<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:
        def getLines(i, j):
            return ((i, j), (i + 1, j)), ((i, j), (i, j + 1)), \
                ((i + 1, j), (i + 1, j + 1)), ((i, j + 1), (i + 1, j + 1))

        n = len(grid)
        parents = {}
        for i in range(n):
            for j in range(n):
                lines = getLines(i, j)
                for p in lines:
                    parents[p] = p

        def find(l):
            if parents[l] != l:
                parents[l] = find(parents[l])
            return parents[l]

        def union(l1, l2):
            p1 = find(l1)
            p2 = find(l2)
            parents[p1] = p2

        for i in range(n):
            for j in range(n):
                lines = getLines(i, j)
                if grid[i][j] == " ":
                    union(lines[0], lines[1])
                    union(lines[0], lines[2])
                    union(lines[0], lines[3])
                elif grid[i][j] == "/":
                    union(lines[0], lines[1])
                    union(lines[2], lines[3])
                else:
                    union(lines[0], lines[2])
                    union(lines[1], lines[3])
        
        res = set()
        for i in range(n):
            for j in range(n):
                lines = getLines(i, j)
                res.add(find(lines[0]))
                res.add(find(lines[1]))
                res.add(find(lines[2]))
                res.add(find(lines[3]))

        return len(res)
        
23323