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;
    scanf("%d",&n);
    printf("%d:",n);
    while(1) {
        for(i = 2;;i++ ) {
            if(!(n % i)) {
                printf(" ");
                printf("%d",i);
                n /= i;
                break;
            }
        }
        if(n == 1) {
            break;
        }
    }
    puts("");
    return 0;
}