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 i,n;
    scanf("%d", &n);
    printf("%d:", n);
    i=2;
    while(i <=n){
        while(n%i == 0){
            n = n/i;
            printf(" %d", i);
        }
        i++;
    }
    printf("\n");
    return 0; 
    
}