input: 
  import re
  
  def is_numeric_string(string: str) -> bool:
      """ Check if the given string is a valid numeric string.
      >>> is_numeric_string("123456789")
      True
      >>> is_numeric_string("abcdef")
      False
      >>> is_numeric_string("123g456")
      False
      """
      pattern = '^[0-9]+$'
      return bool(re.match(pattern, string))
  
output:     return bool(re.match(pattern, string))