<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:
        parent=defaultdict(int)
        for i in range(len(grid)):
            for j in range(len(grid[i])):
                parent[(i,j)]=(i,j)
        
        rank=[[0 for j in range(len(grid[0]))] for i in range(len(grid))]
        directions=[(1,0),(0,1)]
        def inbound(row,col):
            return 0<=row<=len(grid)-1 and 0<=col<=len(grid[0])-1
        def find(x):
            root=x
            while root!=parent[root]:
                root=parent[root]
            
            while x!=root:
                temp=parent[x]
                parent[x]=root
                x=temp
            return root
            
        def union(pair1,pair2):
            parentX=find(pair1)
            parentY=find(pair2)
            if parentX==parentY:return
            if rank[parentX[0]][parentX[1]]==rank[parentY[0]][parentY[1]]:
                rank[parentX[0]][parentX[1]]+=1
            if rank[parentX[0]][parentX[1]]>rank[parentY[0]][parentY[1]]:
                parent[parentY]=parentX
            else:
                parent[parentX]=parentY
        right = {1: {1, 3, 5}, 2: {}, 3: {}, 4: {1, 3, 5}, 5: {}, 6: {1, 3, 5}}
        down = {1: {}, 2: {2, 5, 6}, 3: {2, 5, 6}, 4: {2, 5, 6}, 5: {}, 6: {}}
        for row in range(len(grid)):
            for col in range(len(grid[i])):
                for change_row,change_col in directions:
                    new_row=row+change_row
                    new_col=col+change_col
                    if inbound(new_row,new_col)and  grid[new_row][new_col] in right[grid[row][col]] and new_col-col==1:
                        
                        union((row,col),(new_row,new_col))
                    if inbound(new_row,new_col)and  grid[new_row][new_col] in down[grid[row][col]] and new_row-row==1:
                        union((row,col),(new_row,new_col))
        return find((0,0))==find((len(grid)-1,len(grid[-1])-1))
                
            
        
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