<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 solve(vector<vector<int>>&grid,int i,int j){
        int n = grid.size();
        int m = grid[0].size();
        if(i==n-1 && j==m-1) return true;
        bool result = false;
        int temp = grid[i][j];
        grid[i][j]=0;
        if(temp==1){
             if(j+1<m && (grid[i][j+1]==3 || grid[i][j+1]==5 || grid[i][j+1]==1)) result = solve(grid,i,j+1);
             if(!result && j-1>=0 &&(grid[i][j-1]==1 || grid[i][j-1]==4 || grid[i][j-1]==6)) result  = solve(grid,i,j-1);
        } else if(temp==2){
             if(i+1<n && (grid[i+1][j]==2 || grid[i+1][j]== 5 || grid[i+1][j]==6)) result  = solve(grid,i+1,j);
             if(!result && i-1>=0 && (grid[i-1][j]==2 || grid[i-1][j]== 3 || grid[i-1][j]==4)) result = solve(grid,i-1,j);
        } else if(temp==3){
            if(i+1<n && (grid[i+1][j]==2 || grid[i+1][j]== 5 || grid[i+1][j]== 6)) result = solve(grid,i+1,j);
            if(!result && j-1>=0 && (grid[i][j-1]==1 || grid[i][j-1]==4 || grid[i][j-1]==6)) result = solve(grid,i,j-1);
        } else if(temp==4){
            if(j+1<m &&(grid[i][j+1]==1 || grid[i][j+1]==3 || grid[i][j+1]==5)) result = solve(grid,i,j+1);
            if(!result && i+1<n && ( grid[i+1][j]==2 || grid[i+1][j]==5 || grid[i+1][j]==6)) result = solve(grid,i+1,j);
        } else if(temp==5){ 
            if(i-1>=0 && (grid[i-1][j]==3 || grid[i-1][j]==4 || grid[i-1][j]==2)) result = solve(grid,i-1,j);
            if(!result && j-1>=0 && (grid[i][j-1]==6 || grid[i][j-1]==4 || grid[i][j-1]==1)) result = solve(grid,i,j-1);
        } else if(temp==6){
            if(i-1>=0 && (grid[i-1][j]==4 || grid[i-1][j]==3 || grid[i-1][j]==2)) result = solve(grid,i-1,j);
            if(!result && j+1<m &&(grid[i][j+1]==5 || grid[i][j+1]== 3 || grid[i][j+1]==1)) result = solve(grid,i,j+1);
        }
        grid[i][j]=temp;
        return result;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);
        
        int n = grid.size();
        int m = grid[0].size();
        return solve(grid,0,0);
    }
};
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