<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 {

private:
    int searchLesser(map<int, int> &m, int i) {
        auto it = m.lower_bound(i);
        if (it == begin(m)) return 0;
        return (--it) -> second;
    }

    int lis(vector<vector<int>> &envelopes) {
        map<int, int> m;
        vector<int> dp(envelopes.size(), 1);
        m[envelopes[0][1]] = 1;

        for (int i = 1; i < envelopes.size(); i++) {
            dp[i] += searchLesser(m, envelopes[i][1]);

            m[envelopes[i][1]] = dp[i];

            auto it = m.find(envelopes[i][1]);
            it++;
            while (it != m.end() and it->second < dp[i]) it = m.erase(it);
        }

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

public:
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        sort(begin(envelopes), end(envelopes), [](vector<int> &a, vector<int> &b){
            if (a[0] == b[0]) return a[1] > b[1];
            return a[0] < b[0];
        });

        return lis(envelopes);
    }
};

auto init = [](){
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    return 0;
}();

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