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())
n2=str(n)
def factorint(N):
    i=2
    fct=[]
    while i**2<=N:
        if N%i!=0:
            i+=1
        else:
            N//=i
            fct.append(i)
    if N>1:
        fct.append(N)
    return fct

print(n2+":"," ".join(map(str,factorint(n))))