


'''simple docstring'''






from typing import Dict, Optional

import numpy as np

import datasets


__A					:  Union[str, Any]											=      "\nIoU is the area of overlap between the predicted segmentation and the ground truth divided by the area of union\nbetween the predicted segmentation and the ground truth. For binary (two classes) or multi-class segmentation,\nthe mean IoU of the image is calculated by taking the IoU of each class and averaging them.\n"

__A					:  int											=      "\nArgs:\n    predictions (`List[ndarray]`):\n        List of predicted segmentation maps, each of shape (height, width). Each segmentation map can be of a different size.\n    references (`List[ndarray]`):\n        List of ground truth segmentation maps, each of shape (height, width). Each segmentation map can be of a different size.\n    num_labels (`int`):\n        Number of classes (categories).\n    ignore_index (`int`):\n        Index that will be ignored during evaluation.\n    nan_to_num (`int`, *optional*):\n        If specified, NaN values will be replaced by the number defined by the user.\n    label_map (`dict`, *optional*):\n        If specified, dictionary mapping old label indices to new label indices.\n    reduce_labels (`bool`, *optional*, defaults to `False`):\n        Whether or not to reduce all label values of segmentation maps by 1. Usually used for datasets where 0 is used for background,\n        and background itself is not included in all classes of a dataset (e.g. ADE20k). The background label will be replaced by 255.\n\nReturns:\n    `Dict[str, float | ndarray]` comprising various elements:\n    - *mean_iou* (`float`):\n        Mean Intersection-over-Union (IoU averaged over all categories).\n    - *mean_accuracy* (`float`):\n        Mean accuracy (averaged over all categories).\n    - *overall_accuracy* (`float`):\n        Overall accuracy on all images.\n    - *per_category_accuracy* (`ndarray` of shape `(num_labels,)`):\n        Per category accuracy.\n    - *per_category_iou* (`ndarray` of shape `(num_labels,)`):\n        Per category IoU.\n\nExamples:\n\n    >>> import numpy as np\n\n    >>> mean_iou = datasets.load_metric(\"mean_iou\")\n\n    >>> # suppose one has 3 different segmentation maps predicted\n    >>> predicted_1 = np.array([[1, 2], [3, 4], [5, 255]])\n    >>> actual_1 = np.array([[0, 3], [5, 4], [6, 255]])\n\n    >>> predicted_2 = np.array([[2, 7], [9, 2], [3, 6]])\n    >>> actual_2 = np.array([[1, 7], [9, 2], [3, 6]])\n\n    >>> predicted_3 = np.array([[2, 2, 3], [8, 2, 4], [3, 255, 2]])\n    >>> actual_3 = np.array([[1, 2, 2], [8, 2, 1], [3, 255, 1]])\n\n    >>> predicted = [predicted_1, predicted_2, predicted_3]\n    >>> ground_truth = [actual_1, actual_2, actual_3]\n\n    >>> results = mean_iou.compute(predictions=predicted, references=ground_truth, num_labels=10, ignore_index=255, reduce_labels=False)\n    >>> print(results) # doctest: +NORMALIZE_WHITESPACE\n    {'mean_iou': 0.47750000000000004, 'mean_accuracy': 0.5916666666666666, 'overall_accuracy': 0.5263157894736842, 'per_category_iou': array([0.   , 0.   , 0.375, 0.4  , 0.5  , 0.   , 0.5  , 1.   , 1.   , 1.   ]), 'per_category_accuracy': array([0.        , 0.        , 0.75      , 0.66666667, 1.        , 0.        , 0.5       , 1.        , 1.        , 1.        ])}\n"

__A					:  int											=      "\\n@software{MMSegmentation_Contributors_OpenMMLab_Semantic_Segmentation_2020,\nauthor = {{MMSegmentation Contributors}},\nlicense = {Apache-2.0},\nmonth = {7},\ntitle = {{OpenMMLab Semantic Segmentation Toolbox and Benchmark}},\nurl = {https://github.com/open-mmlab/mmsegmentation},\nyear = {2020}\n}"







def 				UpperCamelCase_			(    A__					:   Optional[int]							,    A__					:   Dict							,    A__					:   Union[str, Any]							,    A__					:   bool							,    A__					:   Optional[Dict[int, int]] = None							,    A__					:   bool = False							,    ):
  '''simple docstring'''





  if label_map is not None:
    for old_id, new_id in label_map.items():
      lowerCAmelCase_			:      List[Any]			=   new_id

    # turn into Numpy arrays
  lowerCAmelCase_			:      Tuple			=   np.array(A__					)
  lowerCAmelCase_			:      List[Any]			=   np.array(A__					)

  if reduce_labels:
    lowerCAmelCase_			:      Any			=   2_55
    lowerCAmelCase_			:      int			=   label - 1
    lowerCAmelCase_			:      str			=   2_55

  lowerCAmelCase_			:      Any			=   label != ignore_index
  lowerCAmelCase_			:      str			=   np.not_equal(A__							,    A__					)
  lowerCAmelCase_			:      int			=   pred_label[mask]
  lowerCAmelCase_			:      Any			=   np.array(A__					)[mask]

  lowerCAmelCase_			:      Optional[int]			=   pred_label[pred_label == label]

  lowerCAmelCase_			:      Optional[int]			=   np.histogram(A__							,    bins=A__							,    range=(0, num_labels - 1)					)[0]
  lowerCAmelCase_			:      int			=   np.histogram(A__							,    bins=A__							,    range=(0, num_labels - 1)					)[0]
  lowerCAmelCase_			:      Optional[Any]			=   np.histogram(A__							,    bins=A__							,    range=(0, num_labels - 1)					)[0]

