<p>There is a strange printer with the following two special requirements:</p>

<ul>
	<li>On each turn, the printer will print a solid rectangular pattern of a single color on the grid. This will cover up the existing colors in the rectangle.</li>
	<li>Once the printer has used a color for the above operation, <strong>the same color cannot be used again</strong>.</li>
</ul>

<p>You are given a <code>m x n</code> matrix <code>targetGrid</code>, where <code>targetGrid[row][col]</code> is the color in the position <code>(row, col)</code> of the grid.</p>

<p>Return <code>true</code><em> if it is possible to print the matrix </em><code>targetGrid</code><em>,</em><em> otherwise, return </em><code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/print1.jpg" style="width: 600px; height: 175px;" />
<pre>
<strong>Input:</strong> targetGrid = [[1,1,1,1],[1,2,2,1],[1,2,2,1],[1,1,1,1]]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/print2.jpg" style="width: 600px; height: 367px;" />
<pre>
<strong>Input:</strong> targetGrid = [[1,1,1,1],[1,1,3,3],[1,1,3,4],[5,5,1,4]]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> targetGrid = [[1,2,1],[2,1,2],[1,2,1]]
<strong>Output:</strong> false
<strong>Explanation:</strong> It is impossible to form targetGrid because it is not allowed to print the same color in different turns.
</pre>

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

<ul>
	<li><code>m == targetGrid.length</code></li>
	<li><code>n == targetGrid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 60</code></li>
	<li><code>1 &lt;= targetGrid[row][col] &lt;= 60</code></li>
</ul>

class Solution:

    def isPrintable(self, grid: List[List[int]]) -> bool:      
        # You search limits of each color's rectangle  
        rectangle = {}
        for i, row in enumerate(grid):
            for j, color in enumerate(row):
                curr = rectangle.get(color, None)
                if not curr:
                    rectangle[color] = [i, i + 1, j, j + 1]
                else:
                    if i < curr[0]:
                        curr[0] = i
                    elif i >= curr[1]:
                        curr[1] = i + 1
                    if j < curr[2]:
                        curr[2] = j
                    elif j >= curr[3]:
                        curr[3] = j + 1
                    rectangle[color] = curr
        
        # You construct the dependecies graph
        to_do_after = {}
        for c1 in rectangle.keys():
            x, X, y, Y = rectangle[c1]
            to_do_after[c1] = set()
            for row in grid[x: X]:
                for c2 in row[y: Y]:
                    if c2 != c1:                        
                        if c1 in to_do_after.get(c2, []):
                            return False
                        to_do_after[c1].add(c2)
        
        # You check if there is no cycle in the dependencies graph

        def cycle(node):
            status[node] = IN_PROGRESS
            for nn in to_do_after[node]:
                if status[nn] is IN_PROGRESS:
                    return True
                elif status[nn] is NOT_VISITED:
                    if cycle(nn):
                        return True
            status[node] = VISITED
            return False
        
        NOT_VISITED, IN_PROGRESS, VISITED = 1, 2, 3
        status = {c: NOT_VISITED for c in to_do_after.keys()}
        for c in to_do_after.keys():
            if status[c] == NOT_VISITED and cycle(c):
                return False
        return True
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