Let $$p, q$$ be two-digit numbers neither of which are divisible by $$10$$. Let $$r$$ be the four-digit number by putting the digits of $$p$$ followed by the digits of $$q$$ (in order). As $$p, q$$ vary, a computer prints $$r$$ on the screen if $$\gcd(p,q)=1$$ and $$p+q$$ divides $$r$$. Suppose that the largest number that is printed by the computer is $$N$$. Determine the number formed by the last two digits of $$N$$ (in the same order).