  lowerCAmelCase_			:      Tuple			=   area_pred_label + area_label - area_intersect

  return area_intersect, area_union, area_pred_label, area_label







def 				UpperCamelCase_			(    A__					:   Dict							,    A__					:   int							,    A__					:   Union[str, Any]							,    A__					:   bool							,    A__					:   Optional[Dict[int, int]] = None							,    A__					:   bool = False							,    ):
  '''simple docstring'''





  lowerCAmelCase_			:      Union[str, Any]			=   np.zeros((num_labels,)							,    dtype=np.floataa					)
  lowerCAmelCase_			:      Union[str, Any]			=   np.zeros((num_labels,)							,    dtype=np.floataa					)
  lowerCAmelCase_			:      Dict			=   np.zeros((num_labels,)							,    dtype=np.floataa					)
  lowerCAmelCase_			:      Tuple			=   np.zeros((num_labels,)							,    dtype=np.floataa					)
  for result, gt_seg_map in zip(A__							,    A__					):
    lowerCAmelCase_,							lowerCAmelCase_,							lowerCAmelCase_,							lowerCAmelCase_			:      List[str]			=   intersect_and_union(
        A__							,    A__							,    A__							,    A__							,    A__							,    A__					)
    total_area_intersect += area_intersect
    total_area_union += area_union
    total_area_pred_label += area_pred_label
    total_area_label += area_label
  return total_area_intersect, total_area_union, total_area_pred_label, total_area_label







def 				UpperCamelCase_			(    A__					:   Dict							,    A__					:   Tuple							,    A__					:   List[Any]							,    A__					:   bool							,    A__					:   Optional[int] = None							,    A__					:   Optional[Dict[int, int]] = None							,    A__					:   bool = False							,    ):
  '''simple docstring'''





  lowerCAmelCase_,							lowerCAmelCase_,							lowerCAmelCase_,							lowerCAmelCase_			:      List[Any]			=   total_intersect_and_union(
      A__							,    A__							,    A__							,    A__							,    A__							,    A__					)

  # compute metrics
  lowerCAmelCase_			:      int			=   {}

  lowerCAmelCase_			:      Optional[Any]			=   total_area_intersect.sum() / total_area_label.sum()
  lowerCAmelCase_			:      List[Any]			=   total_area_intersect / total_area_union
  lowerCAmelCase_			:      Optional[int]			=   total_area_intersect / total_area_label

  lowerCAmelCase_			:      Optional[int]			=   np.nanmean(A__					)
  lowerCAmelCase_			:      int			=   np.nanmean(A__					)
  lowerCAmelCase_			:      List[Any]			=   all_acc
  lowerCAmelCase_			:      Optional[Any]			=   iou
  lowerCAmelCase_			:      Any			=   acc

  if nan_to_num is not None:
    lowerCAmelCase_			:      List[Any]			=   {metric: np.nan_to_num(A__							,    nan=A__					) for metric, metric_value in metrics.items()}

  return metrics






@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION	,_KWARGS_DESCRIPTION)
class    __snake_case       (   datasets.Metric):







    """simple docstring"""



    def __lowercase   (   self    :  int		)   ->  Tuple:
      return datasets.MetricInfo(
          description=_DESCRIPTION    ,						citation=_CITATION    ,						inputs_description=_KWARGS_DESCRIPTION    ,						features=datasets.Features(
              # 1st Seq - height dim, 2nd - width dim
              {
                  """predictions""": datasets.Sequence(datasets.Sequence(datasets.Value("""uint16"""		)		)		),
                  """references""": datasets.Sequence(datasets.Sequence(datasets.Value("""uint16"""		)		)		),
              }		)    ,						reference_urls=[
              """https://github.com/open-mmlab/mmsegmentation/blob/71c201b1813267d78764f306a297ca717827c4bf/mmseg/core/evaluation/metrics.py"""
          ]    ,						)





    def __lowercase   (   self    :  Tuple    ,						lowerCamelCase    :  List[Any]    ,						lowerCamelCase    :  Optional[Any]    ,						lowerCamelCase    :  int    ,						lowerCamelCase    :  bool    ,						lowerCamelCase    :  Optional[int] = None    ,						lowerCamelCase    :  Optional[Dict[int, int]] = None    ,						lowerCamelCase    :  bool = False    ,						)   ->  str:
      lowerCAmelCase_			:      Dict			=   mean_iou(
          results=lowerCamelCase    ,						gt_seg_maps=lowerCamelCase    ,						num_labels=lowerCamelCase    ,						ignore_index=lowerCamelCase    ,						nan_to_num=lowerCamelCase    ,						label_map=lowerCamelCase    ,						reduce_labels=lowerCamelCase    ,						)
      return iou_result







'''simple docstring'''






def 				UpperCamelCase_			(    A__					:   int = 1_00					):
  '''simple docstring'''





  lowerCAmelCase_			:      int			=   set()

  lowerCAmelCase_			:      Tuple			=   0

  lowerCAmelCase_			:      str			=   n + 1  # maximum limit

  for a in range(2							,    A__					):
    for b in range(2							,    A__					):
      lowerCAmelCase_			:      str			=   a**b  # calculates the current power
      collect_powers.add(A__					)  # adds the result to the set
  return len(A__					)


if __name__ == "__main__":
  print("Number of terms ", solution(int(str(input()).strip())))



