code: 
  
  
  
  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 			__lowercase     (				a__							,     a__ = 5_12     )       ->				Union[str, Any]:
  							__SCREAMING_SNAKE_CASE								=      x.shape[1] if len(x.shape     ) > 1 else 1
  							__SCREAMING_SNAKE_CASE								=      1 + np.arange(0							,     feature_num * offset							,     a__							,     dtype=np.intaa     )
  							__SCREAMING_SNAKE_CASE								=      x + feature_offset
  							return x
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__=True     )       ->				str:
  							requires_backends(a__							,     ['cython']     )
  
  							if keep_features and "edge_attr" in item.keys():  # edge_attr
  														__SCREAMING_SNAKE_CASE								=      np.asarray(item['edge_attr']							,     dtype=np.intaa     )
  							else:
  														__SCREAMING_SNAKE_CASE								=      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
  														__SCREAMING_SNAKE_CASE								=      np.asarray(item['node_feat']							,     dtype=np.intaa     )
  							else:
  														__SCREAMING_SNAKE_CASE								=      np.ones((item['num_nodes'], 1)							,     dtype=np.intaa     )  # same embedding for all
  
  							__SCREAMING_SNAKE_CASE								=      np.asarray(item['edge_index']							,     dtype=np.intaa     )
  
  							__SCREAMING_SNAKE_CASE								=      convert_to_single_emb(a__     ) + 1
  							__SCREAMING_SNAKE_CASE								=      item['num_nodes']
  
  							if len(edge_attr.shape     ) == 1:
  														__SCREAMING_SNAKE_CASE								=      edge_attr[:, None]
  							__SCREAMING_SNAKE_CASE								=      np.zeros([num_nodes, num_nodes, edge_attr.shape[-1]]							,     dtype=np.intaa     )
  							__SCREAMING_SNAKE_CASE								=      convert_to_single_emb(a__     ) + 1
  
  							# node adj matrix [num_nodes, num_nodes] bool
  							__SCREAMING_SNAKE_CASE								=      np.zeros([num_nodes, num_nodes]							,     dtype=a__     )
  							__SCREAMING_SNAKE_CASE								=      True
  
  							__SCREAMING_SNAKE_CASE							, __SCREAMING_SNAKE_CASE								=      algos_graphormer.floyd_warshall(a__     )
  							__SCREAMING_SNAKE_CASE								=      np.amax(a__     )
  
  							__SCREAMING_SNAKE_CASE								=      algos_graphormer.gen_edge_input(a__							,     a__							,     a__     )
  							__SCREAMING_SNAKE_CASE								=      np.zeros([num_nodes + 1, num_nodes + 1]							,     dtype=np.single     )  # with graph token
  
  							# combine
  							__SCREAMING_SNAKE_CASE								=      input_nodes + 1  # we shift all indices by one for padding
  							__SCREAMING_SNAKE_CASE								=      attn_bias
  							__SCREAMING_SNAKE_CASE								=      attn_edge_type
  							__SCREAMING_SNAKE_CASE								=      shortest_path_result.astype(np.intaa     ) + 1  # we shift all indices by one for padding
  							__SCREAMING_SNAKE_CASE								=      np.sum(a__							,     axis=1     ).reshape(-1     ) + 1  # we shift all indices by one for padding
  							__SCREAMING_SNAKE_CASE								=      item['in_degree']  # for undirected graph
  							__SCREAMING_SNAKE_CASE								=      input_edges + 1  # we shift all indices by one for padding
  							if "labels" not in item:
  														__SCREAMING_SNAKE_CASE								=      item['y']
  
  							return item
  
  class      UpperCAmelCase_						:
  
  						'''simple docstring'''
  
  
  
  
  						def __init__(					self   ,							_A=20   ,							_A=False	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													if not is_cython_available():
  																				raise ImportError('Graphormer preprocessing needs Cython (pyximport)'	)
  
  													__SCREAMING_SNAKE_CASE								=      spatial_pos_max
  													__SCREAMING_SNAKE_CASE								=      on_the_fly_processing
  
  
  
  
  
  
  						def __call__(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													if self.on_the_fly_processing:
  																				__SCREAMING_SNAKE_CASE								=      [preprocess_item(_A	) for i in features]
  
  													if not isinstance(features[0]   ,							_A	):
  																				__SCREAMING_SNAKE_CASE								=      [vars(_A	) for f in features]
  													__SCREAMING_SNAKE_CASE								=      {}
  
