<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 {
    int m , n;
public:
    bool hasValidPath(vector<vector<int>>& grid) {
        queue<pair<int,int>> q;
        q.push({0,0});
        grid[0][0] = -grid[0][0];
        m = grid.size();
        n = grid[0].size();
        
        vector<vector<vector<int>>> mp(7, vector<vector<int>> (4 , vector<int>(7, 0)));

        // 1 , 0
        mp[1][0][1] = 1;
        mp[1][0][4] = 1;
        mp[1][0][6] = 1;

        // 1 , 1
        mp[1][1][1] = 1;
        mp[1][1][3] = 1;
        mp[1][1][5] = 1;

        // 2 , 2
        mp[2][2][2] = 1;
        mp[2][2][3] = 1;
        mp[2][2][4] = 1;

        // 2 , 3
        mp[2][3][2] = 1;
        mp[2][3][5] = 1;
        mp[2][3][6] = 1;

        //3 0
        mp[3][0][1] = 1;
        mp[3][0][4] = 1;
        mp[3][0][6] = 1;

        //3 3
        mp[3][3][2] = 1;
        mp[3][3][5] = 1;
        mp[3][3][6] = 1;
        
        // 4 1
        mp[4][1][1] = 1;
        mp[4][1][3] = 1;
        mp[4][1][5] = 1;
        

        // 4 3
        mp[4][3][2] = 1;
        mp[4][3][5] = 1;
        mp[4][3][6] = 1;

        // 5 0
        mp[5][0][1] = 1;
        mp[5][0][4] = 1;
        mp[5][0][6] = 1;

        // 5 2
        mp[5][2][2] = 1;
        mp[5][2][2] = 1;
        mp[5][2][4] = 1;

        // 6 1
        mp[6][1][1] = 1;
        mp[6][1][3] = 1;
        mp[6][1][5] = 1;

        // 6 2
        mp[6][2][2] = 1;
        mp[6][2][3] = 1;
        mp[6][2][4] = 1;


        while(!q.empty())
        {
               int x = q.front().first;
               int y = q.front().second;
               int pos = -grid[x][y];
               q.pop();

               if(x == m-1 && y == n-1)
               return true;
               
               // 0  -> Left       
               if(y-1>=0)
               {
                   if(grid[x][y-1] > 0 && mp[pos][0][grid[x][y-1]])
                   {
                       q.push({x,y-1});
                       grid[x][y-1] = -grid[x][y-1];
                   }               
                }   

               // 1  -> Right
               if(y+1 < n)
               {
                   if(grid[x][y+1] > 0 && mp[pos][1][grid[x][y+1]])
                   {
                       q.push({x,y+1});
                       grid[x][y+1] = -grid[x][y+1];
                   }               
                }   

               // 2   -> Up
               if(x-1>=0)
               {
                   if(grid[x-1][y] > 0 && mp[pos][2][grid[x-1][y]])
                   {
                       q.push({x-1,y});
                       grid[x-1][y] = -grid[x-1][y];
                   }
               }   

               // 3   ->  Down     
               if(x+1<m)
               {
                   if(grid[x+1][y] > 0 && mp[pos][3][grid[x+1][y]])
                   {
                       q.push({x+1,y});
                       grid[x+1][y] = -grid[x+1][y];
                   }               
                }   
        }

        return false;
    }
};
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