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 Ruby (judge verdict: Time Limit Exceeded)

n = gets.to_i
print n.to_s + ':'
loop do
  2.upto(n) do |i|
    next unless n % i == 0
    print ' ' + i.to_s
    n /= i
    break
  end
  if n == 1
    puts ""
    break
  end
end