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)

#include <stdio.h>

int main(void) {
	int n, i, j;
	scanf("%d", &n);
	printf("%d:", n);
	
	for(i=2; i<=n; i++){
		while(n%i == 0){
			printf(" %d", i);
			n = n / i;
		}
	}
	putchar('\n');
	return 0;
}