input: Write a python function to determine the length of the longest increasing subsequence within a provided sequence.
  assert longest_increasing_subsequence([10, 22, 9, 33, 21, 50, 41, 60]) == 5
  assert longest_increasing_subsequence([3, 10, 2, 1, 20]) == 3
  assert longest_increasing_subsequence([50, 3, 10, 7, 40, 80]) == 4
output: def longest_increasing_subsequence(nums):
      if not nums:
          return 0
      lis = [1] * len(nums)
      for i in range(1, len(nums)):
          for j in range(i):
              if nums[i] > nums[j]:
                  lis[i] = max(lis[i], lis[j] + 1)
      return max(lis)