



"""simple docstring"""
def        A_  (      _lowercase = 100     ):







						'''simple docstring'''


						snake_case_			:int						=      [[0 for _ in range(lowerCamelCase_     )] for _ in range(m + 1     )]
						for i in range(m + 1     ):
												snake_case_			:List[str]						=      1

						for n in range(m + 1     ):
												for k in range(1, lowerCamelCase_     ):
																		memo[n][k] += memo[n][k - 1]
																		if n > k:
																								memo[n][k] += memo[n - k - 1][k]

						return memo[m][m - 1] - 1


if __name__ == "__main__":
						print(solution(int(input("Enter a number: ").strip())))





"""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, _lowercase = 512     ):







						'''simple docstring'''


						snake_case_			:int						=      x.shape[1] if len(x.shape     ) > 1 else 1
						snake_case_			:List[Any]						=      1 + np.arange(0, feature_num * offset, _lowercase, dtype=np.intaa     )
						snake_case_			:int						=      x + feature_offset
						return x
def        A_  (      _lowercase, _lowercase=True     ):







						'''simple docstring'''


						requires_backends(_lowercase, ["""cython"""]     )

						if keep_features and "edge_attr" in item.keys():  # edge_attr
												snake_case_			:Tuple						=      np.asarray(item["""edge_attr"""], dtype=np.intaa     )
						else:
												snake_case_			:List[str]						=      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
												snake_case_			:Dict						=      np.asarray(item["""node_feat"""], dtype=np.intaa     )
						else:
												snake_case_			:Tuple						=      np.ones((item["""num_nodes"""], 1), dtype=np.intaa     )  # same embedding for all

						snake_case_			:Any						=      np.asarray(item["""edge_index"""], dtype=np.intaa     )

						snake_case_			:str						=      convert_to_single_emb(_lowercase     ) + 1
						snake_case_			:str						=      item["""num_nodes"""]

						if len(edge_attr.shape     ) == 1:
												snake_case_			:Any						=      edge_attr[:, None]
						snake_case_			:Dict						=      np.zeros([num_nodes, num_nodes, edge_attr.shape[-1]], dtype=np.intaa     )
						snake_case_			:str						=      convert_to_single_emb(_lowercase     ) + 1

						# node adj matrix [num_nodes, num_nodes] bool
						snake_case_			:List[str]						=      np.zeros([num_nodes, num_nodes], dtype=_lowercase     )
						snake_case_			:int						=      True

						snake_case_,	snake_case_			:Tuple						=      algos_graphormer.floyd_warshall(_lowercase     )
						snake_case_			:List[str]						=      np.amax(_lowercase     )

						snake_case_			:Dict						=      algos_graphormer.gen_edge_input(_lowercase, _lowercase, _lowercase     )
						snake_case_			:Tuple						=      np.zeros([num_nodes + 1, num_nodes + 1], dtype=np.single     )  # with graph token

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

						return item

class     lowerCamelCase  :






					'''simple docstring'''





					def __init__(	self:							Dict						,					snake_case:							Optional[int]=20						,					snake_case:							List[Any]=False						)       ->     Union[str, Any]:
											if not is_cython_available():
																	raise ImportError("""Graphormer preprocessing needs Cython (pyximport)"""						)

											snake_case_			:List[str]						=      spatial_pos_max
											snake_case_			:int						=      on_the_fly_processing






					def __call__(	self:							str						,					snake_case:							List[dict]						)       ->     Dict[str, Any]:
											if self.on_the_fly_processing:
																	snake_case_			:int						=      [preprocess_item(snake_case						) for i in features]

											if not isinstance(features[0]						,					snake_case						):
																	snake_case_			:Tuple						=      [vars(snake_case						) for f in features]
											snake_case_			:Any						=      {}

											snake_case_			:Dict						=      max(len(i["""input_nodes"""]						) for i in features						)
											snake_case_			:List[Any]						=      len(features[0]["""input_nodes"""][0]						)
											snake_case_			:Dict						=      len(features[0]["""attn_edge_type"""][0][0]						)
											snake_case_			:List[Any]						=      max(len(i["""input_edges"""][0][0]						) for i in features						)
											snake_case_			:Any						=      len(features[0]["""input_edges"""][0][0][0]						)
											snake_case_			:List[str]						=      len(snake_case						)

											snake_case_			:Union[str, Any]						=      torch.zeros(snake_case						,					max_node_num + 1						,					max_node_num + 1						,					dtype=torch.float						)
											snake_case_			:int						=      torch.zeros(snake_case						,					snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Optional[Any]						=      torch.zeros(snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Tuple						=      torch.zeros(snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Dict						=      torch.zeros(snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Union[str, Any]						=      torch.zeros(
											    snake_case						,					snake_case						,					snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)

											for ix, f in enumerate(snake_case						):
																	for k in ["attn_bias", "attn_edge_type", "spatial_pos", "in_degree", "input_nodes", "input_edges"]:
																							snake_case_			:List[str]						=      torch.tensor(f[k]						)

																	if len(f["""attn_bias"""][1:, 1:][f["""spatial_pos"""] >= self.spatial_pos_max]						) > 0:
																							snake_case_			:Union[str, Any]						=      float("""-inf"""						)

																	snake_case_			:Optional[Any]						=      f["""attn_bias"""]
																	snake_case_			:int						=      f[
																	    """attn_edge_type"""
																	]
																	snake_case_			:Dict						=      f["""spatial_pos"""]
																	snake_case_			:Tuple						=      f["""in_degree"""]
																	snake_case_			:List[Any]						=      f["""input_nodes"""]
																	snake_case_			:List[Any]						=      f["""input_edges"""]

											snake_case_			:int						=      batch["""in_degree"""]

											snake_case_			:Any						=      features[0]["""labels"""]
											if len(snake_case						) == 1:  # one task
																	if isinstance(sample[0]						,					snake_case						):  # regression
																							snake_case_			:Dict						=      torch.from_numpy(np.concatenate([i["""labels"""] for i in features]						)						)
																	else:  # binary classification
																							snake_case_			:str						=      torch.from_numpy(np.concatenate([i["""labels"""] for i in features]						)						)
											else:  # multi task classification, left to float to keep the NaNs
																	snake_case_			:Optional[int]						=      torch.from_numpy(np.stack([i["""labels"""] for i in features]						,					axis=0						)						)

											return batch
