<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:
        nodes = set()
        graph = defaultdict(set)
        m, n = len(targetGrid), len(targetGrid[0])
        indegrees = defaultdict(int)
        for c in range(1, 61):
            l,r,t,b = n,-1,m,-1
			#to specify the covered range of color c
            for i in range(m):
                for j in range(n):
                    if targetGrid[i][j] == c:
                        nodes.add(c)
                        l = min(l, j)
                        r = max(r, j)
                        t = min(t, i)
                        b = max(b, i)
			#to find the contained colors
            for i in range(t, b + 1):
                for j in range(l, r + 1):
                    if targetGrid[i][j] != c:
                        graph[targetGrid[i][j]].add(c)

        q = deque()

        for u in graph:
            for v in graph[u]:
                indegrees[v] += 1

        for c in nodes:
            if indegrees[c] == 0:
                q.append(c)
        
        
        tsort = []
        while q:
            node = q.popleft()
            tsort.append(node)
            for v in graph[node]:
                indegrees[v] -= 1
                if indegrees[v] == 0:
                    q.append(v)
        return len(tsort) == len(nodes)
            
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