<p>There are&nbsp;<code>n</code>&nbsp;items each&nbsp;belonging to zero or one of&nbsp;<code>m</code>&nbsp;groups where <code>group[i]</code>&nbsp;is the group that the <code>i</code>-th item belongs to and it&#39;s equal to <code>-1</code>&nbsp;if the <code>i</code>-th item belongs to no group. The items and the groups are zero indexed. A group can have no item belonging to it.</p>

<p>Return a sorted list of the items such that:</p>

<ul>
	<li>The items that belong to the same group are next to each other in the sorted list.</li>
	<li>There are some&nbsp;relations&nbsp;between these items where&nbsp;<code>beforeItems[i]</code>&nbsp;is a list containing all the items that should come before the&nbsp;<code>i</code>-th item in the sorted array (to the left of the&nbsp;<code>i</code>-th item).</li>
</ul>

<p>Return any solution if there is more than one solution and return an <strong>empty list</strong>&nbsp;if there is no solution.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/11/1359_ex1.png" style="width: 191px; height: 181px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 8, m = 2, group = [-1,-1,1,0,0,1,0,-1], beforeItems = [[],[6],[5],[6],[3,6],[],[],[]]
<strong>Output:</strong> [6,3,4,1,5,2,0,7]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 8, m = 2, group = [-1,-1,1,0,0,1,0,-1], beforeItems = [[],[6],[5],[6],[3],[],[4],[]]
<strong>Output:</strong> []
<strong>Explanation:</strong>&nbsp;This is the same as example 1 except that 4 needs to be before 6 in the sorted list.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>group.length == beforeItems.length == n</code></li>
	<li><code>-1 &lt;= group[i] &lt;= m - 1</code></li>
	<li><code>0 &lt;= beforeItems[i].length &lt;= n - 1</code></li>
	<li><code>0 &lt;= beforeItems[i][j] &lt;= n - 1</code></li>
	<li><code>i != beforeItems[i][j]</code></li>
	<li><code>beforeItems[i]&nbsp;</code>does not contain&nbsp;duplicates elements.</li>
</ul>

class Solution {
public:
    vector<int> sortItems(int n, int m, vector<int>& group, vector<vector<int>>& beforeItems) {
        // treat no group as unique groups
        // run two topological sorts
        int mx = 0;
        for (int i = 0; i < group.size(); i++) {
            mx = max(mx, group[i]);
        }

        mx++;
        map<int, vector<int>> groups;
        for (int i = 0; i < group.size(); i++) {
            if (group[i] == -1) group[i] = mx++;
            // cout << "Group: " << group[i] << " " << i << endl;
            groups[group[i]].push_back(i);
        }

        vector<int> gdeg(mx);
        vector<int> ideg(n);
        vector<vector<int>> adj(n + 1);
        vector<unordered_set<int>> gadj(mx + 1);

        for (int i = 0; i < beforeItems.size(); i++) {
            for (int j = 0; j < beforeItems[i].size(); j++) {
                adj[beforeItems[i][j]].push_back(i);                
                ideg[i]++;
                if (group[beforeItems[i][j]] != group[i]){
                    gadj[group[beforeItems[i][j]]].insert(group[i]);
                    // gdeg[group[i]]++;
                }
            }
        }

        for (int i = 0; i < gadj.size(); i++) {
            for (auto x : gadj[i]) {
                gdeg[x]++;
            }
        }

        vector<int> ans;

        queue<int> topo;
        for (int i = 0; i < gdeg.size(); i++) {
            if (gdeg[i] == 0) {
                topo.push(i);
            }
        }

        while (topo.size()) {
            int cur = topo.front();
            topo.pop();

            // run the second topo sort
            queue<int> inner;
            vector<int> cur_group = groups[cur];
            // cout << "Group: ";
            // for (auto x : cur_group) cout << x << " ";
            // cout << endl;
            for (int i = 0; i < cur_group.size(); i++) {
                if (ideg[cur_group[i]] == 0) {
                    inner.push(cur_group[i]);
                }
            }

            while (inner.size()) {
                int ind = inner.front();
                inner.pop();

                ans.push_back(ind);
                // cout << cur << " " << ind << endl;

                for (auto x : adj[ind]) {
                    ideg[x]--;
                    if (ideg[x] == 0 && group[x] == cur) {
                        inner.push(x);
                    }
                }
            }

            // cout << "Next deps: ";
            for (auto x : gadj[cur]) {
                // cout << x << " ";
                gdeg[x]--;
                if (gdeg[x] == 0) {
                    topo.push(x);
                }
            }
            // cout << endl;
            // for (auto x : gdeg) {
            //     cout << x << " ";
            // }
            // cout << endl;
        }
        // for (auto x : ans) cout << x << " ";
        if (ans.size() != group.size()) return {};

        return ans;
    }
};
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