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 PHP (judge verdict: Time Limit Exceeded)

<?php
	$n = trim(fgets(STDIN));
	$s = null;
	$rootn = sqrt($n);
	for($i = 2; $i <= $rootn; ++$i){
		while(true){
			if(($n % $i) == 0){
				$s = $s . " " . $i;
			}
			else{
				break;
			}
		}
	}
	echo $n . ":" . $s;
?>