Path Existence in a Grid

You are given an \(n \times n\) grid represented by a list of strings. Each string consists of the characters '.' (representing an empty cell) and '#' (representing a blocked cell). Your task is to determine whether there exists a path from any cell in the leftmost column to any cell in the rightmost column by moving only up, down, left, or right through empty cells.

Note: The path can start at any cell in the leftmost column and end at any cell in the rightmost column.

Mathematically, given a grid \(G\) where \(G_{ij}\) is either '.' or '#', determine if there exists a sequence of valid moves starting from some cell \(G_{i,0}\) (with \(G_{i,0} = '.'\)) to some cell \(G_{j,n-1}\) (with \(G_{j,n-1} = '.'\)).

inputFormat

The first line of input contains a single integer \(n\), denoting the size of the grid.

The following \(n\) lines each contain a string of length \(n\) consisting only of the characters '.' and '#', representing the grid.

outputFormat

Output a single line with the string YES if there exists a path from the leftmost column to the rightmost column through empty cells; otherwise, output NO.

## sample

5
..##.
#..#.
.#..#
.#..#
.##..

YES

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