Maze Path Existence

You are given a maze represented as a grid of characters. Each cell in the maze is represented by one of the following characters:

• S - The starting point of the maze.
• D - The destination point.
• . - An open cell that can be traversed.
• # - A wall that cannot be traversed.

Your task is to determine whether there exists a path from the starting point S to the destination D by moving only in the four cardinal directions (up, down, left, right). Diagonal moves are not allowed.

The problem can be formulated using the following BFS (Breadth-First Search) approach:

Find S and D in the grid. Then, starting at S, explore all reachable cells by moving in the four directions until either D is reached or no more cells can be reached.

If there exists a path, print YES; otherwise, print NO.

Note: If any formula is required, use the LaTeX formatting. For instance, you may denote grid boundaries as \(0 \leq x < n\) and \(0 \leq y < m\).

inputFormat

The input is given via stdin and consists of:

1. A single integer n on the first line, which denotes the number of rows in the maze. (\(1 \leq n \leq 100\))
2. Followed by n lines, each containing a string of equal length that represents a row of the maze. All rows have the same number of characters \(m\) (\(1 \leq m \leq 100\)).

It is guaranteed that the maze contains exactly one S and exactly one D.

outputFormat

Output a single line to stdout:

• YES if a path exists from S to D.
• NO otherwise.

## sample

4
S....
.###.
.#D#.
...#.

YES