Bachgold Problem Time Limit: 1 Sec Memory Limit: 256 MB 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.