input: Write a function to determine the maximum length of an increasing subsequence in a specified list.
  
  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(arr):
      if not arr:
          return 0
      n = len(arr)
      lis = [1] * n
      for i in range(1, n):
          for j in range(i):
              if arr[i] > arr[j]:
                  lis[i] = max(lis[i], lis[j] + 1)
      return max(lis)