Robot Navigation on a Grid

You are given an n x n grid. Each cell in the grid is either open ('.') or blocked ('#'). A robot starts at the top-left cell (0, 0) and needs to reach the bottom-right cell (n-1, n-1). The robot can move one cell at a time in the four cardinal directions (up, down, left, right) but can only move onto open cells. Your task is to determine if there exists a path from the start to the destination.

Note: The start or the destination might be blocked. If either of them is blocked, the answer is immediately NO.

The problem can be mathematically described as follows: Find if there exists a sequence of moves such that starting from (0,0) and applying moves in the set \(\{(\pm1,0), (0,\pm1)\}\), you eventually reach \((n-1, n-1)\), while remaining in the bounds \(0 \leq x, y < n\) and only stepping on cells where the grid value is ..

inputFormat

The input is given via standard input with the following format:

n
row1
row2
...
rown

Where:

• n is an integer representing the size of the grid.
• Each row is a string of length n consisting of the characters . (open) and # (blocked).

outputFormat

Output a single line: YES if there exists a path from the top-left to the bottom-right cell; otherwise, output NO.

4
....
.##.
.#..
....

YES