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, div = 2;

	scanf("%d", &n);

	printf("%d:", n);
	while(n != 1){
		if(n % div == 0){
			n /= div;
			printf(" %d", div);
		}else{
			div++;
		}
	}
	printf("\n");

	return 0;
}