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: Accepted)

#!/usr/bin/env ruby

require 'prime'

n = gets().chomp().to_i()



print "#{n}:"
if Prime.prime?(n) then
  print " #{n}"
else
  Prime.each(n).each do|i|
    loop do
      if n % i == 0 then
        print " #{i}"
        n = n/i
      else
        break
      end
    end
    if i > n then
      break
    end
  end
end
puts ""