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: Time Limit Exceeded)

p=lambda x:print(x,end=' ')
n=input()
p(n+':')
n=int(n);s=n**.5
while n%2==0 and n>3:
    p(2)
    n//=2
d=3
while n>d+1:
    if s>d and n%d==0:
        p(d)
        n//=d
    else:d+=2
print(n)