Valid Path in a Grid

You are given an n x m grid where each cell contains either a 0 or a 1. A cell with 0 represents an open space, and a cell with 1 represents an obstacle. Your task is to determine whether there exists a valid path from the top-left corner (0, 0) to the bottom-right corner (n-1, m-1). You can move up, down, left, or right from a cell as long as you remain within the grid and do not step onto an obstacle.

The movement can be understood mathematically: a move from cell (i, j) to cell (i + dx, j + dy) is valid if

[ 0 \leq i + dx < n, \quad 0 \leq j + dy < m, \quad \text{and} \quad grid[i+dx][j+dy] = 0. ]

Determine if such a path exists. For example, consider the grid below:

3 3
0 0 1
0 1 0
0 0 0

The answer is True because there is a path from the top-left corner to the bottom-right corner.

inputFormat

The input is given via stdin in the following format:

 n m
 row1
 row2
 ...
 row n

Here, n and m are the number of rows and columns respectively. Each of the next n lines contains m space-separated integers (either 0 or 1) representing a row of the grid.

outputFormat

Output a single line via stdout containing either True or False. True indicates that there exists a valid path from the top-left corner to the bottom-right corner, and False otherwise.

## sample

3 3
0 0 1
0 1 0
0 0 0

True