<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 helper(vector<vector<int>>& grid,int i,int j,int m,int n,vector<vector<bool>>& visited){
        if(i<0 || j<0 || i>=m || j>=n || visited[i][j]==true)
            return false;
        if(i==m-1 && j==n-1)
            return true;
        visited[i][j]=true;
        bool a=false,b=false,c=false,d=false,e=false,f=false,g=false,h=false,o=false,p=false,k=false,l=false;
        if(grid[i][j]==1){
            if(j-1>=0 && (grid[i][j-1]==1 || grid[i][j-1]==4 || grid[i][j-1]==6))
                a=helper(grid,i,j-1,m,n,visited);
            if(j+1<n && (grid[i][j+1]==1 || grid[i][j+1]==3 || grid[i][j+1]==5))
                b=helper(grid,i,j+1,m,n,visited);
        }
        if(grid[i][j]==2){
            if(i-1>=0 && (grid[i-1][j]==2 || grid[i-1][j]==3 || grid[i-1][j]==4))
                c=helper(grid,i-1,j,m,n,visited);
            if(i+1<m && (grid[i+1][j]==2 || grid[i+1][j]==5 || grid[i+1][j]==6))
                d=helper(grid,i+1,j,m,n,visited);
        }
        if(grid[i][j]==3){
            if(j-1>=0 && (grid[i][j-1]==1 || grid[i][j-1]==4 || grid[i][j-1]==6))
                e=helper(grid,i,j-1,m,n,visited);
            if(i+1<m && (grid[i+1][j]==2 || grid[i+1][j]==5 || grid[i+1][j]==6))
                f=helper(grid,i+1,j,m,n,visited);
        }
        if(grid[i][j]==4){
            if(j+1<n && (grid[i][j+1]==1 || grid[i][j+1]==3 || grid[i][j+1]==5))
                g=helper(grid,i,j+1,m,n,visited);
            if(i+1<m && (grid[i+1][j]==2 || grid[i+1][j]==5 || grid[i+1][j]==6))
                h=helper(grid,i+1,j,m,n,visited);
        }
        if(grid[i][j]==5){
            if(i-1>=0 && (grid[i-1][j]==2 || grid[i-1][j]==3 || grid[i-1][j]==4))
                o=helper(grid,i-1,j,m,n,visited);
            if(j-1>=0 && (grid[i][j-1]==1 || grid[i][j-1]==4 || grid[i][j-1]==6))
                p=helper(grid,i,j-1,m,n,visited);
        }
        if(grid[i][j]==6){
            if(i-1>=0 && (grid[i-1][j]==2 || grid[i-1][j]==3 || grid[i-1][j]==4))
                k=helper(grid,i-1,j,m,n,visited);
            if(j+1<n && (grid[i][j+1]==1 || grid[i][j+1]==3 || grid[i][j+1]==5))
                l=helper(grid,i,j+1,m,n,visited);
        }
        return (a || b || c || d || e || f || g || h || o || p || k || l);
        
    }
    
    bool hasValidPath(vector<vector<int>>& grid) {
        int m=grid.size(),n=grid[0].size();
        vector<vector<bool>> visited(m,vector<bool>(n,false));
        return helper(grid,0,0,m,n,visited);
    }
};
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