<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:
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        const int N = envelopes.size();
        int mx = 0;
        map<int,set<int,greater<>>> env;
        for (auto & vec: envelopes) {
            env[vec[0]].insert(vec[1]);
        }
        vector<int> LIS(N+1);
        // vector<int> nLIS(N+1);
        LIS[0] = -1;
        int mxL = 0;
        for (auto &[h, st]: env){
            // int curMxL = mxL;
            for (auto & w: st) {
                int l = 1, r = mxL;
                while (l<r) {
                    int m = l+(r-l)/2;
                    if (w > LIS[m]) {
                        l = m+1;
                    } else {
                        r = m;
                    }
                }
                if (w > LIS[l]) {
                    ++mxL;
                    LIS[mxL] = w;
                } else {
                    LIS[l] = min(LIS[l], w);
                }
            }
            // LIS = nLIS;
            // mxL = curMxL;
            // cout << "h = " << h << ": ";
            // for (auto & e: LIS) cout << e << " "; cout << endl;
        }
        return mxL;
    }
};
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