The points $P(x_1,y_1)$ and $Q(x_2,y_2)$ are plotted at integer co-ordinates and are joined to the origin, $O(0,0)$, to form $\mathrm{△}OPQ$.

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between $0$ and $2$ inclusive; that is, $0\le x_1,y_1,x_2,y_2\le 2$.

Given that $0\le x_1,y_1,x_2,y_2\le 50$, how many right triangles can be formed?