<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 generateBlock(pattern):
            # 0: left, 1: right, 2: top, 3: bottom
            cons = [[True] * 4 for _ in range(4)]
            if pattern == '\\':
                cons = [[False] * 4 for _ in range(4)]
                cons[0][3] = True
                cons[3][0] = True
                cons[1][2] = True
                cons[2][1] = True
                return cons
            if pattern == '/' :
                cons = [[False] * 4 for _ in range(4)]
                cons[0][2] = True
                cons[2][0] = True
                cons[1][3] = True
                cons[3][1] = True
                return cons
            return cons
        
        n, m = len(grid), len(grid[0])
        graph = [[None] * m for _ in range(n)]
        for x, s in enumerate(grid):
            for y, c in enumerate(s):
                if x == 0 and y == 1: print(c, c == '/', generateBlock(c))
                graph[x][y] = generateBlock(c)
        
        colors = [[] for _ in range(n)]
        for x in range(n):
            for _ in range(m):
                colors[x].append([0] * 4)
        def isInside(x, y):
            return 0 <= x < n and 0 <= y < m
        
        def dfs(x, y, i, color):
            for j in range(4):
                if i != j and not graph[x][y][i][j]:
                    continue
                colors[x][y][j] = color
                if colors[x][y][j] == 0:
                    dfs(x, y, j, color)
            
            matchColor = [1, 0, 3, 2]
            for j, (dx, dy) in enumerate([(0, -1), (0, 1), (-1, 0), (1, 0)]):
                u, v = x + dx, y + dy
                if isInside(u, v) and (j == i or graph[x][y][i][j]) and colors[u][v][matchColor[j]] == 0:
                    dfs(u, v, matchColor[j], color)

        color = 1
        for x in range(n):
            for y in range(m):
                for i in range(4):
                    if colors[x][y][i] == 0:
                        dfs(x, y, i, color)
                        color += 1
        return color - 1
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