input: Write a function to find the longest increasing subsequence in a given list.
  assert find_longest_increasing_sequence([3, 2, 1, 4, 5, 6, 7, 8]) == [4, 5, 6, 7, 8]
  assert find_longest_increasing_sequence([1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]
  assert find_longest_increasing_sequence([5, 1, 2, 3, 4]) == [1, 2, 3, 4]
  assert find_longest_increasing_sequence([10, 9, 8, 7]) == [10]
  assert find_longest_increasing_sequence([1, 1, 1, 1]) == [1]
output: def find_longest_increasing_sequence(nums):
      if not nums:
          return []
  
      n = len(nums)
      lengths = [1] * n
      previous = [-1] * n
  
      for i in range(1, n):
          for j in range(i):
              if nums[i] > nums[j] and lengths[i] < lengths[j] + 1:
                  lengths[i] = lengths[j] + 1
                  previous[i] = j
  
      max_length = max(lengths)
      max_index = lengths.index(max_length)
  
      lis = []
      while max_index != -1:
          lis.append(nums[max_index])
          max_index = previous[max_index]
  
      return lis[::-1]