<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 Street{
public:
    bool left;
    bool right;
    bool up;
    bool down;
    Street():left(false),right(false),up(false),down(false){}
};
class Solution {
private:
    vector<Street> directions;
    bool compatibl(int from ,int to,int direction){//direction 1 = up , 2 = down , 3 = left ,4 =right
        return  direction == 1 && directions[from].up    && directions[to].down
            ||  direction == 2 && directions[from].down  && directions[to].up
            ||  direction == 3 && directions[from].left  && directions[to].right
            ||  direction == 4 && directions[from].right && directions[to].left;
    }
public:
    Solution():directions(7){
        directions[1].left  = directions[1].right   = true;
        directions[2].up    = directions[2].down    = true;
        directions[3].left  = directions[3].down    = true;
        directions[4].right = directions[4].down    = true;
        directions[5].left  = directions[5].up      = true;
        directions[6].up    = directions[6].right   = true;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        queue<pair<int,int>> q;
        q.push({0,0});
        grid[0][0] *= -1;
        int m = grid.size() , n = grid[0].size();
        while(!q.empty()){
            int i = q.front().first , j = q.front().second; q.pop();
            if(i == m-1 && j == n-1) return true;
            if(i != 0   && grid[i-1][j] > 0 && compatibl(grid[i][j]*-1,grid[i-1][j],1))  grid[i-1][j] *= -1 , q.push({i-1,j});
            if(i != m-1 && grid[i+1][j] > 0 && compatibl(grid[i][j]*-1,grid[i+1][j],2))  grid[i+1][j] *= -1 , q.push({i+1,j});
            if(j != 0   && grid[i][j-1] > 0 && compatibl(grid[i][j]*-1,grid[i][j-1],3))  grid[i][j-1] *= -1 , q.push({i,j-1});
            if(j != n-1 && grid[i][j+1] > 0 && compatibl(grid[i][j]*-1,grid[i][j+1],4))  grid[i][j+1] *= -1 , q.push({i,j+1});
        }
        return false;
    }
};
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