<p>You are given an <code>m x n</code> <code>grid</code>. Each cell of <code>grid</code> represents a street. The street of <code>grid[i][j]</code> can be:</p>

<ul>
	<li><code>1</code> which means a street connecting the left cell and the right cell.</li>
	<li><code>2</code> which means a street connecting the upper cell and the lower cell.</li>
	<li><code>3</code> which means a street connecting the left cell and the lower cell.</li>
	<li><code>4</code> which means a street connecting the right cell and the lower cell.</li>
	<li><code>5</code> which means a street connecting the left cell and the upper cell.</li>
	<li><code>6</code> which means a street connecting the right cell and the upper cell.</li>
</ul>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/05/main.png" style="width: 450px; height: 708px;" />
<p>You will initially start at the street of the upper-left cell <code>(0, 0)</code>. A valid path in the grid is a path that starts from the upper left cell <code>(0, 0)</code> and ends at the bottom-right cell <code>(m - 1, n - 1)</code>. <strong>The path should only follow the streets</strong>.</p>

<p><strong>Notice</strong> that you are <strong>not allowed</strong> to change any street.</p>

<p>Return <code>true</code><em> if there is a valid path in the grid or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/05/e1.png" style="width: 455px; height: 311px;" />
<pre>
<strong>Input:</strong> grid = [[2,4,3],[6,5,2]]
<strong>Output:</strong> true
<strong>Explanation:</strong> As shown you can start at cell (0, 0) and visit all the cells of the grid to reach (m - 1, n - 1).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/05/e2.png" style="width: 455px; height: 293px;" />
<pre>
<strong>Input:</strong> grid = [[1,2,1],[1,2,1]]
<strong>Output:</strong> false
<strong>Explanation:</strong> As shown you the street at cell (0, 0) is not connected with any street of any other cell and you will get stuck at cell (0, 0)
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,2]]
<strong>Output:</strong> false
<strong>Explanation:</strong> You will get stuck at cell (0, 1) and you cannot reach cell (0, 2).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 300</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 6</code></li>
</ul>

class Solution:
    def hasValidPath(self, grid: List[List[int]]) -> bool:
        rows = len(grid)
        cols = len(grid[0])

        if not grid:
            return False
        
        if len(grid) == 1 and len(grid[0]) == 1:
            return True
        
        visited = set()
        def trek(r, c, direction):
            print(r, c, direction)
            visited.add((r, c))
            cur = grid[r][c]
            # print(cur)
            if direction == "right":
                c += 1
            elif direction == "left":
                c -= 1
            elif direction == "down":
                r += 1
            elif direction == "up":
                r -= 1

            if (r not in range(rows)) or (c not in range(cols)):
                return False

            if (r, c) in visited:
                return False

            # print(grid[r][c])
            if cur == 1:
                if direction == "right":
                    if grid[r][c] != 1 and grid[r][c] != 3 and grid[r][c] != 5:
                        return False
                if direction == "left":
                    if grid[r][c] != 1 and grid[r][c] != 4 and grid[r][c] != 6:
                        return False
            if cur == 2:
                if direction == "down":
                    if grid[r][c] != 2 and grid[r][c] != 5 and grid[r][c] != 6:
                        return False
                if direction == "up":
                    if grid[r][c] != 2 and grid[r][c] != 3 and grid[r][c] != 4:
                        return False
            if cur == 3:
                if direction == "left":
                    if grid[r][c] != 1 and grid[r][c] != 4 and grid[r][c] != 6:
                        return False
                if direction == "down":
                    if grid[r][c] != 2 and grid[r][c] != 5 and grid[r][c] != 6:
                        return False
            if cur == 4:
                if direction == "right":
                    if grid[r][c] != 1 and grid[r][c] != 3 and grid[r][c] != 5:
                        return False
                if direction == "down":
                    if grid[r][c] != 2 and grid[r][c] != 5 and grid[r][c] != 6:
                        return False
            if cur == 5:
                if direction == "left":
                    if grid[r][c] != 1 and grid[r][c] != 4 and grid[r][c] != 6:
                        return False
                if direction == "up":
                    if grid[r][c] != 2 and grid[r][c] != 3 and grid[r][c] != 4:
                        return False
            if cur == 6:
                if direction == "right":
                    if grid[r][c] != 1 and grid[r][c] != 3 and grid[r][c] != 5:
                        return False
                if direction == "up":
                    if grid[r][c] != 2 and grid[r][c] != 3 and grid[r][c] != 4:
                        return False

            if r == rows - 1 and c == cols - 1:
                return True

            newDirection = ""
            if direction == "right":
                if grid[r][c] == 1:
                    newDirection = "right"
                if grid[r][c] == 3:
                    newDirection = "down"
                if grid[r][c] == 5:
                    newDirection = "up"
            elif direction == "left":
                if grid[r][c] == 1:
                    newDirection = "left"
                if grid[r][c] == 4:
                    newDirection = "down"
                if grid[r][c] == 6:
                    newDirection = "up"
            elif direction == "down":
                if grid[r][c] == 2:
                    newDirection = "down"
                if grid[r][c] == 5:
                    newDirection = "left"
                if grid[r][c] == 6:
                    newDirection = "right"
            elif direction == "up":
                if grid[r][c] == 2:
                    newDirection = "up"
                if grid[r][c] == 3:
                    newDirection = "left"
                if grid[r][c] == 4:
                    newDirection = "right"

            return trek(r, c, newDirection)

        startDirection1 = ""
        startDirection2 = ""
        if grid[0][0] == 1:
            startDirection1 = "right"
        elif grid[0][0] == 2:
            startDirection1 = "down"
        elif grid[0][0] == 3:
            startDirection1 = "down"
        elif grid[0][0] == 4:
            startDirection1 = "right"
            startDirection2 = "down"
        elif grid[0][0] == 5:
            return False
        elif grid[0][0] == 6: 
            startDirection1 = "right"

        if startDirection1 and startDirection2:
            return trek(0, 0, startDirection1) or trek(0, 0, startDirection2)
        else:
            return trek(0, 0, startDirection1)
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