<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)
        size = n * n * 4
        parent = [i for i in range(size)]

        def find(x):
            if parent[x] != x:
                parent[x] = find(parent[x])
            
            return parent[x]
        
        def union(x, y):
            nonlocal size
            p_x, p_y = find(x), find(y)

            if p_x != p_y:
                parent[p_x] = p_y
                size -= 1
        
        for r in range(n):
            for c in range(n):
                v = grid[r][c]

                order = 4 * (r * n + c)
                # inside order
                # \     0   /
                # 1\       /2
                #  /       \
                # /   3     \
                # order + 2 is always connected with right triangle (order + 4 (next) + 1)
                # order + 3 is always connected with below triangle (order + 4 * n (below))
                if r < n - 1:
                    union(order + 3, order + 4 * n)
                
                if c < n - 1:
                    union(order + 2, order + 4 + 1)
                
                if v == '/':
                    union(order, order + 1)
                    union(order + 2, order + 3)
                
                elif v == '\\':
                    union(order, order + 2)
                    union(order + 1, order + 3)
                
                else:
                    union(order, order + 1)
                    union(order + 1, order + 2)
                    union(order + 2, order + 3)
        return size
18973