<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>

struct pair_hash {
    inline std::size_t operator()(const std::pair<int,int> & v) const {
        return v.first*31 + v.second;
    }
};

class Solution {
public:
    void dfs(vector<vector<int>> &grid, unordered_set<pair<int, int>, pair_hash> &visited, int curRow, int curCol, bool &possible) {
        if (possible) return;
        if (visited.find(make_pair(curRow, curCol)) != visited.end()) return;
        visited.insert(make_pair(curRow, curCol));
        int numRows = grid.size(), numCols = grid[0].size();
        if (curRow == numRows - 1 && curCol == numCols - 1) possible = true;
        if (curRow < 0 || curCol < 0 || curRow >= numRows || curCol >= numCols) return;
        int curStreet = grid[curRow][curCol];
        int nextRow, nextCol, nextStreet;
        if (curStreet == 1) {
            nextRow = curRow; nextCol = curCol - 1;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 1 || nextStreet == 4 || nextStreet == 6) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
            nextRow = curRow; nextCol = curCol + 1;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 1 || nextStreet == 3 || nextStreet == 5) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
        } else if (curStreet == 2) {
            nextRow = curRow - 1; nextCol = curCol;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 2 || nextStreet == 3 || nextStreet == 4) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
            nextRow = curRow + 1; nextCol = curCol;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 2 || nextStreet == 5 || nextStreet == 6) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
        } else if (curStreet == 3) {
            nextRow = curRow; nextCol = curCol - 1;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 1 || nextStreet == 4 || nextStreet == 6) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
            nextRow = curRow + 1; nextCol = curCol;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 2 || nextStreet == 5 || nextStreet == 6) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
        } else if (curStreet == 4) {
            nextRow = curRow; nextCol = curCol + 1;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 1 || nextStreet == 3 || nextStreet == 5) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
            nextRow = curRow + 1; nextCol = curCol;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 2 || nextStreet == 5 || nextStreet == 6) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
        } else if (curStreet == 5) {
            nextRow = curRow - 1; nextCol = curCol;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 2 || nextStreet == 3 || nextStreet == 4) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
            nextRow = curRow; nextCol = curCol - 1;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 1 || nextStreet == 4 || nextStreet == 6) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
        } else if (curStreet == 6) {
            nextRow = curRow - 1; nextCol = curCol;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 2 || nextStreet == 3 || nextStreet == 4) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
            nextRow = curRow; nextCol = curCol + 1;
            if (nextRow >= 0 && nextCol >= 0 && nextRow < numRows && nextCol < numCols) {
                nextStreet = grid[nextRow][nextCol];
                if (nextStreet == 1 || nextStreet == 3 || nextStreet == 5) {
                    dfs(grid, visited, nextRow, nextCol, possible);
                }
            }
        }
    }

    bool hasValidPath(vector<vector<int>>& grid) {
        bool possible = false;
        unordered_set<pair<int, int>, pair_hash> visited;
        dfs(grid, visited, 0, 0, possible);
        return possible;
    }
};
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