<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:
    bool static cmp(vector<int> a1, vector<int> &a2){
        if(a1[0] == a2[0]) return a1[1]> a2[1];

        return a1[0]<a2[0];
    }

    int maxEnvelopes(vector<vector<int>>& arr) {
        int n  =arr.size();

        sort(arr.begin(),arr.end(),cmp);
        vector<int> dp(n+1,1);
        vector<int> ans ;
        ans.push_back(arr[0][1]);

        for(int i =0;i<n;i++){
            if(ans.back() < arr[i][1]){
                ans.push_back(arr[i][1]);
            }
            else{
                int ind= lower_bound(ans.begin(),ans.end(),arr[i][1]) - ans.begin();
                ans[ind] = arr[i][1];
            }
        }

        return ans.size();

        return *max_element(dp.begin(),dp.end());
    }
};
277171