'''simple docstring'''




from __future__ import annotations






def __lowerCAmelCase				(							UpperCamelCase__       ,						UpperCamelCase__       ,						UpperCamelCase__       ,						)			->					list[float | int]:
    if not all((nth_term, start_term_a, common_ratio_r)       ):
        return []
    __lowerCamelCase						=						[]
    __lowerCamelCase						=						1
    __lowerCamelCase						=						common_ratio_r
    for _ in range(int(UpperCamelCase__       )       ):
        if not series:
            series.append(UpperCamelCase__       )
        else:
            power += 1
            series.append(float(start_term_a * multiple       )       )
            __lowerCamelCase						=						pow(float(UpperCamelCase__       )       ,						UpperCamelCase__       )
    return series


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  __UpperCAmelCase  							=    float(input("Enter the last number (n term) of the Geometric Series"))
  __UpperCAmelCase  							=    float(input("Enter the starting term (a) of the Geometric Series"))
  __UpperCAmelCase  							=    float(
      input("Enter the common ratio between two terms (r) of the Geometric Series")
  )
  print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
  print(geometric_series(nth_term, start_term_a, common_ratio_r))

'''simple docstring'''




from __future__ import annotations






def __lowerCAmelCase				(							UpperCamelCase__       ,						UpperCamelCase__       )			->					list:
    __lowerCamelCase						=						[None] * (len(UpperCamelCase__       ) + len(UpperCamelCase__       ))

    __lowerCamelCase						=						0  # pointer to current index for left Half
    __lowerCamelCase						=						0  # pointer to current index for the right Half
    __lowerCamelCase						=						0  # pointer to current index for the sorted array Half

    while pointera < len(UpperCamelCase__       ) and pointera < len(UpperCamelCase__       ):
        if left_half[pointera] < right_half[pointera]:
            __lowerCamelCase						=						left_half[pointera]
            pointera += 1
            index += 1
        else:
            __lowerCamelCase						=						right_half[pointera]
            pointera += 1
            index += 1
    while pointera < len(UpperCamelCase__       ):
        __lowerCamelCase						=						left_half[pointera]
        pointera += 1
        index += 1

    while pointera < len(UpperCamelCase__       ):
        __lowerCamelCase						=						right_half[pointera]
        pointera += 1
        index += 1

    return sorted_array






def __lowerCAmelCase				(							UpperCamelCase__       )			->					list:
    if len(UpperCamelCase__       ) <= 1:
        return array
    # the actual formula to calculate the middle element = left + (right - left) // 2
    # this avoids integer overflow in case of large N
    __lowerCamelCase						=						0 + (len(UpperCamelCase__       ) - 0) // 2

    # Split the array into halves till the array length becomes equal to One
    # merge the arrays of single length returned by mergeSort function and
    # pass them into the merge arrays function which merges the array
    __lowerCamelCase						=						array[:middle]
    __lowerCamelCase						=						array[middle:]

    return merge(merge_sort(UpperCamelCase__       )       ,						merge_sort(UpperCamelCase__       )       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
