<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:
    height = len(grid)
    length = len(grid[0])
    visited = set()
    
    if height == 1 and height == length:
      return True
    
    # entry from 0:top, 1:right, 2:bottom, 3:left
    def checkValid(entry, current):
      match entry:
        case 0:
          return current in [2, 5, 6]
        case 1:
          return current in [1, 4, 6]
        case 2:
          return current in [2, 3, 4]
        case 3:
          return current in [1, 3, 5]

    def followPath(x, y, entry):
      if 0>x or x>=length or 0>y or y>=height:
        return False

      current = grid[y][x]

      if x==length-1 and y==height-1:
        return checkValid(entry, current)

      if (x, y) in visited:
        return False
      visited.add((x, y))

      match current:
        case 1:
          match entry:
            case 1:
              return followPath(x-1, y, 1)
            case 3:
              return followPath(x+1, y, 3)
        case 2:
          match entry:
            case 0:
              return followPath(x, y+1, 0)
            case 2:
              return followPath(x, y-1, 2)
        case 3:
          match entry:
            case 2:
              return followPath(x-1, y, 1)
            case 3:
              return followPath(x, y+1, 0)
        case 4:
          match entry:
            case 1:
              return followPath(x, y+1, 0)
            case 2:
              return followPath(x+1, y, 3)
        case 5:
          match entry:
            case 0:
              return followPath(x-1, y, 1)
            case 3:
              return followPath(x, y-1, 2)
        case 6:
          match entry:
            case 0:
              return followPath(x+1, y, 3)
            case 1:
              return followPath(x, y-1, 2)
      
      return False

    if grid[0][0] in [1, 6]:
      return followPath(1, 0, 3)
    elif grid[0][0] in [2, 3]:
      visited.clear()
      return followPath(0, 1, 0)
    elif grid[0][0] == 4:
      path1 = followPath(1, 0, 3)
      visited.clear()
      path2 = followPath(0, 1, 0)
      return path1 or path2
    return False
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