '')

while n%2 == 0:
    n = n/2
    L.append(2)

while i <= m:
    while n%i == 0:
        n = n/i
        L.append(i)
    i += 2
    
if len(L) == 0:
    L.append(N)
            
print(' '.join(map(str, L)))