In the quiet hours of a long evening, you find yourself with a box of matchsticks and a growing curiosity. With these simple sticks, you begin constructing triangles, starting with a classic 3-4-5 triangle. After counting 12 matchsticks to form this first shape, a question sparks in your mind: How many distinct triangles can be formed using at most $$$N$$$ matchsticks? Each side of these triangles must be made up of an integer number of matchsticks, and the triangles must have a positive area.

To add to the complexity, triangles that are merely rotations or reflections of each other are considered the same. For example, triangles with sides 3-4-5, 4-5-3, and 5-3-4 are indistinguishable under these rules.

Because this number can be very large print it modulo $$$10^9 + 7$$$