Visible Squares

There are N axis-aligned squares on a plane. Every vertex of every square has integer coordinates, and no two squares touch or overlap.

Count how many squares are visible from the origin O(0, 0).

A square is considered visible from the origin if there exist two distinct points A and B on its boundary such that the interior of triangle OAB, excluding the boundary of the triangle, is not crossed by any other square.

The first line contains the number of squares N (1 <= N <= 1,000).

Each of the next N lines contains three integers X, Y, and L (1 <= X, Y, L <= 10,000), describing one square. Its lower-left vertex is (X, Y), and its side length is L.

Print the number of squares visible from the origin.