문제<\/h2>
Eva loves painting. Today she is working with a square canvas of $n<\/mi>\times<\/mo>n<\/mi><\/mrow>n \times n<\/math><\/span><\/span> n<\/span> <\/span> \times<\/span> <\/span><\/span> <\/span> n<\/span><\/span><\/span><\/span> unit cells. Each cell is painted white, painted black, or empty --- not painted at all.<\/p> Eva is going to draw a black triangle inside each empty cell. She wants each triangle to be right-angled and have an area of 1<\/mn>2<\/mn><\/mfrac><\/mrow>\frac{1}{2}<\/math><\/span><\/span> <\/span> <\/span> 2<\/span><\/span><\/span><\/span> <\/span> <\/span><\/span> <\/span> 1<\/span><\/span><\/span><\/span><\/span> <\/span><\/span> <\/span><\/span><\/span><\/span><\/span> <\/span><\/span><\/span><\/span><\/span> square unit cells. Thus, there are four ways to draw a single triangle:<\/p> Each triangle is a piece of art, and Eva wants them to be easily distinguishable from the rest of the painting. To achieve that, no two black triangles may share a common side with each other, and no black triangle may share a common side with a black square. Note that two black squares are allowed to share a common side.<\/p> Help Eva to find out how many ways there are to finish her painting. Since the number can be large, calculate it modulo$

Easily Distinguishable Triangles