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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

public class Prime{
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
         
        var primeFactors = PrimeFactors(n);
         
        string output = primeFactors.Count() == 0 
                        ? n.ToString() 
                        : string.Join(" ", primeFactors.Select (f => f.ToString()).ToArray()); //AOJ??¨
                        //:string.Join(" ", primeFactors);
        Console.WriteLine("{0}: {1}", n, output);
    }
     
    public static IEnumerable<int> PrimeFactors(int n)
    {
        int i = 2;
        int tmp = n;
         
        while (i <= tmp)
        {
            if(tmp % i == 0){
                tmp /= i;
                yield return i;
            }else{
                i++;
            }
             
            if(i > Math.Sqrt(n)){
                i = int.MaxValue; //???????????????
                yield return tmp;
            }
        }
    }
}