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 = 2;

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