<p>An <code>n x n</code> grid is composed of <code>1 x 1</code> squares where each <code>1 x 1</code> square consists of a <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or blank space <code>&#39; &#39;</code>. These characters divide the square into contiguous regions.</p>

<p>Given the grid <code>grid</code> represented as a string array, return <em>the number of regions</em>.</p>

<p>Note that backslash characters are escaped, so a <code>&#39;\&#39;</code> is represented as <code>&#39;\\&#39;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/1.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;/ &quot;]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/2.png" style="width: 200px; height: 198px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;  &quot;]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/4.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot;/\\&quot;,&quot;\\/&quot;]
<strong>Output:</strong> 5
<strong>Explanation: </strong>Recall that because \ characters are escaped, &quot;\\/&quot; refers to \/, and &quot;/\\&quot; refers to /\.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or <code>&#39; &#39;</code>.</li>
</ul>

class Solution:
    def regionsBySlashes(self, grid: List[str]) -> int:
        N = len(grid)
        count = 0
        unionset = {}
        for i in range(N):
            for j in range(N):
                for k in range(4):
                    unionset[(i,j,k)] = (i,j,k) 
                    count += 1
        
        def root(x):
            if unionset[x] != x:
                unionset[x] = root(unionset[x])
            return unionset[x]

        def union(x,y):
            if root(x) != root(y):
                unionset[root(x)] = root(y)
                nonlocal count
                count -= 1 

        for i in range(0,N):
            for j in range(0,N):
                if j != 0:
                    union((i,j-1,2), (i,j,1))
                if i != 0:
                    union((i-1,j,3), (i,j,0))
                if grid[i][j] == " ":
                    union((i,j,0), (i,j,1))
                    union((i,j,1), (i,j,2))
                    union((i,j,2), (i,j,3))
                    continue
                if grid[i][j]  == "\\":
                    union((i,j,0), (i,j,2))
                    union((i,j,1), (i,j,3))
                    continue
                if grid[i][j]  == "/":
                    union((i,j,0), (i,j,1))
                    union((i,j,3), (i,j,2))
                    continue
        return count
            


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