<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:
    void helper(int r, int c, int n, int m, vector<vector<int>>& grid,
                vector<vector<bool>>& visted) {
        visted[r][c] = true;
        if (r == n - 1 && c == m - 1) {
            return;
        }
        int left = 0, right = 0, up = 0, down = 0;
        if (grid[r][c] == 1) {
            left = 1;
            right = 1;
        } else if (grid[r][c] == 2) {
            up = 1;
            down = 1;
        } else if (grid[r][c] == 3) {
            left = 1;
            down = 1;
        } else if (grid[r][c] == 4) {
            right = 1;
            down = 1;
        } else if (grid[r][c] == 5) {
            left = 1;
            up = 1;
        } else if (grid[r][c] == 6) {
            right = 1;
            up = 1;
        }
        int nr, nc;
        if (up) {
            nr = r - 1;
            nc = c;
            if (nr >= 0 && nr < n && nc >= 0 && nc < m &&
                (grid[nr][nc] == 2 || grid[nr][nc] == 3 || grid[nr][nc] == 4) &&
                !visted[nr][nc]) {
                helper(nr, nc, n, m, grid, visted);
            }
        }
        if (down) {
            nr = r + 1;
            nc = c;
            if (nr >= 0 && nr < n && nc >= 0 && nc < m &&
                (grid[nr][nc] == 2 || grid[nr][nc] == 5 || grid[nr][nc] == 6) &&
                !visted[nr][nc]) {
                helper(nr, nc, n, m, grid, visted);
            }
        }
        if (left) {
            nr = r;
            nc = c - 1;
            if (nr >= 0 && nr < n && nc >= 0 && nc < m &&
                (grid[nr][nc] == 1 || grid[nr][nc] == 4 || grid[nr][nc] == 6) &&
                !visted[nr][nc]) {
                helper(nr, nc, n, m, grid, visted);
            }
        }
        if (right) {
            nr = r;
            nc = c + 1;
            if (nr >= 0 && nr < n && nc >= 0 && nc < m &&
                (grid[nr][nc] == 1 || grid[nr][nc] == 3 || grid[nr][nc] == 5) &&
                !visted[nr][nc]) {
                helper(nr, nc, n, m, grid, visted);
            }
        }
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        vector<vector<bool>> visited(n, vector<bool>(m,false));
        helper(0, 0, n, m, grid, visited);

        return visited[n - 1][m - 1];
    }
};
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