<p>You are given a 2D array of integers <code>envelopes</code> where <code>envelopes[i] = [w<sub>i</sub>, h<sub>i</sub>]</code> represents the width and the height of an envelope.</p>

<p>One envelope can fit into another if and only if both the width and height of one envelope are greater than the other envelope&#39;s width and height.</p>

<p>Return <em>the maximum number of envelopes you can Russian doll (i.e., put one inside the other)</em>.</p>

<p><strong>Note:</strong> You cannot rotate an envelope.</p>

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

<pre>
<strong>Input:</strong> envelopes = [[5,4],[6,4],[6,7],[2,3]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The maximum number of envelopes you can Russian doll is <code>3</code> ([2,3] =&gt; [5,4] =&gt; [6,7]).
</pre>

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

<pre>
<strong>Input:</strong> envelopes = [[1,1],[1,1],[1,1]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= envelopes.length &lt;= 10<sup>5</sup></code></li>
	<li><code>envelopes[i].length == 2</code></li>
	<li><code>1 &lt;= w<sub>i</sub>, h<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    class comp{
        public:
        bool operator()(const vector<int> &v1,const vector<int> &v2){
            if(v1[0] != v2[0])return v1[0] < v2[0];
            else return v1[1] > v2[1];
        }
    };
    int b_search(vector<int> a,int num){
        int start = 0,end = a.size()-1;
        while(start <= end){
            int mid = (start+end)>>1;
            if(a[mid] == num)return mid;
            else if(a[mid] < num)start = mid+1;
            else end = mid-1;
        }
        return start;
    }
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        vector<int> a;
        comp c1;
        int n = envelopes.size();
        sort(envelopes.begin(),envelopes.end(),c1);
        for(int i = 0;i < n;i++){
            a.push_back(envelopes[i][1]);
        }
        vector<int> ans;
        for(int i = 0;i < n;i++){
           if(ans.empty() or ans.back() < a[i])ans.push_back(a[i]);
           else{
              ans[b_search(ans,a[i])] = a[i];
           }
       }
        return ans.size();
    }
};
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