The points P (x₁, y₁) and Q (x₂, y₂) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.

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 x₁, y₁, x₂, y₂ 2.

Given that 0 x₁, y₁, x₂, y₂ 50, how many right triangles can be formed?