Given an increasing sequence of different natural numbers $a_1 < a_2 < a_3 < ... < a_n$ such that for any two distinct numbers in this sequence their sum is not divisible by $10$. It is known that $a_n = 2023$. a) Can $n$ be greater than $800$? b) What is the largest possible value of $n$? c) For the value $n$ found in question b), find the number of such sequences with $a_n = 2023$.