You are given an $m \times n$ grid grid. Each cell in grid represents a street segment. The value of grid[i][j] corresponds to one of the following $6$ street types:

• $1$: Connects the left cell and the right cell.

• $2$: Connects the upper cell and the lower cell.

• $3$: Connects the left cell and the lower cell.

• $4$: Connects the right cell and the lower cell.

• $5$: Connects the left cell and the upper cell.

• $6$: Connects the right cell and the upper cell.

You begin at the top left cell $(0, 0)$ and aim to reach the bottom right cell $(m - 1, n - 1)$. You can move between two adjacent cells if and only if both cells possess street segments that connect to each other.

Return true if there is a valid path from $(0, 0)$ to $(m - 1, n - 1)$, or false otherwise.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq$ m, n $\leq 300$

• $1 \leq$ grid[i][j] $\leq 6$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.