<p>You are given a 2D integer array <code>intervals</code> where <code>intervals[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> represents all the integers from <code>start<sub>i</sub></code> to <code>end<sub>i</sub></code> inclusively.</p>

<p>A <strong>containing set</strong> is an array <code>nums</code> where each interval from <code>intervals</code> has <strong>at least two</strong> integers in <code>nums</code>.</p>

<ul>
	<li>For example, if <code>intervals = [[1,3], [3,7], [8,9]]</code>, then <code>[1,2,4,7,8,9]</code> and <code>[2,3,4,8,9]</code> are <strong>containing sets</strong>.</li>
</ul>

<p>Return <em>the minimum possible size of a containing set</em>.</p>

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

<pre>
<strong>Input:</strong> intervals = [[1,3],[3,7],[8,9]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> let nums = [2, 3, 4, 8, 9].
It can be shown that there cannot be any containing array of size 4.
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[1,3],[1,4],[2,5],[3,5]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> let nums = [2, 3, 4].
It can be shown that there cannot be any containing array of size 2.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> intervals = [[1,2],[2,3],[2,4],[4,5]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> let nums = [1, 2, 3, 4, 5].
It can be shown that there cannot be any containing array of size 4.
</pre>

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

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 3000</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>8</sup></code></li>
</ul>

class Solution {
public:
    int intersectionSizeTwo(vector<vector<int>>& intervals) {
        sort(intervals.begin(),intervals.end());
        vector<vector<int>> v;
        int n=intervals.size();
        stack<vector<int>> st;
        for(int i=0;i<n;i++){
            while(!st.empty()&&st.top()[1]>=intervals[i][1]){
                st.pop();
            }
            st.push(intervals[i]);
        }
        while(!st.empty()){
            v.push_back(st.top());
            st.pop();
        }
        reverse(v.begin(),v.end());
        unordered_map<int,int> mp;
        for(int i=0;i<v.size();i++){
            int cnt=0;
            for(auto it=mp.begin();it!=mp.end();it++){
                if(it->first>=v[i][0]&&it->first<=v[i][1]){
                    cnt++;
                }
            }
            if(cnt==0){
                mp[v[i][1]-1]=1;
                mp[v[i][1]]=1;
            }
            else if(cnt==1){
                mp[v[i][1]]=1;
            }
        }
        return mp.size();
    }
};
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