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 C# (judge verdict: Time Limit Exceeded)

using System;

class Program
{
    static void Main(string[] args)
    {
        int s = int.Parse(Console.ReadLine());
        Console.Write(s + ": ");
        int a = 2;

        while (true)
        {
            if (s % a == 0)
            {
                if (s / a > 1)
                {
                    Console.Write(a+" ");
                }
                else { Console.WriteLine(a); }
                if (s / a == 1) { break; }
                  
                s = s / a;
                a = 2;
            }
            else
            {
                a++;
            }
        }
        Console.ReadLine();
    }
}