A. Triangles

Your task, assigned by the International Office of Paper Pushing (IOPP), is to count triangles on monochrome images. According to IOPP policy:
  • a line is an uninterrupted series of black pixels
  • furthermore a line is always horizontal, vertical or at 45 degrees
  • a triangle is made up of 3 lines connected in 3 different corner pixels
   triangles

Input

PNG files.

Output

Exact number of black triangles in the PNG.