<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:
    struct rectangle{
        int x1,y1;
        int x2,y2;
        int val;
    };
    unordered_map<int,rectangle>findAllRectangles(vector<vector<int>>& targetGrid){
        unordered_map<int,int>minX,minY,maxX,maxY;
        unordered_map<int,rectangle>rect;
        for(int i=0;i<(int)targetGrid.size();i++)
            for(int j=0;j<(int)targetGrid[i].size();j++){
                int val = targetGrid[i][j];
                if(!minX.count(val))minX[val] = INT_MAX;
                if(!minY.count(val))minY[val] = INT_MAX;
                if(!maxX.count(val))maxX[val] = INT_MIN;
                if(!maxY.count(val))maxY[val] = INT_MIN;
                minX[val] = min(minX[val],j);
                maxX[val] = max(maxX[val],j);
                minY[val] = min(minY[val],i);
                maxY[val] = max(maxY[val],i);
            }
        for(auto &[val,mn]:minX){
            rectangle rec = {minX[val],minY[val],maxX[val],maxY[val],val};
            rect[val] = rec;
        }
        return rect;
    }
    bool isPrintable(vector<vector<int>>& targetGrid) {
        // each color uniquely identifies a rectangle
        unordered_map<int,rectangle>grids = findAllRectangles(targetGrid);
        unordered_map<int,vector<int>>graph;
        unordered_map<int,int>inDegreeOfColor;
        for(auto &[color,rect]:grids){
            graph[color]={};
            inDegreeOfColor[color]={};
        }
        for(auto &[color,rect]:grids){
            for (int i = rect.y1; i <=rect.y2; ++i) {
                for (int j = rect.x1; j <=rect.x2 ; ++j) {
                    if(targetGrid[i][j]==color)continue;
                    graph[color].push_back(targetGrid[i][j]);
                    inDegreeOfColor[targetGrid[i][j]]++;
                }
            }
        }
        // topologicalSort
        queue<int>color;
        for(auto &i:inDegreeOfColor)if(i.second==0)color.push(i.first);
        vector<int>colorsOrder;
        while(!color.empty()){
            int c = color.front();color.pop();
            colorsOrder.push_back(c);
            for(auto &to:graph[c]){
                inDegreeOfColor[to]--;
                if(inDegreeOfColor[to]==0)color.push(to);
            }
        }
        return colorsOrder.size() == grids.size();

    }
};
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