<p>Given an array&nbsp;of <code>intervals</code>&nbsp;where <code>intervals[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>, merge all overlapping intervals, and return <em>an array of the non-overlapping intervals that cover all the intervals in the input</em>.</p>

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

<pre>
<strong>Input:</strong> intervals = [[1,3],[2,6],[8,10],[15,18]]
<strong>Output:</strong> [[1,6],[8,10],[15,18]]
<strong>Explanation:</strong> Since intervals [1,3] and [2,6] overlap, merge them into [1,6].
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[1,4],[4,5]]
<strong>Output:</strong> [[1,5]]
<strong>Explanation:</strong> Intervals [1,4] and [4,5] are considered overlapping.
</pre>

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

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 10<sup>4</sup></code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>0 &lt;= start<sub>i</sub> &lt;= end<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    vector<vector<int>> merge(vector<vector<int>>& intervals) {
        vector<pair<int, bool>> points; //bool is whether it's a start
        for(auto x: intervals){
            points.push_back({x[0], true});
            points.push_back({x[1], false});
        }
        std::sort(points.begin(), points.end(), [](auto& left, auto& right){
            return left.first<right.first ||(left.first == right.first&&left.second&&!right.second);
        });        
        vector<vector<int>> answer;
        int curr_on = 0;
        int interval_begin = 0;
        for(auto point: points){
            if(point.second){
                if(curr_on ==0){
                    interval_begin = point.first;
                }
                curr_on ++;
            }
            else{
                if(curr_on == 1){
                    answer.push_back({interval_begin, point.first});
                }
                curr_on--;
            }
        }
        return answer;
    }
};
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