552D - Vanya and Triangles in this problem, shortly you should count all number of triangles with non-zero area.

My idea was to count all triangle I could which is NC3 then I will subtract zero-area triangles

zero-area triangle will occur if there is 3 points on the same line(horizontal, vertical) or have same diagonal.

Unfortunately I received (Wrong answer) and I can't prove why my solution is wrong, I tested it on several testcases and it gives Right answer.

https://ideone.com/iiuxuP Any help