CF749A 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

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.