Path in a Parking Lot

You are given a rectangular parking lot represented as a grid with r rows and c columns. Each cell in the grid is one of the following characters:

• .: a free space where you can drive.
• #: a wall that cannot be passed.
• C: a parked car which acts as an obstacle.

Your task is to determine whether there exists a path from the top-left corner (cell at position (0,0)) to the bottom-right corner (cell at position (r-1, c-1)). You are only allowed to move in the four cardinal directions (up, down, left, right) and you can only traverse cells that are free (.).

Note: For the purpose of this problem, you can assume the grid dimensions satisfy \(1 \le r, c \le 1000\).

inputFormat

The input is provided through standard input as follows:

1. The first line contains two integers r and c, the number of rows and columns respectively.
2. The next r lines each contain a string of length c representing a row of the parking lot. The characters will be either ., #, or C.

Example:

4 4
...#
.#..
.#C.
....

outputFormat

Output a single line to standard output containing YES if a valid path exists from the top-left corner to the bottom-right corner, and NO otherwise.

## sample

4 4
...#
.#..
.#C.
....

YES