<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:
        M, N = len(grid), len(grid[0])
        mat = [[0 for _ in range(3*N)] for _ in range(3*M)] 

        # 3x magnify original grid
        for i in range(M):
            for j in range(N):
                if grid[i][j] == "/":
                    ptr = 3 * (j + 1) -1
                    for k in range(3):
                        mat[3*i + k][ptr - k] = "/"
                elif grid[i][j] == "\\":
                    for k in range(3):
                        mat[3*i + k][3*j + k] = "\\"
        
        visited = set()
        directions = [(-1, 0), (0, -1), (1, 0), (0, 1)]
        def dfs(i, j):
            if i < 0 or i >= len(mat) or j < 0 or j >= len(mat[0]): return
            if mat[i][j] != 0 or (i, j) in visited: return

            mat[i][j] = -1

            visited.add((i, j))
            for d in directions:
                dfs(i + d[0], j + d[1])
            visited.remove((i, j))
        
        for m in mat:
            print(m)

        output = 0
        for i in range(len(mat)):
            for j in range(len(mat[0])):
                if mat[i][j] == 0:
                    output += 1
                    dfs(i, j)

        return output








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