A. Bachgold Problemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputBachgold 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. InputThe only line of the input contains a single integer n (2 ≤ n ≤ 100 000).OutputThe 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.ExamplesInput5Output22 3Input6Output32 2 2
Input5
Output22 3
['greedy', 'implementation', 'math', 'number theory', '*800']