<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:
    static bool cmp(vector<int> &a,vector<int> &b){
        if(a[0]==b[0]){
            return a[1]>b[1];
        }
        return a[0]<b[0];
    }
    
    int solve_binary_search(vector<int> nums,int n){
    if(n==0){
        return 0;
    }

    vector<int> ans;
    ans.push_back(nums[0]);

    for(int i=1;i<n;i++){
        if(nums[i]>ans.back()){
            ans.push_back(nums[i]);
        }
        else{
            //find index of just bigger
            int index=lower_bound(ans.begin(),ans.end(),nums[i])-ans.begin();
            ans[index]=nums[i];
        }
    }
    return ans.size();
    }
   
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        int n=envelopes.size();
        vector<int>ans1;
        sort(envelopes.begin(),envelopes.end(),cmp);
        for(int i=0;i<n;i++){
            ans1.push_back(envelopes[i][1]);
        }
        return solve_binary_search(ans1,n);
    }
};
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