input: from typing import List
  
  def find_deepest_nesting(paren_string: str) -> List[int]:
      """ This function receives a string containing multiple segments of nested parentheses separated by spaces.
      It returns the depth of the deepest level of nesting for each segment.
      For example, (()()) nests at two levels while ((())) nests at three levels.
  
      >>> find_deepest_nesting('(()()) ((())) () ((())()())')
      [2, 3, 1, 3]
      """
output:     segments = paren_string.split()
      results = []
      for segment in segments:
          max_depth = 0
          current_depth = 0
          for char in segment:
              if char == '(':
                  current_depth += 1
                  if current_depth > max_depth:
                      max_depth = current_depth
              elif char == ')':
                  current_depth -= 1
          results.append(max_depth)
      return results