Let p, q be two-digit numbers neither of which are divisible by 10...

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 $\operatorname{gcd}(p, q)=1$ 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).