<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 isValid(int i, int j, vector<vector<int>>& grid) {
        if (i < 0 || i >= grid.size() || j < 0 || j >= grid[0].size()) {
            return false;
        }
        return true;
    }
    bool dfs(int i, int j, vector<vector<int>>& grid, vector<vector<bool>>& visited) {
        int left = 0, right = 0, up = 0, down = 0;
        if (i == grid.size()-1 && j == grid[0].size()-1) {
            return true;
        }
        if (grid[i][j] == 1) {
            left = right = 1;
        }
        else if (grid[i][j] == 2) {
            up = down = 1;
        }
        else if (grid[i][j] == 3) {
            left = down = 1;
        }
        else if (grid[i][j] == 4) {
            right = down = 1;
        }
        else if (grid[i][j] == 5) {
            left = up = 1;
        }
        else if (grid[i][j] == 6) {
            up = right = 1;
        }
        if (up) {
            int new_i = i-1;
            int new_j = j;
            if (isValid(new_i, new_j, grid) && !visited[new_i][new_j] && (grid[new_i][new_j] == 2 || grid[new_i][new_j] == 3 || grid[new_i][new_j] == 4)) {
                visited[new_i][new_j] = true;
                if (dfs(new_i, new_j, grid, visited)) {
                    return true;
                }
            }
        }
        if (down) {
            int new_i = i+1;
            int new_j = j;
            if (isValid(new_i, new_j, grid) && !visited[new_i][new_j] && (grid[new_i][new_j] == 2 || grid[new_i][new_j] == 5 || grid[new_i][new_j] == 6)) {
                visited[new_i][new_j] = true;
                if (dfs(new_i, new_j, grid, visited)) {
                    return true;
                }
            }
        }
        if (left) {
            int new_i = i;
            int new_j = j-1;
            if (isValid(new_i, new_j, grid) && !visited[new_i][new_j] && (grid[new_i][new_j] == 1 || grid[new_i][new_j] == 4 || grid[new_i][new_j] == 6)) {
                visited[new_i][new_j] = true;
                if (dfs(new_i, new_j, grid, visited)) {
                    return true;
                }
            }
        }
        if (right) {
            int new_i = i;
            int new_j = j+1;
            if (isValid(new_i, new_j, grid) && !visited[new_i][new_j] && (grid[new_i][new_j] == 5 || grid[new_i][new_j] == 3 || grid[new_i][new_j] == 1)) {
                visited[new_i][new_j] = true;
                if (dfs(new_i, new_j, grid, visited)) {
                    return true;
                }
            }
        }
        return false;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<bool>> visited(m, vector<bool>(n, false));
        return dfs(0, 0, grid, visited);
    }
};
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