I want to go from $(0,0)$ to $(8,8)$ in this $8\times8$ grid. I can only move up or right.

However, I have to avoid the points $(3,3), (3,4), (4,3), (4,4)$ ($a,b,c,d$ in the figure). How many distinct paths are possible?
I want to go from $(0,0)$ to $(8,8)$ in this $8\times8$ grid. I can only move up or right.

However, I have to avoid the points $(3,3), (3,4), (4,3), (4,4)$ ($a,b,c,d$ in the figure). How many distinct paths are possible?