Taco: Grid Path with One Obstacle Removal

You are given an m by n grid where each cell is either free (denoted by .) or contains an obstacle (denoted by #). Starting from the top-left corner, your goal is to determine whether it is possible to reach the bottom-right corner by moving only to the right or down. You are allowed to remove at most one obstacle from the grid.

A valid path is one that only moves in the right ((0, 1)) or down ((1, 0)) directions and traverses cells containing . (free cells). Formally, if we denote the cell coordinates by \((i,j)\) with \(0 \leq i \lt m\) and \(0 \leq j \lt n\), you need to check whether there exists a path from \((0,0)\) to \((m-1,n-1)\) after optionally converting one \(#\) into a free cell.

The problem can be stated in mathematical terms as follows:

Determine if there exists a sequence of moves \(\{(i_k, j_k)\}\) such that

[ \begin{aligned} &(i_0, j_0) = (0,0),,\ &(i_{K}, j_{K}) = (m-1, n-1),,\ &(i_{k+1} - i_k, j_{k+1} - j_k) \in {(0,1),(1,0)},,\ &\text{and for each } (i,j) \text{ in the path, the cell is free (possibly after one removal)}. \end{aligned} ]

inputFormat

The input is provided via standard input (stdin) and consists of the following lines:

• The first line contains two integers m and n --- the number of rows and columns respectively.
• The following m lines each contain a string of length n composed of characters . and #, representing the grid.

You can assume that 1 ≤ m, n ≤ 100.

outputFormat

Output a single line via standard output (stdout) containing either Yes if it is possible to reach the bottom-right cell under the given conditions or No otherwise.

## sample

3 3
..#
.#.
...

Yes