'''simple docstring'''




def 	_UpperCAmelCase       (				_UpperCamelCase       :      int,  _UpperCamelCase       :      int = 10_00  )      -> str:
    if (not isinstance(lowercase_,  lowercase_  )) or (digit_position <= 0):
        raise ValueError('''Digit position must be a positive integer'''  )
    elif (not isinstance(lowercase_,  lowercase_  )) or (precision < 0):
        raise ValueError('''Precision must be a nonnegative integer'''  )

    # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
    # accurate
    A_      =  (
        4 * _subsum(lowercase_,  1,  lowercase_  )
        - 2 * _subsum(lowercase_,  4,  lowercase_  )
        - _subsum(lowercase_,  5,  lowercase_  )
        - _subsum(lowercase_,  6,  lowercase_  )
    )

    # return the first hex digit of the fractional part of the result
    return hex(int((sum_result % 1) * 16  )  )[2:]





def 	_UpperCAmelCase       (				_UpperCamelCase       :      int,  _UpperCamelCase       :      int,  _UpperCamelCase       :      int  )      -> float:
    A_      =  0.0
    for sum_index in range(digit_pos_to_extract + precision  ):
        A_      =  8 * sum_index + denominator_addend
        if sum_index < digit_pos_to_extract:
            # if the exponential term is an integer and we mod it by the denominator
            # before dividing, only the integer part of the sum will change;
            # the fractional part will not
            A_      =  pow(
                16,  digit_pos_to_extract - 1 - sum_index,  lowercase_  )
        else:
            A_      =  pow(16,  digit_pos_to_extract - 1 - sum_index  )
        total += exponential_term / denominator
    return total


if __name__ == "__main__":
  import doctest

  doctest.testmod()







"""simple docstring"""







def       A__    (	lowercase_     :	list						)  ->							list:

   for insert_index, insert_value in enumerate(collection[1:]						):
      __lowerCamelCase    		=					insert_index
      while insert_index >= 0 and insert_value < collection[insert_index]:
         __lowerCamelCase    		=					collection[insert_index]
         insert_index -= 1
      if insert_index != temp_index:
         __lowerCamelCase    		=					insert_value
   return collection


if __name__ == "__main__":
     from doctest import testmod

     testmod()

     _SCREAMING_SNAKE_CASE	:		List[str]   =   input('''Enter numbers separated by a comma:\n''').strip()
     _SCREAMING_SNAKE_CASE	:		Optional[int]   =   [int(item) for item in user_input.split(''',''')]
     print(F"{insertion_sort(unsorted) = }")






