Problem 91: Right triangles with integer coordinates

FCC link

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.

a graph plotting points P (x_1, y_1) and Q(x_2, y_2) at integer coordinates that are joined to the origin O (0, 0)

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.

a diagram showing the 14 triangles containing a right angle that can be formed when each coordinate is between 0 and 2

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

Test

{{test}}

Console output