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.to_i
max_root=Math.sqrt(n).to_i
prime=Array.new
m=n
i=2
while i <= max_root
	if n%i==0
		prime << i
		n=n/i
	elsif i==2
		i+=1
	else
		i+=2
	end
end
puts n
if m==n || n!=1
	prime << n
end

print "#{m}: #{prime.join(" ")}\n"