




from __future__ import annotations



def   lowerCAmelCase						(						_lowerCAmelCase							:				Optional[int]		) ->    Tuple:




 """simple docstring"""







 UpperCAmelCase__								=  {1}
 UpperCAmelCase__								=  [1]
 for _ in range(2  ,							depth + 1		):
  UpperCAmelCase__								=  [*previous_coefficients, 0]
  UpperCAmelCase__								=  [0, *previous_coefficients]
  UpperCAmelCase__								=  []
  for x, y in zip(SCREAMING_SNAKE_CASE_  ,							SCREAMING_SNAKE_CASE_		):
   coefficients.add(x + y		)
   previous_coefficients.append(x + y		)
 return coefficients



def   lowerCAmelCase						(						_lowerCAmelCase							:				int		) ->    Optional[Any]:




 """simple docstring"""







 UpperCAmelCase__								=  set()
 for number in unique_coefficients:
  UpperCAmelCase__								=  2
  UpperCAmelCase__								=  number
  while divisor**2 <= copy_number:
   UpperCAmelCase__								=  0
   while copy_number % divisor == 0:
    copy_number //= divisor
    multiplicity += 1
   if multiplicity >= 2:
    non_squarefrees.add(SCREAMING_SNAKE_CASE_		)
    break
   divisor += 1

 return unique_coefficients.difference(SCREAMING_SNAKE_CASE_		)



def   lowerCAmelCase						(						_lowerCAmelCase							:				Union[str, Any] = 51		) ->    Union[str, Any]:




 """simple docstring"""







 UpperCAmelCase__								=  get_pascal_triangle_unique_coefficients(SCREAMING_SNAKE_CASE_		)
 UpperCAmelCase__								=  get_squarefrees(SCREAMING_SNAKE_CASE_		)
 return sum(SCREAMING_SNAKE_CASE_		)


if __name__ == "__main__":
  print(F'''{solution() = }''')











_lowerCAmelCase  :				dict[str, float]						=				{
    "kilogram": 1,
    "gram": pow(1_0, 3),
    "milligram": pow(1_0, 6),
    "metric-ton": pow(1_0, -3),
    "long-ton": 0.0_0_0_9_8_4_2_0_7_3,
    "short-ton": 0.0_0_1_1_0_2_3_1_2_2,
    "pound": 2.2_0_4_6_2_4_4_2_0_2,
    "stone": 0.1_5_7_4_7_3_1_7_2_8,
    "ounce": 3_5.2_7_3_9_9_0_7_2_3,
    "carrat": 5_0_0_0,
    "atomic-mass-unit": 6.0_22_13_66_52E26,
}

_lowerCAmelCase  :				dict[str, float]						=				{
    "kilogram": 1,
    "gram": pow(1_0, -3),
    "milligram": pow(1_0, -6),
    "metric-ton": pow(1_0, 3),
    "long-ton": 1_0_1_6.0_4_6_0_8,
    "short-ton": 9_0_7.1_8_4,
    "pound": 0.4_5_3_5_9_2,
    "stone": 6.3_5_0_2_9,
    "ounce": 0.0_2_8_3_4_9_5,
    "carrat": 0.0_0_0_2,
    "atomic-mass-unit": 1.6_60_54_01_99E-27,
}



def   lowerCAmelCase						(						_lowerCAmelCase							:				str  ,							_lowerCAmelCase							:				str  ,							_lowerCAmelCase							:				float		):




 """simple docstring"""







 if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
  UpperCAmelCase__								=  (
      F'''Invalid \'from_type\' or \'to_type\' value: {from_type!r}, {to_type!r}\n'''
      F'''Supported values are: {", ".join(_lowerCAmelCase		)}'''
  )
  raise ValueError(_lowerCAmelCase		)
 return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]


if __name__ == "__main__":
  import doctest

  doctest.testmod()





