Square-free Grid 2

Color every cell of a $256\times256$ grid either black or white.

If the four distinct cells $(r,c)$, $(r,c+d)$, $(r+d,c)$, and $(r+d,c+d)$ are all inside the grid and $d\geq1$, they form the corners of an axis-aligned square. For every such square, at least one of its four corner cells must be white.

Print any grid satisfying this condition. Let $x$ be the number of black cells. The score of the printed grid is $x$ points. A score of at least $13100$ is accepted.

There is no input.

Print $256$ lines, each containing $256$ characters without spaces. Use # for a black cell and . for a white cell.

The printed grid must satisfy both conditions in the statement.

• Row and column indices each range from $0$ to $255$.
• A score of at least $13100$ is required for acceptance.