<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:
    struct Node {
        int r, c;
        vector<int> cell;
    };
    unordered_map<int, vector<Node>> pos;
    int visited[305][305];
    bool dfs(int r, int c, vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        if(r==n-1 && c==m-1) return true;
        visited[r][c]=1;
        cout<<r<<" "<<c<<"\n";
            for(int i=0; i<2; i++) {
                int dirr = pos[grid[r][c]][i].r;
                int dirc = pos[grid[r][c]][i].c;
                int nr = r+dirr;
                int nc = c+dirc;
                if(nr<0 || nc<0 || nr>=n || nc>=m || visited[nr][nc]) continue;
                int val = grid[nr][nc];
                bool found = false;
                vector<int> cells = pos[grid[r][c]][i].cell;
                for(int j=0; j<cells.size(); j++) 
                    if (val == cells[j]) found = true;
                if (found && dfs(nr, nc, grid)) return true;
            }
            return false;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        Node n;
        n.r=0; n.c=1; n.cell.push_back(3); n.cell.push_back(5); n.cell.push_back(1);
        pos[1].push_back(n);
        n.cell.clear();
        n.r=0; n.c=-1; n.cell.push_back(4); n.cell.push_back(6); n.cell.push_back(1);
        pos[1].push_back(n);
        n.cell.clear();
        n.r=1; n.c=0; n.cell.push_back(5); n.cell.push_back(6); n.cell.push_back(2);
        pos[2].push_back(n);
        n.cell.clear();
        n.r=-1; n.c=0; n.cell.push_back(3); n.cell.push_back(4); n.cell.push_back(2);
        pos[2].push_back(n);
        n.cell.clear();
        n.r=0; n.c=-1; n.cell.push_back(4); n.cell.push_back(6); n.cell.push_back(1);
        pos[3].push_back(n);
        n.cell.clear();
        n.r=1; n.c=0; n.cell.push_back(5); n.cell.push_back(6); n.cell.push_back(2);
        pos[3].push_back(n);
        n.cell.clear();
        n.r=0; n.c=1; n.cell.push_back(5); n.cell.push_back(3); n.cell.push_back(1);
        pos[4].push_back(n);
        n.cell.clear();
        n.r=1; n.c=0; n.cell.push_back(5); n.cell.push_back(6); n.cell.push_back(2);
        pos[4].push_back(n);
        n.cell.clear();
        n.r=0; n.c=-1; n.cell.push_back(4); n.cell.push_back(6); n.cell.push_back(1);
        pos[5].push_back(n);
        n.cell.clear();
        n.r=-1; n.c=0; n.cell.push_back(4); n.cell.push_back(3); n.cell.push_back(2);
        pos[5].push_back(n);
        n.cell.clear();
        n.r=0; n.c=1; n.cell.push_back(1); n.cell.push_back(3); n.cell.push_back(5);
        pos[6].push_back(n);
        n.cell.clear();
        n.r=-1; n.c=0; n.cell.push_back(2); n.cell.push_back(3); n.cell.push_back(4);
        pos[6].push_back(n);
        n.cell.clear();
        memset(visited, 0, sizeof(visited));
        return dfs(0, 0, grid);
    }
};
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