Eva loves painting. Today she is working with a square canvas of $n \times n$ unit cells. Each cell is painted white, painted black, or empty~--- not painted at all.

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 $\frac{1}{2}$ square unit cells. Thus, there are four ways to draw a single triangle:

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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.

Help Eva to find out how many ways there are to finish her painting. Since the number can be large, calculate it modulo $998\,244\,353$.