<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 {
public:
    bool isPrintable(vector<vector<int>>& targetGrid) {
        unordered_map<int, vector<int>> pos;  // map to store min/max coordinates for each color
        int n = targetGrid.size();
        int m = targetGrid[0].size();
        
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                int color = targetGrid[i][j];
                if (pos.find(color) == pos.end()) {
                    pos[color] = {n, m, -1, -1};  // Initialize with extreme values
                }
                pos[color][0] = min(pos[color][0], i);  // min row
                pos[color][1] = min(pos[color][1], j);  // min column
                pos[color][2] = max(pos[color][2], i);  // max row
                pos[color][3] = max(pos[color][3], j);  // max column
            }
        }
        
        unordered_set<int> colors;
        for (auto& p : pos) {
            colors.insert(p.first);
        }
        
        while (!colors.empty()) {
            unordered_set<int> next;
            for (int color : colors) {
                if (!erase(targetGrid, pos[color], color)) {
                    next.insert(color);
                }
            }
            if (colors.size() == next.size()) {
                return false;
            }
            colors = next;
        }
        
        return true;
    }

private:
    bool erase(vector<vector<int>>& targetGrid, vector<int>& coord, int color) {
        for (int i = coord[0]; i <= coord[2]; i++) {
            for (int j = coord[1]; j <= coord[3]; j++) {
                if (targetGrid[i][j] > 0 && targetGrid[i][j] != color) {
                    return false;
                }
            }
        }
        for (int i = coord[0]; i <= coord[2]; i++) {
            for (int j = coord[1]; j <= coord[3]; j++) {
                targetGrid[i][j] = 0;
            }
        }
        return true;
    }
};

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