python
from typing import List
class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        if not nums:
            return 0
        dp = []
        for i in range(len(nums)):
            dp.append(1)
            for j in range(i):
                if nums[i] > nums[j]:
                    dp[i] = max(dp[i], dp[j] + 1)
        return len(dp)
print(Solution().lengthOfLIS([3, 2, 1, 1, 2]))

python
from typing import List
from bisect import bisect_left
class Solution:
    def maxEnvelopes(self, arr: List[List[int]]) -> int:
        # sort increasing in first dimension and decreasing on second
        arr.sort(key=lambda x: (x[0], -x[1]))
        def lis(nums):
            dp = []
            for i in range(len(nums)):
                idx = bisect_left(dp, nums[i])
                if idx == len(dp):
                    dp.append(nums[i])
                else:
                    dp[idx] = nums[i]
            return len(dp)
        # extract the second dimension and run the LIS
        return lis([i[1] for i in arr])
print(Solution().maxEnvelopes([[5,4],[6,4],[6,7],[2,3]]))