<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 inf = 1e9 + 20;
        int n = envelopes.size();

        sort(envelopes.begin(), envelopes.end(), cmp);

        vector<int> h(n + 1, 0);
        h[0] = inf;

        for (int i = 0; i < n; ++i){
            int x = envelopes[i][1];
            int id = lower_bound(h.begin(), h.end(), x, greater<int>()) - h.begin();
            h[id] = max(h[id], x);
        }

        return lower_bound(h.begin(), h.end(), 0, greater<int>()) - h.begin() - 1;
    }
private:
    static bool cmp(vector<int> a, vector<int> b){
        if (a[0] == b[0]) return a[1] < b[1];
        return a[0] > b[0];
    }
};
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