"""simple docstring"""







from typing import Any, Dict, List, Mapping

import numpy as np
import torch

from ...utils import is_cython_available, requires_backends


if is_cython_available():
     import pyximport

     pyximport.install(setup_args={'''include_dirs''': np.get_include()})
     from . import algos_graphormer  # noqa E402



def       A__    (	lowercase_     :	List[Any]      , lowercase_     :	int = 512						)  ->							List[Any]:
   __lowerCamelCase    		=					x.shape[1] if len(x.shape						) > 1 else 1
   __lowerCamelCase    		=					1 + np.arange(0      , feature_num * offset      , lowercase_      , dtype=np.intaa						)
   __lowerCamelCase    		=					x + feature_offset
   return x



def       A__    (	lowercase_     :	Optional[Any]      , lowercase_     :	Union[str, Any]=True						)  ->							str:
   requires_backends(lowercase_      , ['cython']						)

   if keep_features and "edge_attr" in item.keys():  # edge_attr
      __lowerCamelCase    		=					np.asarray(item['edge_attr']      , dtype=np.intaa						)
   else:
      __lowerCamelCase    		=					np.ones((len(item['edge_index'][0]						), 1)      , dtype=np.intaa						)  # same embedding for all

   if keep_features and "node_feat" in item.keys():  # input_nodes
      __lowerCamelCase    		=					np.asarray(item['node_feat']      , dtype=np.intaa						)
   else:
      __lowerCamelCase    		=					np.ones((item['num_nodes'], 1)      , dtype=np.intaa						)  # same embedding for all

   __lowerCamelCase    		=					np.asarray(item['edge_index']      , dtype=np.intaa						)

   __lowerCamelCase    		=					convert_to_single_emb(lowercase_						) + 1
   __lowerCamelCase    		=					item['num_nodes']

   if len(edge_attr.shape						) == 1:
      __lowerCamelCase    		=					edge_attr[:, None]
   __lowerCamelCase    		=					np.zeros([num_nodes, num_nodes, edge_attr.shape[-1]]      , dtype=np.intaa						)
   __lowerCamelCase    		=					convert_to_single_emb(lowercase_						) + 1

   # node adj matrix [num_nodes, num_nodes] bool
   __lowerCamelCase    		=					np.zeros([num_nodes, num_nodes]      , dtype=lowercase_						)
   __lowerCamelCase    		=					True

   __lowerCamelCase		,__lowerCamelCase    		=					algos_graphormer.floyd_warshall(lowercase_						)
   __lowerCamelCase    		=					np.amax(lowercase_						)

   __lowerCamelCase    		=					algos_graphormer.gen_edge_input(lowercase_      , lowercase_      , lowercase_						)
   __lowerCamelCase    		=					np.zeros([num_nodes + 1, num_nodes + 1]      , dtype=np.single						)  # with graph token

   # combine
   __lowerCamelCase    		=					input_nodes + 1  # we shift all indices by one for padding
   __lowerCamelCase    		=					attn_bias
   __lowerCamelCase    		=					attn_edge_type
   __lowerCamelCase    		=					shortest_path_result.astype(np.intaa						) + 1  # we shift all indices by one for padding
   __lowerCamelCase    		=					np.sum(lowercase_      , axis=1						).reshape(-1						) + 1  # we shift all indices by one for padding
   __lowerCamelCase    		=					item['in_degree']  # for undirected graph
   __lowerCamelCase    		=					input_edges + 1  # we shift all indices by one for padding
   if "labels" not in item:
      __lowerCamelCase    		=					item['y']

   return item






class      _SCREAMING_SNAKE_CASE							:



   '''simple docstring'''



   def __init__(	self ,				_SCREAMING_SNAKE_CASE=20 ,				_SCREAMING_SNAKE_CASE=False	):


      '''simple docstring'''

      if not is_cython_available():
         raise ImportError('Graphormer preprocessing needs Cython (pyximport)'	)

      __lowerCamelCase    		=					spatial_pos_max
      __lowerCamelCase    		=					on_the_fly_processing







   def __call__(	self ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      if self.on_the_fly_processing:
         __lowerCamelCase    		=					[preprocess_item(_SCREAMING_SNAKE_CASE	) for i in features]

      if not isinstance(features[0] ,				_SCREAMING_SNAKE_CASE	):
         __lowerCamelCase    		=					[vars(_SCREAMING_SNAKE_CASE	) for f in features]
      __lowerCamelCase    		=					{}

      __lowerCamelCase    		=					max(len(i['input_nodes']	) for i in features	)
      __lowerCamelCase    		=					len(features[0]['input_nodes'][0]	)
      __lowerCamelCase    		=					len(features[0]['attn_edge_type'][0][0]	)
      __lowerCamelCase    		=					max(len(i['input_edges'][0][0]	) for i in features	)
      __lowerCamelCase    		=					len(features[0]['input_edges'][0][0][0]	)
      __lowerCamelCase    		=					len(_SCREAMING_SNAKE_CASE	)

      __lowerCamelCase    		=					torch.zeros(_SCREAMING_SNAKE_CASE ,				max_node_num + 1 ,				max_node_num + 1 ,				dtype=torch.float	)
      __lowerCamelCase    		=					torch.zeros(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.long	)
      __lowerCamelCase    		=					torch.zeros(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.long	)
      __lowerCamelCase    		=					torch.zeros(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.long	)
      __lowerCamelCase    		=					torch.zeros(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.long	)
      __lowerCamelCase    		=					torch.zeros(
          _SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.long	)

      for ix, f in enumerate(_SCREAMING_SNAKE_CASE	):
         for k in ["attn_bias", "attn_edge_type", "spatial_pos", "in_degree", "input_nodes", "input_edges"]:
            __lowerCamelCase    		=					torch.tensor(f[k]	)

         if len(f['attn_bias'][1:, 1:][f['spatial_pos'] >= self.spatial_pos_max]	) > 0:
            __lowerCamelCase    		=					float('-inf'	)

         __lowerCamelCase    		=					f['attn_bias']
         __lowerCamelCase    		=					f[
             'attn_edge_type'
         ]
         __lowerCamelCase    		=					f['spatial_pos']
         __lowerCamelCase    		=					f['in_degree']
         __lowerCamelCase    		=					f['input_nodes']
         __lowerCamelCase    		=					f['input_edges']

      __lowerCamelCase    		=					batch['in_degree']

      __lowerCamelCase    		=					features[0]['labels']
      if len(_SCREAMING_SNAKE_CASE	) == 1:  # one task
         if isinstance(sample[0] ,				_SCREAMING_SNAKE_CASE	):  # regression
            __lowerCamelCase    		=					torch.from_numpy(np.concatenate([i['labels'] for i in features]	)	)
         else:  # binary classification
            __lowerCamelCase    		=					torch.from_numpy(np.concatenate([i['labels'] for i in features]	)	)
      else:  # multi task classification, left to float to keep the NaNs
         __lowerCamelCase    		=					torch.from_numpy(np.stack([i['labels'] for i in features] ,				axis=0	)	)

      return batch









from __future__ import annotations





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





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

    return unique_coefficients.difference(__A						)





def 				__a							(       __A = 51						):
    SCREAMING_SNAKE_CASE__         =    get_pascal_triangle_unique_coefficients(__A						)
    SCREAMING_SNAKE_CASE__         =    get_squarefrees(__A						)
    return sum(__A						)


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


