The Well known Doublet $(x,y)$

For $x,y,n\in\mathbb N$ , $a,b\in\mathbb N_0$ and $n\geq3$ , solve the following equation if the $\gcd(x,y)=1$

$\large x^2+2^a\cdot3^b=y^n$

If the sum of possible values of $n$ is $p$ and the number of ordered doublets $(x,y)$ is $q$ .

Then enter your answer as $p+q$ .

Try more here and here