<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:
    class Node{
    public:
        const int ID;
        int iTop;
        int iBot;
        int jL;
        int jR;
        Node(int i,int j,int id):ID(id){
            iTop = i;
            iBot = i;
            jL = j;
            jR = j;
        }
        void record(int i,int j){
            iTop = min(iTop,i);
            iBot = max(iBot,i);
            jL = min(jL,j);
            jR = max(jR,j);
            posList.push_back({i,j});
        }
        vector<pair<int,int>> posList;
        bool contains(int i,int j) {
            return (i >= iTop && i <= iBot && j >= jL && j <= jR);
        }
        bool contains(const Node* a){
            for(const auto& pair:a->posList){
                if(contains(pair.first,pair.second)){
                    return true;
                }
            }
            return false;
        }

    };

    bool isPrintable(vector<vector<int>>& g) {
        map<int,Node*> m;
        int row = g.size();
        int col = g[0].size();
        for(int i = 0;i < row; ++i){
            for(int j = 0;j < col; ++j){
                int node = g[i][j];
                if(m.count(node) == 0){
                    m[node] = new Node(i,j,node);
                }
                else{
                    m[node]->record(i,j);
                }

            }
        }

        map<int,set<int>> fromToMap;
        map<int,int> visCntMap;
        for(auto& a:m){
            for(auto& b:m){
                if(a.first == b.first)
                    continue;

                if(a.second->contains(b.second)){
                    fromToMap[a.first].insert(b.first);
                    visCntMap[b.first]++;
                }
                else if(b.second->contains(a.second)){
                    fromToMap[b.first].insert(a.first);
                    visCntMap[a.first]++;
                }
            }
        } 
        for(auto& item:m){
            int node = item.first;
            set<int> vis;
            queue<int> q;
            q.push(node);
            vis.insert(node);
            while(q.size() > 0){
                int cur = q.front();
                q.pop();
                for(auto next:fromToMap[cur]){
                    if(next == node){
                        return false;
                    }
                    if(vis.count(next)){
                        continue;
                    }
                    vis.insert(next);
                    q.push(next);
                }
            }
        }
        return true;
    }
};
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