<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 {
public:
    bool pathExists(vector<vector<int>>& grid, int row, int column){
        if(row==grid.size()-1 && column==grid[0].size()-1) return true;
        if(row<0||row>=grid.size()||column<0||column>=grid[0].size()||grid[row][column] == -1) return false;
        bool left=0,right=0,up=0,down=0;
        int val = grid[row][column];
        cout<<row<<column<<" "<<val;
        grid[row][column] = -1;
        if((val==1 || val==3 || val==5)&&column>0&&(grid[row][column-1]==1 || grid[row][column-1]==6 || grid[row][column-1]==4))  left = pathExists(grid,row,column-1);
        if((val==1 || val==6 || val==4)&&column<grid[0].size()-1&&(grid[row][column+1]==1 || grid[row][column+1]==3 || grid[row][column+1]==5))  right = pathExists(grid,row,column+1);
        if((val==6 || val==5 || val==2)&&row>0&&(grid[row-1][column]==4 || grid[row-1][column]==3 || grid[row-1][column]==2))  up = pathExists(grid,row-1,column);
        if((val==4 || val==3 || val==2)&&row<grid.size()-1&&(grid[row+1][column]==6 || grid[row+1][column]==5 || grid[row+1][column]==2))  down = pathExists(grid,row+1,column);
        grid[row][column] = val;

        return left||right||up||down;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        return pathExists(grid,0,0);
    }
};
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