<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) {
        sort(begin(envelopes), end(envelopes), [](auto& e1, auto& e2) {
            if (e1[0] != e2[0]) {
                return e1[0] < e2[0];
            }

            return e1[1] > e2[1];
        });

        int i = 0;
        for (auto& env: envelopes) {
            auto idx = std::lower_bound(
                begin(envelopes), 
                begin(envelopes) + i, 
                env[1], 
                [] (vector<int>& e1, int val) {
                    return e1[1] < val;
                }) - begin(envelopes);

            if (idx == i) {
                i++;
            }

            envelopes[idx] = env;
        }

        return i;
    }
};
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