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