<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:
        #1- right/left [row,col+-1]
        #2- down/up [row+-1,col]
        #3- right+down [row+1,col+1] or [row-1,col-1]
        #4- left+down
        #5-right+up
        #6- down+right
        row_m = len(grid)
        col_n = len(grid[0])
        visited = [[0]*col_n for each in range(row_m)]
        row, col= 0,0

        directions = {
            1: [(0,1),(0,-1)],
            2: [(-1,0),(1,0)],
            3: [(1,0),(0,-1)],
            4: [(1,0),(0,1)],
            5: [(-1,0),(0,-1)],
            6: [(-1,0),(0,1)]
        }

        dependencies = {
            1: {3,4,5,6},
            2: {3,4,5,6},
            3: {1,2,4,5,6},
            4: {1,2,3,5,6},
            5: {1,2,3,4,6},
            6: {1,2,3,4,5}
        }

        def dfs(i,j):

            visited[i][j] = 1
            if i == row_m -1 and j == col_n-1:
                return True
           
            for d in directions[grid[i][j]]:
                ni = i+d[0]
                nj = j+d[1]
                if ni>=0 and nj>=0 and ni<row_m and nj<col_n and visited[ni][nj] == 0 and (-d[0], -d[1]) in directions[grid[ni][nj]]:
                    if dfs(ni,nj):
                        return True
        
            return False
        return dfs(0,0)
           
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