






"""simple docstring"""





def      lowerCamelCase__       (							_lowerCamelCase       :		list )      ->				list:
  if any(not isinstance(UpperCAmelCase_		,				UpperCAmelCase_ ) or x < 0 for x in sequence ):
    raise TypeError('Sequence must be list of non-negative integers' )
  for _ in range(len(UpperCAmelCase_ ) ):
    for i, (rod_upper, rod_lower) in enumerate(zip(UpperCAmelCase_		,				sequence[1:] ) ):
      if rod_upper > rod_lower:
        sequence[i] -= rod_upper - rod_lower
        sequence[i + 1] += rod_upper - rod_lower
  return sequence


if __name__ == "__main__":
  assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
  assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]








'''simple docstring'''



from numpy import exp, pi, sqrt



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				Optional[int]      ,    UpperCAmelCase_    :				float = 0.0      ,    UpperCAmelCase_    :				float = 1.0							)     ->		int:
     return 1 / sqrt(2 * pi * sigma**2							) * exp(-((x - mu) ** 2) / (2 * sigma**2)							)


if __name__ == "__main__":
      import doctest

      doctest.testmod()






