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())

# n<= 10**9なので、高速化する
# 約数列挙でroot N に抑えるか？
def prime_divide(n):
    res = []
    i = 2
    while True:
        if n % i == 0:
            res.append(i)
            n //= i
        else:
            i += 1
            if i > n ** (0.5):
                break
    if n != 1:
        res.append(n)
    return res


print(n, end="")
print(":", *prime_divide(n))