
"""simple docstring"""




import math
import sys




class 	UpperCamelCase      :

				"""simple docstring"""



				def __init__(							self     )       ->       str:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      0
									SCREAMING_SNAKE_CASE           =      []
									SCREAMING_SNAKE_CASE           =      {}  # To store the pos of node in array


				def 				A   (							self     )       ->       List[str]:
									"""simple docstring"""







									return self.cur_size == 0


				def 				A   (							self						,      lowercase__     )       ->       Optional[int]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      self.left(lowercase__     )
									SCREAMING_SNAKE_CASE           =      self.right(lowercase__     )
									if lc < self.cur_size and self.array(lowercase__     )[0] < self.array(lowercase__     )[0]:
														SCREAMING_SNAKE_CASE           =      lc
									else:
														SCREAMING_SNAKE_CASE           =      idx
									if rc < self.cur_size and self.array(lowercase__     )[0] < self.array(lowercase__     )[0]:
														SCREAMING_SNAKE_CASE           =      rc
									if smallest != idx:
														self.swap(lowercase__						,      lowercase__     )
														self.min_heapify(lowercase__     )


				def 				A   (							self						,      lowercase__     )       ->       List[Any]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      self.cur_size
									self.cur_size += 1
									self.array.append((sys.maxsize, tup[1])     )
									self.decrease_key((sys.maxsize, tup[1])						,      tup[0]     )


				def 				A   (							self     )       ->       List[str]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      self.array[0][1]
									SCREAMING_SNAKE_CASE           =      self.array[self.cur_size - 1]
									self.cur_size -= 1
									self.min_heapify(1     )
									del self.pos[min_node]
									return min_node


				def 				A   (							self						,      lowercase__     )       ->       List[str]:
									"""simple docstring"""







									return 2 * i + 1


				def 				A   (							self						,      lowercase__     )       ->       List[Any]:
									"""simple docstring"""







									return 2 * i + 2


				def 				A   (							self						,      lowercase__     )       ->       List[str]:
									"""simple docstring"""







									return math.floor(i / 2     )


				def 				A   (							self						,      lowercase__						,      lowercase__     )       ->       List[Any]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      j
									SCREAMING_SNAKE_CASE           =      i
									SCREAMING_SNAKE_CASE           =      self.array[i]
									SCREAMING_SNAKE_CASE           =      self.array[j]
									SCREAMING_SNAKE_CASE           =      temp




				def 				A   (							self						,      lowercase__						,      lowercase__     )       ->       Optional[int]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      self.pos[tup[1]]
									# assuming the new_d is atmost old_d
									SCREAMING_SNAKE_CASE           =      (new_d, tup[1])
									while idx > 0 and self.array[self.par(lowercase__     )][0] > self.array[idx][0]:
														self.swap(lowercase__						,      self.par(lowercase__     )     )
														SCREAMING_SNAKE_CASE           =      self.par(lowercase__     )






class 	UpperCamelCase      :

				"""simple docstring"""



				def __init__(							self						,      lowercase__     )       ->       Dict:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      {}  # To store graph: u -> (v,w)
									SCREAMING_SNAKE_CASE           =      num  # Number of nodes in graph
									# To store the distance from source vertex
									SCREAMING_SNAKE_CASE           =      [0] * self.num_nodes
									SCREAMING_SNAKE_CASE           =      [-1] * self.num_nodes  # To store the path


				def 				A   (							self						,      lowercase__						,      lowercase__						,      lowercase__     )       ->       Union[str, Any]:
									"""simple docstring"""







									if u in self.adjList:
														self.adjList[u].append((v, w)     )
									else:
														SCREAMING_SNAKE_CASE           =      [(v, w)]

									# Assuming undirected graph
									if v in self.adjList:
														self.adjList[v].append((u, w)     )
									else:
														SCREAMING_SNAKE_CASE           =      [(u, w)]


				def 				A   (							self     )       ->       Dict:
									"""simple docstring"""







									for u in self.adjList:
														print(lowercase__						,      '->'						,      ' -> '.join(str(f'''{v}({w})'''     ) for v, w in self.adjList[u]     )     )


				def 				A   (							self						,      lowercase__     )       ->       int:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      [-1] * self.num_nodes
									# src is the source node
									SCREAMING_SNAKE_CASE           =      0
									SCREAMING_SNAKE_CASE           =      PriorityQueue()
									q.insert((0, src)     )  # (dist from src, node)
									for u in self.adjList:
														if u != src:
																			SCREAMING_SNAKE_CASE           =      sys.maxsize  # Infinity
																			SCREAMING_SNAKE_CASE           =      -1

									while not q.is_empty():
														SCREAMING_SNAKE_CASE           =      q.extract_min()  # Returns node with the min dist from source
														# Update the distance of all the neighbours of u and
														# if their prev dist was INFINITY then push them in Q
														for v, w in self.adjList[u]:
																			SCREAMING_SNAKE_CASE           =      self.dist[u] + w
																			if self.dist[v] > new_dist:
																								if self.dist[v] == sys.maxsize:
																													q.insert((new_dist, v)     )
																								else:
																													q.decrease_key((self.dist[v], v)						,      lowercase__     )
																								SCREAMING_SNAKE_CASE           =      new_dist
																								SCREAMING_SNAKE_CASE           =      u

