<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 is_valid(int x,int y,vector<vector<int> > &grid)
    {
        if(x<0 || y<0 || x>=grid.size() || y>=grid[0].size())
            return 0;
        return 1;
    }
    void dfs(int x,int y,vector<vector<bool> > &visited,vector<vector<int> > &grid){
        if(visited[x][y])
            return;
        visited[x][y] = 1;
        int up,down,left,right;
        up=down=left=right=0;
        if(grid[x][y] == 1)
            left=right=1;
        else if(grid[x][y] == 2)
            up=down=1;
        else if(grid[x][y] == 3)
            left=down=1;
        else if(grid[x][y] == 4)
            down=right=1;
        else if(grid[x][y] == 5)
            up = left = 1;
        else
            right=up=1;
        if(up)
        {
            int new_x=x-1,new_y=y;
            if(is_valid(new_x,new_y,grid) && (grid[new_x][new_y]==2 || grid[new_x][new_y]==3 || grid[new_x][new_y]==4))
               dfs(new_x,new_y,visited,grid);
        }
        if(down)
        {
            int new_x=x+1,new_y=y;
            if(is_valid(new_x,new_y,grid) && (grid[new_x][new_y]==2 || grid[new_x][new_y]==5 || grid[new_x][new_y]==6))
               dfs(new_x,new_y,visited,grid);
        }
        if(left)
       {
            int new_x=x,new_y=y-1;
            if(is_valid(new_x,new_y,grid) && (grid[new_x][new_y]==1 || grid[new_x][new_y]==4 || grid[new_x][new_y]==6))
               dfs(new_x,new_y,visited,grid);
       }
        if(right)
       {
            int new_x=x,new_y=y+1;
            if(is_valid(new_x,new_y,grid) && (grid[new_x][new_y]==1 || grid[new_x][new_y]==3 || grid[new_x][new_y]==5))
                dfs(new_x,new_y,visited,grid);
       }
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        int n = grid.size();
        if(!n)
            return 1;
        int m = grid[0].size();
        vector <vector<bool> > visited(n,vector<bool>(m,0));
        dfs(0,0,visited,grid);
        return visited[n-1][m-1];
    }
};
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