<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 comp(vector<int>&a, vector<int>&b) {
    if(a[0]==b[0]){
        return a[1]>b[1];
    }
    return a[0]<b[0];
}
int bs(vector<int>dp, int l, int r, int t) {
    while(l<r) {
        int mid = l+(r-l)/2;
        if(dp[mid]>=t){
            r = mid;
        }else{
            l = mid+1;
        }
    }
    return l;
}
int lis(vector<int>&a) {
    int n = a.size();

    vector<int>dp;
    dp.push_back(a[0]);

    for(int i=1; i<n; i++) {
        if(a[i]>dp[dp.size()-1]){
            dp.push_back(a[i]);
        }else{
            int temp = bs(dp, 0, dp.size()-1, a[i]);
            dp[temp] = a[i];
        }
    }
    return dp.size();
}
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        sort(envelopes.begin(), envelopes.end(), comp);

        vector<int>h;
        for(auto x:envelopes) {
            h.push_back(x[1]);
        }

        return lis(h);
    }
};
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