  													__SCREAMING_SNAKE_CASE								=      max(len(i['input_nodes']	) for i in features	)
  													__SCREAMING_SNAKE_CASE								=      len(features[0]['input_nodes'][0]	)
  													__SCREAMING_SNAKE_CASE								=      len(features[0]['attn_edge_type'][0][0]	)
  													__SCREAMING_SNAKE_CASE								=      max(len(i['input_edges'][0][0]	) for i in features	)
  													__SCREAMING_SNAKE_CASE								=      len(features[0]['input_edges'][0][0][0]	)
  													__SCREAMING_SNAKE_CASE								=      len(_A	)
  
  													__SCREAMING_SNAKE_CASE								=      torch.zeros(_A   ,							max_node_num + 1   ,							max_node_num + 1   ,							dtype=torch.float	)
  													__SCREAMING_SNAKE_CASE								=      torch.zeros(_A   ,							_A   ,							_A   ,							_A   ,							dtype=torch.long	)
  													__SCREAMING_SNAKE_CASE								=      torch.zeros(_A   ,							_A   ,							_A   ,							dtype=torch.long	)
  													__SCREAMING_SNAKE_CASE								=      torch.zeros(_A   ,							_A   ,							dtype=torch.long	)
  													__SCREAMING_SNAKE_CASE								=      torch.zeros(_A   ,							_A   ,							_A   ,							dtype=torch.long	)
  													__SCREAMING_SNAKE_CASE								=      torch.zeros(
  													    _A   ,							_A   ,							_A   ,							_A   ,							_A   ,							dtype=torch.long	)
  
  													for ix, f in enumerate(_A	):
  																				for k in ["attn_bias", "attn_edge_type", "spatial_pos", "in_degree", "input_nodes", "input_edges"]:
  																											__SCREAMING_SNAKE_CASE								=      torch.tensor(f[k]	)
  
  																				if len(f['attn_bias'][1:, 1:][f['spatial_pos'] >= self.spatial_pos_max]	) > 0:
  																											__SCREAMING_SNAKE_CASE								=      float('-inf'	)
  
  																				__SCREAMING_SNAKE_CASE								=      f['attn_bias']
  																				__SCREAMING_SNAKE_CASE								=      f[
  																				    'attn_edge_type'
  																				]
  																				__SCREAMING_SNAKE_CASE								=      f['spatial_pos']
  																				__SCREAMING_SNAKE_CASE								=      f['in_degree']
  																				__SCREAMING_SNAKE_CASE								=      f['input_nodes']
  																				__SCREAMING_SNAKE_CASE								=      f['input_edges']
  
  													__SCREAMING_SNAKE_CASE								=      batch['in_degree']
  
  													__SCREAMING_SNAKE_CASE								=      features[0]['labels']
  													if len(_A	) == 1:  # one task
  																				if isinstance(sample[0]   ,							_A	):  # regression
  																											__SCREAMING_SNAKE_CASE								=      torch.from_numpy(np.concatenate([i['labels'] for i in features]	)	)
  																				else:  # binary classification
  																											__SCREAMING_SNAKE_CASE								=      torch.from_numpy(np.concatenate([i['labels'] for i in features]	)	)
  													else:  # multi task classification, left to float to keep the NaNs
  																				__SCREAMING_SNAKE_CASE								=      torch.from_numpy(np.stack([i['labels'] for i in features]   ,							axis=0	)	)
  
  													return batch
  
  
  
  
  
  
  
style_context: 
  
  
  
  from itertools import combinations, product
  
  
  
  
  
  
  def 			__lowercase     (				a__							,     a__							,     a__							,     a__     )       ->				bool:
  							if xa == ya == 0 or xa == ya == 0:
  														return False
  							__SCREAMING_SNAKE_CASE								=      xa * xa + ya * ya
  							__SCREAMING_SNAKE_CASE								=      xa * xa + ya * ya
  							__SCREAMING_SNAKE_CASE								=      (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
  							return (
  							    a_square + b_square == c_square
  							    or a_square + c_square == b_square
  							    or b_square + c_square == a_square
  							)
  
  
  
  
  
  
  def 			__lowercase     (				a__ = 50     )       ->				int:
  							return sum(
  							    1
  							    for pta, pta in combinations(product(range(limit + 1     )							,     repeat=2     )							,     2     )
  							    if is_right(*a__							,     *a__     )     )
  
  
  if __name__ == "__main__":
  			print(F'''{solution() = }''')
  
  
  
  
  
  
  