<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:
    vector<int> getDirection(int num,int i ,int j){
        switch(num){
            case 1:
                return {i,j+1,1,i,j-1,3};
            case 2:
                return {i+1,j,2,i-1,j,4};
            case 3:
                return {i+1,j,2,i,j-1,3};
            case 4:
                return {i+1,j,2,i,j+1,1};
            case 5:
                return {i,j-1,3,i-1,j,4};
            case 6:
                return {i,j+1,1,i-1,j,4};
            
        }
        return {-1};
    }

    bool isValid(int num, int prev){
        
        if(prev==0)
            return true;
        switch(num){
            case 1:
                if(prev == 1 || prev ==3)
                    return true;
                return false;
            case 2:
                if(prev == 2|| prev ==4)
                    return true;
                return false;
            case 3:
                if(prev == 1 || prev ==4)
                    return true;
                return false;
            case 4:
                if(prev ==3 || prev ==4)
                    return true;
                return false;
            case 5:
                if(prev ==1 || prev ==2)
                    return true;
                return false;
            case 6:
                if(prev ==2 || prev ==3)
                    return true;
                return false;
            
        }
        return false;
    }

    vector<vector<int>> visited;
    bool hasValidPath(vector<vector<int>>& grid, int i =0, int j =0,int prev = 0) {
        
        if(visited.size()==0)
            visited.resize(grid.size(),vector<int>(grid[0].size(),0)) ;//vector<vector<int>>(grid.size(),vector<int>(grid[0].size()));
        if(i<0 || i>=grid.size() || j <0 || j>=grid[0].size())
            return false;
        if(visited[i][j]==1)
            return false;    
        if(!isValid(grid[i][j],prev))
            return false;
        if(i == grid.size()-1 && j == grid[0].size()-1)
            return true;

        vector<int> next (6);
        next = getDirection(grid[i][j],i,j);
        visited[i][j]=1;
        bool res = hasValidPath(grid,next[0],next[1],next[2]) || hasValidPath(grid,next[3],next[4],next[5]);
        visited[i][j]=0;
        return res;




    }
};
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