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 JavaScript (judge verdict: Time Limit Exceeded)

var input = require('fs').readFileSync('/dev/stdin', 'utf8').trim();
var n = +input;
 
process.stdout.write(n + ': ');
 
var primes = [];
 
for (var i = 1; n > 1; i++) {
    var low = i * 6 - 1;
    var high = i * 6 + 1;
    while (n % low == 0) {
        primes.push(low);
        n /= low;
    }
    while (n % high == 0) {
        primes.push(high);
        n /= high;
    }
}
 
console.log(primes.join(' '));