<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:
    map<int,set<pair<int,int>>> m;
    int n,mm;
    bool dfs(vector<vector<int>>& v, int r, int c, vector<vector<int>>&vis){
        vis[r][c]=1;
        if(r==n-1 && c==mm-1) return true;
        // vector<int> temp=m[v[r][c]];
        for(auto i:m[v[r][c]]){
            int nr=r+i.first;
            int nc=c+i.second;
            if(nr>=0 && nc>=0 && nr<n && nc<mm && vis[nr][nc]==0 && m[v[nr][nc]].find({-1*i.first,-1*i.second})!=m[v[nr][nc]].end()){
                /* in this checking if current node has right than its child must have left and so on */
                if(dfs(v,nr,nc,vis)) return true;
            }
        }
        return false;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        m[1]={{0,-1},{0,1}};
        m[2]={{-1,0},{1,0}};
        m[3]={{0,-1},{1,0}};
        m[4]={{0,1},{1,0}};
        m[5]={{0,-1},{-1,0}};
        m[6]={{0,1},{-1,0}};
        n=grid.size();
        mm=grid[0].size();
        vector<vector<int>> vis(n,vector<int>(mm,0));
        return dfs(grid,0,0,vis);
    }
    
};
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