Rules -- Proof of Quilt

Proof of Quilt was invented by the Japanese puzzle company Nikoli (under the name Shakashaka) in 2008. 

1. Place black isosceles right triangles in some of the white cells in the grid. Each triangle must occupy exactly half of its cell, but may be in one of four orientations (◢, ◣, ◤, or ◥). A white cell may only contain one triangle.
2. Every contiguous region of white must be shaped like a rectangle (or a square).
3. A number in a black cell represents how many triangles share an edge with that cell.