We'll call a positive integer "almost prime", if it is not divisible by any prime from the interval $[3,19]$. We'll call a number "very non-prime", if it has at least 2 primes from interval $[3,19]$ dividing it. What is the greatest amount of almost prime numbers can be selected, such that the sum of any two of them is a very non-prime number? Proposed by S. Berlov, S. Ivanov