input: def sort_by_digit_sum(nums):
      """
      Write a function that arranges a list of integers
      in increasing order based on the sum of their digits.
      Note: if multiple items have the same digit sum,
      maintain their original order from the list.
  
      For instance:
      >>> sort_by_digit_sum([1, 11, -1, -11, -12]) == [-1, -11, 1, -12, 11]
      >>> sort_by_digit_sum([]) == []
      """
output:     
      def digit_sum(n):
          return sum(int(d) for d in str(abs(n)))
      
      return sorted(nums, key=digit_sum)
  