<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, targetGrid):
        from collections import defaultdict

        colorRect = {}
        n = len(targetGrid)
        m = len(targetGrid[0])

        for i in range(n):
            for j in range(m):
                color = targetGrid[i][j]
                if color not in colorRect:
                    colorRect[color] = [i, j, i, j]
                else:
                    rect = colorRect[color]
                    rect[0] = min(rect[0], i)
                    rect[1] = min(rect[1], j)
                    rect[2] = max(rect[2], i)
                    rect[3] = max(rect[3], j)

        graph = defaultdict(set)
        for color in colorRect:
            for i in range(colorRect[color][0], colorRect[color][2] + 1):
                for j in range(colorRect[color][1], colorRect[color][3] + 1):
                    if targetGrid[i][j] != color:
                        graph[color].add(targetGrid[i][j])

        colorState = {}
        
        def hasCycle(v):
            if colorState.get(v, 0) == 1:
                return True
            if colorState.get(v, 0) == 2:
                return False
            colorState[v] = 1
            if v in graph:
                for u in graph[v]:
                    if hasCycle(u):
                        return True
            colorState[v] = 2
            return False

        for color in colorRect:
            if hasCycle(color):
                return False

        return True

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