<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 {
private:   
    vector<vector<char>> data {{'l','r'},{'t','b'},{'l','b'},{'r','b'},{'l','t'},{'t','r'}}; 
    map<char,vector<int>> dir;
    map<char,char> dir_map;
public:
    bool solve(vector<vector<int>>& grid,char from,int x,int y,vector<vector<bool>> &dp)
    {
    //    cout<<x<<" "<<y<<" "<<from<<endl; 
       if(x >= grid.size() || y >= grid[0].size() || x < 0 || y < 0)
          return false;  
       if(x == grid.size()-1 && y == grid[0].size()-1)
        {   if(data[grid[x][y]-1][0] == from || data[grid[x][y]-1][1] == from)
              return true;
            return false;
        }
       if(dp[x][y])
          return false; 
       if(data[grid[x][y]-1][0] == from)
       {
        char next = data[grid[x][y]-1][1];
        dp[x][y] = true;
        return solve(grid,dir_map[next],x+dir[next][0],y+dir[next][1],dp);
       }
       else if(data[grid[x][y]-1][1] == from)
       {
        
        char next = data[grid[x][y]-1][0];
        dp[x][y] = true;
        return solve(grid,dir_map[next],x+dir[next][0],y+dir[next][1],dp);
       }  
       dp[x][y] = true;
       return false;   
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        if(grid.size() == 1 && grid[0].size() == 1)
           return true;
        dir['l'] = {0,-1};
        dir['r'] = {0,1};
        dir['t'] = {-1,0};
        dir['b'] = {1,0};
        dir_map['l'] = 'r';
        dir_map['r'] = 'l';
        dir_map['t'] = 'b';
        dir_map['b'] = 't';
        
        char next = data[grid[0][0]-1][1];
        char next2 = data[grid[0][0]-1][0];
        vector<bool> dummy (grid[0].size(),false);
        vector<vector<bool>> done(grid.size(),dummy);
        bool output = false;
        output = output | solve(grid,dir_map[next],dir[next][0],dir[next][1],done);
        if(output)
          return true;
        for(int i = 0;i < grid.size();i++)
        {
            for(int j = 0;j < grid[0].size();j++)
              done[i][j] = false;
        }
        output = solve(grid,dir_map[next2],dir[next2][0],dir[next2][1],done);
        return output;
    }
};
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