Right Triangles

Count the number of axis-aligned right triangles formed by three 1s in a binary grid, where one vertex shares a row with a second 1 and a column with a third (i.e., the right angle is at their intersection). With grid sizes up to 1000×1000, the task is to aggregate contributions of each 1 based on counts of 1s in its row and column to achieve an O(n·m) solution.