<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:
     

    auto lower_bound(vector<int> monostack, int val) {
        int lo = 0, hi = monostack.size() - 1;
        while (lo < hi) {
            auto mi = lo + ((hi - lo) >> 1);
            if (monostack[mi] < val) lo = mi + 1;
            else hi = mi;
        }
        return lo;
    }

public:
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        sort(envelopes.begin(), envelopes.end(), [](vector<int>& a, vector<int>& b) {
            // sort by index 0 ascending then index 1 descending
            if (a[0] != b[0]) return a[0] < b[0];
            else return b[1] < a[1];
        });


        vector<int> monostack;
        const int n = envelopes.size();
        // vector<int> dp(n, 1);

        for (int idx = 0; idx < n; idx++) {
            auto num = envelopes[idx][1];
            if (monostack.empty() || num > monostack.back())
                monostack.push_back(num);
            else {
                auto new_idx = lower_bound(monostack, num);
                monostack[new_idx] = num;
            }
        }

        return monostack.size();
        
    }
};
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