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)

require 'prime'

def aux(n)
  f=Prime.prime_division(n)
  f.map{|x| [x[0]]*x[1]}.flatten
end

def main
  fh=STDIN
  #fh=File.new("x.txt", "r")
  n=  fh.gets.chomp.to_i
  puts "#{n}: #{aux(n).map(&:to_s).join(' ')}"
end

if $0 == __FILE__ then
  main
end