A10714. Bachgold Problem

Bachgold problem is very easy to formulate. Given a positive integer $n$ represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than $1$ .

Recall that integer $k$ is called prime if it is greater than $1$ and has exactly two positive integer divisors — $1$ and $k$ .

The only line of the input contains a single integer $n$ ( $2<=n<=100000$ ).

The first line of the output contains a single integer $k$ — maximum possible number of primes in representation.

The second line should contain $k$ primes with their sum equal to $n$ . You can print them in any order. If there are several optimal solution, print any of them.