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: Wrong Answer)

n = gets.chomp
print n + ":"
n = n.to_i
k = Math::sqrt(n)
k = k.to_i
test = 0
for i in 2..k
  while n%i == 0
    print " #{i}"
    n = n/i
    test += 1
  end
end
if test == 0
  puts " #{n}"
else
  puts ""
end