<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) {
        int m = targetGrid.size();
        int n = targetGrid[0].size();

        int maxColor = 0;
        std::unordered_map<int, std::tuple<int, int, int, int>> colors;
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                int color = targetGrid[i][j];
                maxColor = std::max(maxColor, color);
                if (colors.find(color) == colors.end()) {
                    colors[color] = {i, i, j, j};
                } else {
                    auto& [l, r, u, b] = colors[color];
                    l = std::min(l, i);
                    r = std::max(r, i);
                    u = std::min(u, j);
                    b = std::max(b, j);
                }
            }
        }

        int colorCap = maxColor + 1;
        std::vector<std::unordered_set<int>> adjs(colorCap);
        std::vector<int> indegree(colorCap);
        for (auto& [color, range] : colors) {
            auto [l, r, u, b] = range;
            for (int i = l; i <= r; ++i) {
                for (int j = u; j <= b; ++j) {
                    int target = targetGrid[i][j];
                    if (color != target) {
                        if (adjs[color].insert(target).second) {
                            ++indegree[target];
                        }
                    }
                }
            }
        }

        std::queue<int> q;
        for (int i = 0; i < colorCap; ++i) {
            if (indegree[i] == 0) {
                q.push(i);
            }
        }

        while (!q.empty()) {
            auto cur = q.front();
            q.pop();
            for (auto adj : adjs[cur]) {
                if (--indegree[adj] == 0) {
                    q.push(adj);
                }
            }
        }

        for (int i = 0; i < colorCap; ++i) {
            if (indegree[i] > 0) {
                return false;
            }
        }

        return true;
    }
};
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