<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) {
        map<int, set<pair<int,int>>> all_colors;
        for(int i = 0; i < targetGrid.size(); ++i){
            for(int j = 0; j < targetGrid[0].size(); ++j){
                all_colors[targetGrid[i][j]].insert(make_pair(i, j));
            }
        }
        while(true){
            bool could_break = true;
            for(auto itr = all_colors.begin(); itr != all_colors.end(); ++itr){
                int left_x =  61, left_y = 61;
                int right_x = 0, right_y = 0;
                for(auto jtr = itr->second.begin(); jtr != itr->second.end(); ++jtr){
                    left_x = min(left_x, jtr->first);
                    left_y = min(left_y, jtr->second);
                    right_x = max(right_x, jtr->first);
                    right_y = max(right_y, jtr->second);
                }
                cout << itr->first << "color with " << left_x <<"," << left_y << "  " << right_x << "," << right_y << endl;
                // we check if it forms a square
                bool satisfy = true;
                for(int i = left_x; i <= right_x; ++i){
                    for(int j = left_y; j <= right_y; ++j){
                        if(targetGrid[i][j] != itr->first && targetGrid[i][j] != -1){
                            satisfy = false;
                        }
                    }
                }
                if(satisfy){
                    could_break = false;
                    for(int i = left_x; i <= right_x; ++i){
                        for(int j = left_y; j <= right_y; ++j){
                            targetGrid[i][j] = -1;
                        }
                    }
                    all_colors.erase(itr->first);
                    break;
                }
            }
            if(could_break){
                break;
            }
        }

        return all_colors.size() == 0;
    }
};
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