Taco: Path Existence in Grid

You are given a grid consisting of m rows and n columns. Each cell in the grid contains either a 0 or a 1. A cell with a value of 1 is passable, and a cell with a value of 0 is blocked. Given the starting cell at coordinates \((s_x, s_y)\) and the target cell at coordinates \((t_x, t_y)\), your task is to determine whether there exists a path from the starting cell to the target cell moving only in the four cardinal directions (up, down, left, right).

You can assume that the grid indices are 0-indexed and that you cannot move out of bounds. If a cell has already been visited, it cannot be revisited in the same path.

Input/Output Specification: The input is read from standard input and the output is written to standard output.

In mathematical form, there exists a path if and only if there is a sequence of cells \((x_0,y_0), (x_1,y_1), \dots, (x_k,y_k)\) such that:

[ \begin{aligned} (x_0, y_0) &= (s_x, s_y),\ (x_k, y_k) &= (t_x, t_y),\ |x_{i+1} - x_i| + |y_{i+1} - y_i| &= 1 \quad &\text{for all } i,\ \text{and } & grid[x_i][y_i] = 1 \quad &\text{for all } i. \end{aligned} ]

inputFormat

The input is given as follows:

1. The first line contains two integers m and n, representing the number of rows and columns, respectively.
2. The next m lines each contain n integers (0 or 1) separated by spaces, representing the grid.
3. The last line contains four integers: s_x, s_y, t_x, and t_y, which denote the starting cell and the target cell coordinates.

outputFormat

Output a single line containing either True if there exists a path from the starting cell to the target cell; otherwise, output False.

## sample

4 4
1 0 1 1
1 1 0 1
0 1 1 0
1 1 1 1
0 0 3 3

True

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