<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:


    def bin_search(nums, target):
      l,r = 0, len(nums)-1

      while l <= r:
        m = (l+r)//2

        if nums[m] < target:
          l = m + 1
        else:
          r = m - 1
      return l


    envelopes.sort(key=lambda x: (x[0],-x[1]))
    
    def lis(nums):
      dp = []
      for num in nums:
        idx = bin_search(dp, num)

        if idx == len(dp):
          dp.append(num)
        else:
          dp[idx] = num
      print(dp, nums)
      return len(dp)

    return lis([i[1] for i in envelopes])









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