



"""simple docstring"""
import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import (
    TaBlock,
    TaConfig,
    TaLayerNorm,
)

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin
class 							lowerCamelCase    (     a__       ,		a__       ,		a__							):






					'''simple docstring'''





					@register_to_config
					def __init__(			self:				Tuple		,	snake_case:				Tuple		,	snake_case:				Dict		,	snake_case:				Dict		,	snake_case:				Union[str, Any]		,	snake_case:				Optional[Any]		,	snake_case:				str		,	snake_case:				Tuple		,	snake_case:				Any		,	snake_case:				List[str]		,	snake_case:				str = False		,	)  ->      Optional[int]:
											super().__init__()

											snake_case_					:Dict		=     nn.Linear(__A		,	__A		,	bias=__A		)

											snake_case_					:str		=     nn.Embedding(__A		,	__A		)
											snake_case_					:Optional[int]		=     False

											snake_case_					:Any		=     nn.Dropout(p=__A		)

											snake_case_					:str		=     TaConfig(
											    d_model=__A		,	num_heads=__A		,	d_kv=__A		,	d_ff=__A		,	feed_forward_proj=__A		,	dropout_rate=__A		,	is_decoder=__A		,	is_encoder_decoder=__A		,	)
											snake_case_					:int		=     nn.ModuleList()
											for lyr_num in range(__A		):
																	snake_case_					:Any		=     TaBlock(__A		)
																	self.encoders.append(__A		)

											snake_case_					:List[Any]		=     TaLayerNorm(__A		)
											snake_case_					:int		=     nn.Dropout(p=__A		)






					def   lowerCAmelCase_							(			self:				Union[str, Any]		,	snake_case:				Optional[int]		,	snake_case:				Optional[int]		)  ->      Any:
											snake_case_					:List[Any]		=     self.input_proj(__A		)

											# terminal relative positional encodings
											snake_case_					:List[Any]		=     encoder_inputs.shape[1]
											snake_case_					:List[Any]		=     torch.arange(__A		,	device=encoder_inputs.device		)

											snake_case_					:Optional[Any]		=     encoder_inputs_mask.sum(-1		)
											snake_case_					:Optional[Any]		=     torch.roll(input_positions.unsqueeze(0		)		,	tuple(seq_lens.tolist()		)		,	dims=0		)
											x += self.position_encoding(__A		)

											snake_case_					:Tuple		=     self.dropout_pre(__A		)

											# inverted the attention mask
											snake_case_					:Tuple		=     encoder_inputs.size()
											snake_case_					:str		=     self.get_extended_attention_mask(__A		,	__A		)

											for lyr in self.encoders:
																	snake_case_					:Any		=     lyr(__A		,	__A		)[0]
											snake_case_					:int		=     self.layer_norm(__A		)

											return self.dropout_post(__A		), encoder_inputs_mask




'''simple docstring'''




from collections import deque





def 				a_							(    lowercase     )      ->Tuple:






				'''simple docstring'''

				return input(lowercase     ).strip().split(" "     )





def 				a_							(    lowercase				,    lowercase     )      ->dict[int, list[int]]:






				'''simple docstring'''

				__lowerCamelCase		:   dict[int, list[int]]           =       {}
				for i in range(lowercase     ):
								__lowerCamelCase		:   int           =       []

				for e in range(lowercase     ):
								__lowerCamelCase    ,       __lowerCamelCase		:   int           =       (int(lowercase     ) for i in _input(F'Edge {e + 1}: <node1> <node2> '     ))
								graph[x].append(lowercase     )
				return graph





def 				a_							(    lowercase				,    lowercase     )      ->dict[int, list[int]]:






				'''simple docstring'''

				__lowerCamelCase		:   dict[int, list[int]]           =       {}
				for i in range(lowercase     ):
								__lowerCamelCase		:   Any           =       []

				for e in range(lowercase     ):
								__lowerCamelCase    ,       __lowerCamelCase		:   Dict           =       (int(lowercase     ) for i in _input(F'Edge {e + 1}: <node1> <node2> '     ))
								graph[x].append(lowercase     )
								graph[y].append(lowercase     )
				return graph





def 				a_							(    lowercase				,    lowercase     )      ->dict[int, list[tuple[int, int]]]:






				'''simple docstring'''

				__lowerCamelCase		:   dict[int, list[tuple[int, int]]]           =       {}
				for i in range(lowercase     ):
								__lowerCamelCase		:   List[Any]           =       []

				for e in range(lowercase     ):
								__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   int           =       (int(lowercase     ) for i in _input(F'Edge {e + 1}: <node1> <node2> <weight> '     ))
								graph[x].append((y, w)     )
								graph[y].append((x, w)     )
				return graph


if __name__ == "__main__":
				__lowercase		,		__lowercase	:   List[Any]   		=					(int(i) for i in _input("""Number of nodes and edges: """))

				__lowercase	:   Any   		=					int(
				    _input(
				        """Press 1 or 2 or 3 \n"""
				        """1. Unweighted directed \n"""
				        """2. Unweighted undirected \n"""
				        """3. Weighted undirected \n"""
				    )[0]
				)

