<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, A):
        m, n = len(A), len(A[0])
        pos = [[m, n, 0, 0] for i in range(61)]
        colors = set()
        for i in range(m):
            for j in range(n):
                c = A[i][j]
                colors.add(c)
                pos[c][0] = min(pos[c][0], i)
                pos[c][1] = min(pos[c][1], j)
                pos[c][2] = max(pos[c][2], i)
                pos[c][3] = max(pos[c][3], j)

        def test(c):
            for i in range(pos[c][0], pos[c][2] + 1):
                for j in range(pos[c][1], pos[c][3] + 1):
                    if A[i][j] > 0 and A[i][j] != c:
                        return False
            for i in range(pos[c][0], pos[c][2] + 1):
                for j in range(pos[c][1], pos[c][3] + 1):
                    A[i][j] = 0
            return True

        while colors:
            colors2 = set()
            for c in colors:
                if not test(c):
                    colors2.add(c)
            if len(colors2) == len(colors):
                return False
            colors = colors2
        return True
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