<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:
    def maxEnvelopes(self, envelopes: List[List[int]]) -> int:
        envelopes.sort(key = lambda x:(x[0], -x[1]))
        n = len(envelopes)
        lis= []
        lis.append(envelopes[0][1])
                # if envelopes[i][0]>envelopes[j][0]:
                #     lis_2[i] = max(lis_2[j]+1, lis_2[i])
        for i in range(1,n):
            if lis[-1]<envelopes[i][1]:
                lis.append(envelopes[i][1])
            else:
                low, high = 0, len(lis)-1
                while low<high:
                    mid = low + (high-low)//2
                    if lis[mid]<envelopes[i][1]:
                        low = mid+1
                    else:
                        high = mid
                lis[low] = envelopes[i][1]
        return len(lis)

                
        return max(lis_1[n-1])
        
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