				__lowercase	:   Any   		=					{
				    1: initialize_unweighted_directed_graph,
				    2: initialize_unweighted_undirected_graph,
				    3: initialize_weighted_undirected_graph,
				}[graph_choice](n, m)





def 				a_							(    lowercase				,    lowercase     )      ->Tuple:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase		:   Dict           =       {s}, [s]
				print(lowercase     )
				while _s:
								__lowerCamelCase		:   int           =       0
								for i in g[_s[-1]]:
												if i not in vis:
																_s.append(lowercase     )
																vis.add(lowercase     )
																__lowerCamelCase		:   Tuple           =       1
																print(lowercase     )
																break
								if not flag:
												_s.pop()





def 				a_							(    lowercase				,    lowercase     )      ->List[str]:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase		:   Tuple           =       {s}, deque([s]     )
				print(lowercase     )
				while q:
								__lowerCamelCase		:   Optional[Any]           =       q.popleft()
								for v in g[u]:
												if v not in vis:
																vis.add(lowercase     )
																q.append(lowercase     )
																print(lowercase     )





def 				a_							(    lowercase				,    lowercase     )      ->Any:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   Optional[int]           =       {s: 0}, set(), {s: 0}
				while True:
								if len(lowercase     ) == len(lowercase     ) - 1:
												break
								__lowerCamelCase		:   str           =       10_0000
								for i in dist:
												if i not in known and dist[i] < mini:
																__lowerCamelCase		:   Any           =       dist[i]
																__lowerCamelCase		:   List[str]           =       i
								known.add(lowercase     )
								for v in g[u]:
												if v[0] not in known and dist[u] + v[1] < dist.get(v[0]				,    10_0000     ):
																__lowerCamelCase		:   Optional[int]           =       dist[u] + v[1]
																__lowerCamelCase		:   List[str]           =       u
				for i in dist:
								if i != s:
												print(dist[i]     )





def 				a_							(    lowercase				,    lowercase=None				,    lowercase=None     )      ->Optional[Any]:






				'''simple docstring'''

				if q is None:
								__lowerCamelCase		:   int           =       [1]
				if ind is None:
								__lowerCamelCase		:   Any           =       [0] * (len(lowercase     ) + 1)  # SInce oth Index is ignored
								for u in g:
												for v in g[u]:
																ind[v] += 1
								__lowerCamelCase		:   Tuple           =       deque()
								for i in g:
												if ind[i] == 0:
																q.append(lowercase     )
				if len(lowercase     ) == 0:
								return
				__lowerCamelCase		:   Optional[Any]           =       q.popleft()
				print(lowercase     )
				for w in g[v]:
								ind[w] -= 1
								if ind[w] == 0:
												q.append(lowercase     )
				topo(lowercase				,    lowercase				,    lowercase     )





def 				a_							(    )      ->Union[str, Any]:






				'''simple docstring'''

				__lowerCamelCase		:   Tuple           =       input().strip()
				__lowerCamelCase		:   Any           =       []
				for _ in range(lowercase     ):
								a.append(map(lowercase				,    input().strip().split()     )     )
				return a, n





def 				a_							(    lowercase     )      ->List[str]:






				'''simple docstring'''

				((__lowerCamelCase)    ,       (__lowerCamelCase))		:   Optional[int]           =       a_and_n
				__lowerCamelCase		:   Optional[int]           =       list(lowercase     )
				__lowerCamelCase		:   str           =       [[0] * n for i in range(lowercase     )]
				for k in range(lowercase     ):
								for i in range(lowercase     ):
												for j in range(lowercase     ):
																if dist[i][j] > dist[i][k] + dist[k][j]:
																				__lowerCamelCase		:   str           =       dist[i][k] + dist[k][j]
																				__lowerCamelCase		:   Tuple           =       k
				print(lowercase     )





def 				a_							(    lowercase				,    lowercase     )      ->Dict:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase    ,       __lowerCamelCase		:   int           =       {s: 0}, set(), {s: 0}
				while True:
								if len(lowercase     ) == len(lowercase     ) - 1:
												break
								__lowerCamelCase		:   List[Any]           =       10_0000
								for i in dist:
												if i not in known and dist[i] < mini:
																__lowerCamelCase		:   str           =       dist[i]
																__lowerCamelCase		:   Optional[int]           =       i
								known.add(lowercase     )
								for v in g[u]:
												if v[0] not in known and v[1] < dist.get(v[0]				,    10_0000     ):
																__lowerCamelCase		:   Dict           =       v[1]
																__lowerCamelCase		:   List[str]           =       u
				return dist





def 				a_							(    )      ->Union[str, Any]:






				'''simple docstring'''

				__lowerCamelCase    ,       __lowerCamelCase		:   List[Any]           =       map(lowercase				,    input().split(" "     )     )
				__lowerCamelCase		:   Optional[Any]           =       []
				for _ in range(lowercase     ):
								edges.append(map(lowercase				,    input().split(" "     )     )     )
				return edges, n





def 				a_							(    lowercase     )      ->Optional[int]:






				'''simple docstring'''

				((__lowerCamelCase)    ,       (__lowerCamelCase))		:   Any           =       e_and_n
				e.sort(reverse=lowercase				,    key=lambda lowercase     : x[2]     )
				__lowerCamelCase		:   Optional[Any]           =       [{i} for i in range(1				,    n + 1     )]
				while True:
								if len(lowercase     ) == 1:
												break
								print(lowercase     )
								__lowerCamelCase		:   List[str]           =       e.pop()
								for i in range(len(lowercase     )     ):
												if x[0] in s[i]:
																break
								for j in range(len(lowercase     )     ):
												if x[1] in s[j]:
																if i == j:
																				break
																s[j].update(s[i]     )
																s.pop(lowercase     )
																break





def 				a_							(    lowercase     )      ->int:






				'''simple docstring'''

				__lowerCamelCase		:   Tuple           =       []
				for node in graph:
								if not graph[node]:
												isolated.append(lowercase     )
				return isolated





