"""
Given an integer array nums, return the length of the longest strictly increasing subsequence.

A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, [3,6,2,7] is a subsequence of the array [0,3,1,6,2,2,7].



Example 1:

Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
Example 2:

Input: nums = [0,1,0,3,2,3]
Output: 4
Example 3:

Input: nums = [7,7,7,7,7,7,7]
Output: 1


Constraints:

1 <= nums.length <= 2500
-104 <= nums[i] <= 104


Follow up: Can you come up with an algorithm that runs in O(n log(n)) time complexity?
"""
from bisect import bisect_left
from typing import List


class LongestIncreasingSubsequence:
    def lengthOfLIS(self, nums: List[int]) -> int:
        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)