<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 {
    private: 
    bool static compare(pair<int,int>&a, pair<int,int>&b)
    {
        if(a.first!=b.first)
        return (a.first<b.first);

        return (a.second>b.second);
    }
public:
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        int n=envelopes.size();
        vector<pair<int,int>> vec;
        for(int i=0;i<n;i++)
        {
            vec.push_back({envelopes[i][0],envelopes[i][1]});
        }
        sort(vec.begin(),vec.end(),compare);

        vector<int> dp(n,1);
        vector<int> nums;

        for(int i=0;i<n;i++)
        {
            nums.push_back(vec[i].second);
        }

        vector<int>temp;
        temp.push_back(nums[0]);
        int len=1;
       // your code here
       for(int i=1;i<n;i++)
       {
           if(nums[i]>temp.back())
           {
           temp.push_back(nums[i]);
           len++;
           }
           else
           {
               int ind=lower_bound(temp.begin(),temp.end(),nums[i])-temp.begin();
               //got the index of the number which is just greater than a[i]
               temp[ind]=nums[i];
           }
       }
       return len;
    }
};
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