<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 __init__(self):
        self.reached = False
        self.mp = {
        1:[(0,-1),(0,1)],
        2:[(-1,0),(1,0)],
        3:[(0,-1),(1,0)],
        4:[(1,0),(0,1)],
        5:[(-1,0),(0,-1)],
        6:[(-1,0),(0,1)]
    }


    def movetonext(self,x,y,grid,prev):
        if self.reached: return
        if x<0 or x==len(grid) or y<0 or y==len(grid[0]) or grid[x][y]==-1: return
        elem = grid[x][y]
        prev_elem = (-prev[0],-prev[1])
        a,b = self.mp[elem]
        if x==len(grid)-1 and y == len(grid[0])-1:
            if a==prev_elem or b==prev_elem:
                self.reached = True
            return
        grid[x][y] = -1
        if a==prev_elem:
            self.movetonext(x+b[0],y+b[1],grid,b)
        elif b==prev_elem:
            self.movetonext(x+a[0],y+a[1],grid,a)
        else:
            return

    def hasValidPath(self, grid: List[List[int]]) -> bool:
        elem = grid[0][0]
        grid[0][0] = -1
        if len(grid)==1 and len(grid[0])==1: return True
        if elem == 5: return False
        if elem == 4:
            self.movetonext(0+self.mp[elem][0][0],0+self.mp[elem][0][1],grid,self.mp[elem][0])
        self.movetonext(0+self.mp[elem][1][0],0+self.mp[elem][1][1],grid,self.mp[elem][1])
        
        return self.reached
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