Playing in Threes

There are N distinct points on a two-dimensional plane. Choose three of them and count how many choices form a right triangle whose side lengths are exactly A, B, and C.

The lengths satisfy A < B < C and C^2 = A^2 + B^2, so A and B are the two perpendicular sides. Each set of three points is counted once.

The first line contains four integers N, A, B, and C: the number of points and the three side lengths of the right triangle.

• 1 <= N <= 500,000
• 1 <= A < B < C <= 250,000
• C^2 = A^2 + B^2

Each of the next N lines contains two integers x and y, the coordinates of one point.

• -1,000,000,000 <= x, y <= 1,000,000,000
• All N points are distinct.

Print the number of valid choices of three points.