<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:
    void helper(int i,int j,int k,vector<vector<int>> &vis){
        if(k==1){
            for(int p=0;p<3;p++){
                vis[i+1][j+p]=1;
            }
        }
        else if(k==2){
            for(int p=0;p<3;p++){
                vis[i+p][j+1]=1;
            }
        }
        else if(k==3){
            vis[i+1][j]=1;
            vis[i+1][j+1]=1;
            vis[i+2][j+1]=1;
        }
        else if(k==4){
            vis[i+1][j+1]=1;
            vis[i+1][j+2]=1;
            vis[i+2][j+1]=1;
        }
        else if(k==5){
            vis[i+1][j]=1;
            vis[i+1][j+1]=1;
            vis[i][j+1]=1;
        }
        else{
            vis[i+1][j+1]=1;
            vis[i+1][j+2]=1;
            vis[i][j+1]=1;
        }
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        int n=grid.size();
        int m=grid[0].size();
        int size1=n*3;
        int size2=m*3;
        vector<vector<int>> vis(size1,vector<int>(size2,0));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                int a=i*3;
                int b=j*3;
                helper(a,b,grid[i][j],vis);
            }
        }
        // for(int i=0;i<size1;i++){
        //     for(int j=0;j<size2;j++){
        //         cout<<vis[i][j]<<" ";
        //     }
        //     cout<<endl;
        // }
        queue<pair<int,int>> q;
        q.push({1,1});
        vis[1][1]=0;
        int drow[]={0,0,1,-1};
        int dcol[]={1,-1,0,0};
        while(!q.empty()){
            int i=q.front().first;
            int j=q.front().second;
            q.pop();
            if(i==(size1-2) && j==(size2-2)) return true;
            for(int k=0;k<4;k++){
                int a=i+drow[k];
                int b=j+dcol[k];
                if(a>=0 && a<size1 && b>=0 && b<size2 && vis[a][b]==1){
                    q.push({a,b});
                    vis[a][b]=0;
                }
            }
        }
        return false;
    }
};
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