<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 reach(const vector<vector<int>>& grid,pair<int,int> pos){
        const int row = grid.size();
        const int col = grid[0].size();
        vector<vector<bool>> seen(row,vector<bool>(col,false));

        function<bool (int ,int)> valid = [&](int i,int j){
            return i>=0 && i < row && j >=0 && j < col && seen[i][j] == false;
        };
        while(1){
            int i = pos.first;
            int j = pos.second;
            if(i == row-1 && j == col - 1){
                return true;
            }
            int road = grid[i][j];
            seen[i][j] = true;
            if(road == 1){
                int jL = j - 1;
                int jR = j + 1;
                if(valid(i,jL)  ){
                    const int roadL = grid[i][jL];
                    if(roadL == 2 || 3 == roadL || 5 == roadL){
                        return false;
                    }
                    pos = {i,jL};
                }
                else if(valid(i,jR)  ){
                    const int roadR = grid[i][jR];
                    if(roadR == 2 || 4 == roadR || 6 == roadR){
                        return false;
                    }
                    pos = {i,jR};
                }
                else{
                    return false;
                }
            }
            else if(road == 2){
                int iT = i - 1;
                int iB = i+1;
                if(valid(iT,j)){
                    const int roadT = grid[iT][j];
                    if(roadT == 1 || 5 == roadT || 6 == roadT){
                        return false;
                    }
                    pos = {iT,j};
                }
                else if(valid(iB,j)){
                    const int roadB = grid[iB][j];
                    if(1 == roadB || 3 == roadB || 4 == roadB){
                        return false;
                    }
                    pos = {iB,j};
                }
                else{
                    return false;
                }
            }
            else if(road == 3){
                if(valid(i,j-1)){
                    const int road1 = grid[i][j-1];
                    if(road1 == 2 || 3 == road1 || 5 == road1){
                        return false;
                    }
                    pos = {i,j-1};
                }
                else if(valid(i+1,j)){
                    const int road1 = grid[i+1][j];
                    if(road1 == 1 || 3 == road1 || 4 == road1){
                        return false;
                    }
                    pos = {i+1,j};
                }
                else{
                    return false;
                }

            }
            else if(road == 4){
                if(valid(i,j+1)){
                    const int roadR = grid[i][j+1];
                    if(roadR == 2 || 4 == roadR || 6 == roadR){
                        return false;
                    }
                    pos = {i,j+1};
                }
                else if(valid(i+1,j)){
                    const int roadB = grid[i+1][j];
                    if(roadB == 1 || 3== roadB || 4 == roadB){
                        return false;
                    }
                    pos = {i+1,j};
                }
                else{
                    return false;
                }
            }
            
            else if(road == 5){
                if(valid(i-1,j)){
                    const int roadT = grid[i-1][j];
                    if(roadT == 1 || 5 == roadT || 6==roadT){
                        return false;
                    }
                    pos = {i-1,j};
                }
                else if(valid(i,j-1)){
                    const int roadL = grid[i][j-1];
                    if(roadL == 2 || 3 == roadL || 5 == roadL){
                        return false;
                    }
                    pos = {i,j-1};
                }
                else{
                    return false;
                }
            }
            else{
                if(valid(i-1,j)){
                    const int roadT = grid[i-1][j];
                    if(roadT == 1 || 5 == roadT || 6 == roadT){
                        return false;
                    }
                    pos = {i-1,j};
                }
                else if(valid(i,j+1)){
                    const int roadR = grid[i][j+1];
                    if(roadR == 2 || 4 == roadR || 6 == roadR){
                        return false;
                    }
                    pos = {i,j+1};
                }
                else {
                    return false;
                }

            }
        }
        return false;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        if(grid[0][0] == 4){
            return reach(grid,{0,1}) || reach(grid,{1,0});
        }
        else{
            return reach(grid,{0,0});
        }
        
    }
};
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