AT_abc460_d [ABC460D] Repeatedly Repainting

There is a grid with $ H $ rows and $ W $ columns. The cell at the $ i $ -th row from the top and the $ j $ -th column from the left is called cell $ (i, j) $ . Every cell is colored white or black. The grid is described by $ H $ strings $ S_1, S_2, \ldots, S_H $ , each of length $ W $ . If the $ j $ -th character of $ S_i $ is `.`, cell $ (i, j) $ is white; if the $ j $ -th character of $ S_i $ is `#`, cell $ (i, j) $ is black. You perform the following operation $ 10^{100} $ times. - Simultaneously apply the following rules to all cells. - A cell that is white before the operation becomes black if and only if there exists at least one black cell adjacent to it. Here, cells $ (x, y) $ and $ (x', y') $ are adjacent if and only if one of them is within the $ 8 $ -neighborhood of the other, that is, $ \max(|x-x'|, |y-y'|) = 1 $ . - A cell that is black before the operation becomes white. Find the color of each cell after the operations.

The input is given from Standard Input in the following format: > $ H $ $ W $ $ S_1 $ $ S_2 $ $ \vdots $ $ S_H $

Output $ H $ lines. Output one string of length $ W $ consisting of `.` and `#` per line. The $ j $ -th character of the $ i $ -th line should be `.` if cell $ (i, j) $ is white after $ 10^{100} $ operations, and `#` if it is black.

### Sample Explanation 1 Initially, the grid is as follows.  After one operation, the grid is as follows.  After $ 10^{100} $ operations, the grid is as follows.  ### Constraints - $ 1 \leq H \times W \leq 10^6 $ - $ H $ and $ W $ are positive integers. - $ S_i $ is a string of length $ W $ consisting of `.` and `#`.