<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>

using p = pair<int,int>;
class Solution {
public:
    map<p,p> mp;
    p find(p x){
        return mp[x] == x ? x : mp[x] = find(mp[x]);
    }

    void unions(p a, p b){
        a = find(a);
        b = find(b);
        if(a!=b)
            mp[b] = a;
    }
    bool check(int pre, int cur, int c){
        if(c == 1){
            if(pre == 2 && (cur == 2 || cur == 5 || cur == 6)) return true;
            if(pre == 3 && (cur == 2 || cur == 5 || cur == 6)) return true;
            if(pre == 4 && (cur == 2 || cur == 5 || cur == 6)) return true;
        }else{
            if(pre == 1 && (cur == 3 || cur == 5 || cur == 1)) return true;
            if(pre == 4 && (cur == 3 || cur == 5 || cur == 1)) return true;
            if(pre == 6 && (cur == 3 || cur == 5 || cur == 1)) return true;
        }
        return false;
    }
    bool hasValidPath(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        for(int i = 0 ; i < m ; ++i)
            for(int j = 0 ; j < n ; ++j)
                mp[{i,j}] = {i,j};
        for(int i = 0 ; i < m ; ++i){
            for(int j = 0 ; j < n ; ++j){
                if(i == 0 && j == 0 ) continue;
                if(i && check(grid[i-1][j],grid[i][j],1))
                    unions({i-1,j},{i,j});
                if(j && check(grid[i][j-1],grid[i][j],0))
                    unions({i,j-1},{i,j});
            }
        }
        return find({0,0}) == find({m-1,n-1});
    }
};
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