<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 {
    int n, m;
    bool vis[305][305];
    vector<vector<int>> g;

public:
    bool hasValidPath(vector<vector<int>>& grid) {
        n = grid.size();
        m = grid[0].size();
        g = grid;
        memset(vis, false, sizeof(vis));
        dfs(0, 0);
        return vis[n - 1][m - 1];
    }

    void dfs(int ux, int uy) {
        vis[ux][uy] = true;
        int vx, vy;

        if (g[ux][uy] == 1 || g[ux][uy] == 4 || g[ux][uy] == 6) {
            vx = ux, vy = uy + 1;
            if (valid(vx, vy) && L_enter(vx, vy))
                dfs(vx, vy);
        }
        if (g[ux][uy] == 1 || g[ux][uy] == 3 || g[ux][uy] == 5) {
            vx = ux, vy = uy - 1;
            if (valid(vx, vy) && R_enter(vx, vy))
                dfs(vx, vy);
        }
        if (g[ux][uy] == 2 || g[ux][uy] == 3 || g[ux][uy] == 4) {
            vx = ux + 1, vy = uy;
            if (valid(vx, vy) && D_enter(vx, vy))
                dfs(vx, vy);
        }
        if (g[ux][uy] == 2 || g[ux][uy] == 5 || g[ux][uy] == 6) {
            vx = ux - 1, vy = uy;
            if (valid(vx, vy) && U_enter(vx, vy))
                dfs(vx, vy);
        }
    }
    bool valid(int x, int y) {
        if (x >= 0 && y >= 0 && x < n && y < m && !vis[x][y])
            return true;
        return false;
    }
    bool L_enter(int x, int y) {
        if (g[x][y] % 2)
            return true;
        return false;
    }
    bool R_enter(int x, int y) {
        if (g[x][y] == 1 || g[x][y] == 4 || g[x][y] == 6)
            return true;
        return false;
    }
    bool D_enter(int x, int y) {
        if (g[x][y] == 2 || g[x][y] == 5 || g[x][y] == 6)
            return true;
        return false;
    }
    bool U_enter(int x, int y) {
        if (g[x][y] == 2 || g[x][y] == 3 || g[x][y] == 4)
            return true;
        return false;
    }
};
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