<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:
    int m , n;
    bool dfs(int i , int j , vector<vector<int>> &grid , vector<vector<bool>> &visited){
        if(i < 0 || j < 0 || i >= m || j >= n || visited[i][j]) return false;
        if(i == m-1 and j == n-1){
            return true;
            // if(grid[i][j] == 1){
            //     if(j-1 >= 0 and (grid[i][j-1] == 6 || grid[i][j-1] == 1)) return true;
            //     return false;
            // }
            // else if(grid[i][j] == 2){
            //     if(i-1 >= 0 and (grid[i-1][j] == 2 || grid[i-1][j] == 3)) return true;
            //     return false;
            // }
            // else if(grid[i][j] == 3){
            //     if(j-1 >= 0 and (grid[i][j-1] == 6 || grid[i][j-1] == 1)) return true;
            //     return false;
            // }
            // else if(grid[i][j] == 4) return false;
            // else if(grid[i][j] == 5){
            //     if(i-1 >= 0 and (grid[i-1][j] == 3 || grid[i-1][j] == 2)) return true;
            //     if(j-1 >= 0 and (grid[i][j-1] == 1 || grid[i][j-1] == 6)) return true;
            //     return false;
            // }
            // else{
            //     if(i-1 >= 0 and (grid[i-1][j] == 2 || grid[i-1][j] == 3)) return true;
            //     return false;
            // }
        }

        visited[i][j] = true;
        bool one = false;
        if(grid[i][j] == 1){
            bool left1 = (j-1 >= 0 and (grid[i][j - 1] == 1 || grid[i][j - 1] == 4 || grid[i][j - 1] == 6)) ? dfs(i , j-1 , grid , visited) : false;
            bool right1 = (j+1 < n and (grid[i][j + 1] == 1 || grid[i][j + 1] == 3 || grid[i][j + 1] == 5)) ? dfs(i , j+1 , grid , visited) : false;
            one = left1 or right1;

        }

        bool two = false;
        if(grid[i][j] == 2){
            bool upper2 = (i-1 >= 0 and (grid[i - 1][j] == 2 || grid[i - 1][j] == 3 || grid[i - 1][j] == 4)) ? dfs(i-1 , j , grid , visited) : false;
            bool lower2 = (i+1 < m and (grid[i + 1][j] == 2 || grid[i + 1][j] == 5 || grid[i + 1][j] == 6)) ? dfs(i+1 , j , grid , visited) : false;
            two = upper2 or lower2;
        }

        bool three = false;
        if(grid[i][j] == 3){
            bool left3 = (j-1 >= 0 and (grid[i][j - 1] == 1 || grid[i][j - 1] == 4 || grid[i][j - 1] == 6)) ? dfs(i , j-1 , grid , visited) : false;
            bool lower3 = (i+1 < m and (grid[i + 1][j] == 2 || grid[i + 1][j] == 5 || grid[i + 1][j] == 6)) ? dfs(i+1 , j , grid , visited) : false;
            three = left3 or lower3;
        }

        bool four = false;
        if(grid[i][j] == 4){
            bool right4 = (j+1 < n and (grid[i][j + 1] == 1 || grid[i][j + 1] == 3 || grid[i][j + 1] == 5)) ? dfs(i , j+1 , grid , visited) : false;
            bool lower4 = (i+1 < m and (grid[i + 1][j] == 2 || grid[i + 1][j] == 5 || grid[i + 1][j] == 6)) ? dfs(i+1 , j , grid , visited) : false;
            four = right4 or lower4;
        }

        bool five = false;
        if(grid[i][j] == 5){
            bool left5 = (j-1 >= 0 and (grid[i][j - 1] == 1 || grid[i][j - 1] == 4 || grid[i][j - 1] == 6)) ? dfs(i , j-1 , grid , visited) : false;
            bool upper5 = (i-1 >= 0 and (grid[i - 1][j] == 2 || grid[i - 1][j] == 3 || grid[i - 1][j] == 4)) ? dfs(i-1 , j , grid , visited) : false;
            five = left5 or upper5;
        }

        bool six = false;
        if(grid[i][j] == 6){
            bool right6 = (j+1 < n and (grid[i][j + 1] == 1 || grid[i][j + 1] == 3 || grid[i][j + 1] == 5)) ? dfs(i , j+1 , grid , visited) : false;
            bool upper6 = (i+1 < m and (grid[i + 1][j] == 2 || grid[i + 1][j] == 5 || grid[i + 1][j] == 6)) ? dfs(i+1 , j , grid , visited) : false;
            six = right6 or upper6;
        }

        return (one or two or three or four or five or six);
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        m = grid.size();
        n = grid[0].size();
        if(m == 1 and n == 1) return true;
        vector<vector<bool>> visited(m , vector<bool> (n , false));
        return dfs(0,0,grid,visited);
    }
};
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