<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:
        m, n = len(targetGrid), len(targetGrid[0])
        
        # Step 1: Identify the bounding box for each color
        color_bounds = {}
        for color in range(1, 61):
            color_bounds[color] = [m, n, 0, 0]  # min_row, min_col, max_row, max_col
        
        for i in range(m):
            for j in range(n):
                color = targetGrid[i][j]
                min_row, min_col, max_row, max_col = color_bounds[color]
                color_bounds[color] = [
                    min(min_row, i), min(min_col, j),
                    max(max_row, i), max(max_col, j)
                ]
        
        # Step 2: Check if the bounding box can be printed
        def can_print(color):
            min_row, min_col, max_row, max_col = color_bounds[color]
            for i in range(min_row, max_row + 1):
                for j in range(min_col, max_col + 1):
                    if targetGrid[i][j] > 0 and targetGrid[i][j] != color:
                        return False
            return True
        
        # Step 3: Topological sorting
        graph = [[] for _ in range(61)]
        indegree = [0] * 61
        
        for color in range(1, 61):
            if color in color_bounds:
                min_row, min_col, max_row, max_col = color_bounds[color]
                for i in range(min_row, max_row + 1):
                    for j in range(min_col, max_col + 1):
                        if targetGrid[i][j] != color:
                            graph[targetGrid[i][j]].append(color)
                            indegree[color] += 1
        
        queue = []
        for color in range(1, 61):
            if indegree[color] == 0 and color in color_bounds:
                queue.append(color)
        
        while queue:
            color = queue.pop(0)
            for next_color in graph[color]:
                indegree[next_color] -= 1
                if indegree[next_color] == 0:
                    queue.append(next_color)
        
        for color in range(1, 61):
            if indegree[color] > 0:
                return False
        
        return True

# Example usage:
solution = Solution()
targetGrid = [[1,1,1,1],[1,2,2,1],[1,2,2,1],[1,1,1,1]]
print(solution.isPrintable(targetGrid))  # Output: True

targetGrid = [[1,1,1,1],[1,1,3,3],[1,1,3,4],[5,5,1,4]]
print(solution.isPrintable(targetGrid))  # Output: True

targetGrid = [[1,2,1],[2,1,2],[1,2,1]]
print(solution.isPrintable(targetGrid))  # Output: False
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