<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: List[List[int]]) -> bool:
        from collections import deque, defaultdict

        m, n = len(targetGrid), len(targetGrid[0])

        def get_bounds(color):
            top, left, bottom, right = m, n, 0, 0
            for i in range(m):
                for j in range(n):
                    if targetGrid[i][j] == color:
                        top, left = min(top, i), min(left, j)
                        bottom, right = max(bottom, i), max(right, j)
            return top, left, bottom, right

        def can_paint_color(color, top, left, bottom, right):
            for i in range(top, bottom + 1):
                for j in range(left, right + 1):
                    if targetGrid[i][j] != 0 and targetGrid[i][j] != color:
                        return False
            return True

        color_bounds = defaultdict(tuple)
        for i in range(m):
            for j in range(n):
                color = targetGrid[i][j]
                if color != 0 and color not in color_bounds:
                    color_bounds[color] = get_bounds(color)

        dependency_graph = defaultdict(set)
        indegree = defaultdict(int)
        for color, (top, left, bottom, right) in color_bounds.items():
            for i in range(top, bottom + 1):
                for j in range(left, right + 1):
                    if targetGrid[i][j] != color:
                        dependency_graph[targetGrid[i][j]].add(color)

        for color in color_bounds:
            indegree[color] = 0

        for color in dependency_graph:
            for dependent in dependency_graph[color]:
                indegree[dependent] += 1

        zero_indegree = deque([color for color in indegree if indegree[color] == 0])
        painted_count = 0
        while zero_indegree:
            current_color = zero_indegree.popleft()
            top, left, bottom, right = color_bounds[current_color]
            if can_paint_color(current_color, top, left, bottom, right):
                painted_count += 1
                for i in range(top, bottom + 1):
                    for j in range(left, right + 1):
                        targetGrid[i][j] = 0
                for neighbor in dependency_graph[current_color]:
                    indegree[neighbor] -= 1
                    if indegree[neighbor] == 0:
                        zero_indegree.append(neighbor)

        return painted_count == len(color_bounds)
17000