<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>>& a) {
        auto comp = [] (vector<int> f, vector<int> s) {
            if (f[0]==s[0]) {
                return f[1]>s[1];
            }
            return f[0]<s[0];
        };
        sort(a.begin(), a.end(), comp);
        int n = a.size();
        int INF = 1e9;
        vector<int> d(n+1, INF);
        d[0] = -INF;
        for (int i=0;i<n;i++) {
            int idx = upper_bound(d.begin(),d.end(),a[i][1]) - d.begin();
            if (d[idx-1] < a[i][1] && d[idx] > a[i][1]) {
                d[idx] = a[i][1];
            }
        }
        int ans = 0;
        for (int i=0;i<=n;i++) {
            if (d[i] < INF) {
                ans = i;
            }
        }
        return ans;
    }
};
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