<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 dfs(vector<vector<int>>& targetGrid, vector<vector<int>>& bounds, int curColor, vector<bool> &visited, vector<bool>& processed)
    {
        if(processed[curColor] == true)
            return true;
        if(visited[curColor] == true)
            return false;
        visited[curColor] = true;
        for(int i = bounds[curColor][0]; i <= bounds[curColor][1]; i++)
        {
            for(int j = bounds[curColor][2]; j <= bounds[curColor][3]; j++)
            {
                if(targetGrid[i][j] != curColor)
                {
                    if(dfs(targetGrid, bounds, targetGrid[i][j], visited, processed) == false)
                        return false;
                }
            }
        }
        processed[curColor] = true;
        visited[curColor] = false;
        return true;
    }
    bool isPrintable(vector<vector<int>>& targetGrid) {
        int n = targetGrid.size();
        int m = targetGrid[0].size();
        vector<vector<int>> bounds(61, vector<int>(4, -1));
        unordered_set <int> colorSet;
        vector<bool> visited(61, false);
        vector<bool> processed(61, false);
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < m; j++)
            {
                int color = targetGrid[i][j];
                colorSet.insert(color);
                if(bounds[color][0] == -1)
                {
                    bounds[color][0] = i;
                    bounds[color][1] = i;
                    bounds[color][2] = j;
                    bounds[color][3] = j;
                }
                else{
                    bounds[color][0] = min(bounds[color][0], i);
                    bounds[color][1] = max(bounds[color][1], i);
                    bounds[color][2] = min(bounds[color][2], j);
                    bounds[color][3] = max(bounds[color][3], j);
                }
            }
        }
        for(auto it = colorSet.begin(); it != colorSet.end(); it++)
        {
            if(dfs(targetGrid, bounds, *it, visited, processed) == false)
                return false;
        }
        return true;
    }
};
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