        # Show the shortest distances from src
									self.show_distances(lowercase__     )


				def 				A   (							self						,      lowercase__     )       ->       List[Any]:
									"""simple docstring"""







									print(f'''Distance from node: {src}'''     )
									for u in range(self.num_nodes     ):
														print(f'''Node {u} has distance: {self.dist[u]}'''     )




				def 				A   (							self						,      lowercase__						,      lowercase__     )       ->       List[str]:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      []
									SCREAMING_SNAKE_CASE           =      0
									SCREAMING_SNAKE_CASE           =      dest
									# Backtracking from dest to src
									while self.par[temp] != -1:
														path.append(lowercase__     )
														if temp != src:
																			for v, w in self.adjList[temp]:
																								if v == self.par[temp]:
																													cost += w
																													break
														SCREAMING_SNAKE_CASE           =      self.par[temp]
									path.append(lowercase__     )
									path.reverse()

									print(f'''----Path to reach {dest} from {src}----'''     )
									for u in path:
														print(f'''{u}'''						,      end=' '     )
														if u != dest:
																			print('-> '						,      end=''     )

									print('\nTotal cost of path: '						,      lowercase__     )


if __name__ == "__main__":
	snake_case					  =						Graph(9)
	graph.add_edge(0, 1, 4)
	graph.add_edge(0, 7, 8)
	graph.add_edge(1, 2, 8)
	graph.add_edge(1, 7, 1_1)
	graph.add_edge(2, 3, 7)
	graph.add_edge(2, 8, 2)
	graph.add_edge(2, 5, 4)
	graph.add_edge(3, 4, 9)
	graph.add_edge(3, 5, 1_4)
	graph.add_edge(4, 5, 1_0)
	graph.add_edge(5, 6, 2)
	graph.add_edge(6, 7, 1)
	graph.add_edge(6, 8, 6)
	graph.add_edge(7, 8, 7)
	graph.show_graph()
	graph.dijkstra(0)
	graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21


"""simple docstring"""




import inspect
from typing import Callable, List, Optional, Set, Tuple, Union

import torch
from packaging import version
from safetensors.torch import storage_ptr, storage_size
from torch import nn

from .utils import logging


snake_case					  =						[nn.LayerNorm]

snake_case					  =						logging.get_logger(__name__)

snake_case					  =						version.parse(version.parse(torch.__version__).base_version)

snake_case					  =						parsed_torch_version_base >= version.parse('2.0')
snake_case					  =						parsed_torch_version_base >= version.parse('1.12')
snake_case					  =						parsed_torch_version_base >= version.parse('1.11')
snake_case					  =						parsed_torch_version_base < version.parse('1.11')

def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	self     ):
					from torch import _softmax_backward_data

					if is_torch_less_than_1_11:
										return _softmax_backward_data(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	parent.dim,	self     )
					else:
										return _softmax_backward_data(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	parent.dim,	self.dtype     )

def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_ = 0     ):
					SCREAMING_SNAKE_CASE           =      index.to(layer.weight.device     )
					SCREAMING_SNAKE_CASE           =      layer.weight.index_select(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_     ).clone().detach()
					if layer.bias is not None:
										if dim == 1:
															SCREAMING_SNAKE_CASE           =      layer.bias.clone().detach()
										else:
															SCREAMING_SNAKE_CASE           =      layer.bias[index].clone().detach()
					SCREAMING_SNAKE_CASE           =      list(layer.weight.size()     )
					SCREAMING_SNAKE_CASE           =      len(SCREAMING_SNAKE_CASE_     )
					SCREAMING_SNAKE_CASE           =      nn.Linear(new_size[1],	new_size[0],	bias=layer.bias is not None     ).to(layer.weight.device     )
					SCREAMING_SNAKE_CASE           =      False
					new_layer.weight.copy_(W.contiguous()     )
					SCREAMING_SNAKE_CASE           =      True
					if layer.bias is not None:
										SCREAMING_SNAKE_CASE           =      False
										new_layer.bias.copy_(b.contiguous()     )
										SCREAMING_SNAKE_CASE           =      True
					return new_layer




class 	UpperCamelCase      (			nn.Module ):

				"""simple docstring"""



				def __init__(							self						,      lowercase__						,      lowercase__     )       ->       List[Any]:
									"""simple docstring"""







									super().__init__()
									SCREAMING_SNAKE_CASE           =      nf
									SCREAMING_SNAKE_CASE           =      nn.Parameter(torch.empty(lowercase__						,      lowercase__     )     )
									SCREAMING_SNAKE_CASE           =      nn.Parameter(torch.zeros(lowercase__     )     )
									nn.init.normal_(self.weight						,      std=0.02     )




				def 				A   (							self						,      lowercase__     )       ->       str:
									"""simple docstring"""







									SCREAMING_SNAKE_CASE           =      x.size()[:-1] + (self.nf,)
									SCREAMING_SNAKE_CASE           =      torch.addmm(self.bias						,      x.view(-1						,      x.size(-1     )     )						,      self.weight     )
									SCREAMING_SNAKE_CASE           =      x.view(lowercase__     )
									return x






def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_ = 1     ):
					SCREAMING_SNAKE_CASE           =      index.to(layer.weight.device     )
					SCREAMING_SNAKE_CASE           =      layer.weight.index_select(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_     ).clone().detach()
					if dim == 0:
										SCREAMING_SNAKE_CASE           =      layer.bias.clone().detach()
					else:
										SCREAMING_SNAKE_CASE           =      layer.bias[index].clone().detach()
					SCREAMING_SNAKE_CASE           =      list(layer.weight.size()     )
					SCREAMING_SNAKE_CASE           =      len(SCREAMING_SNAKE_CASE_     )
					SCREAMING_SNAKE_CASE           =      ConvaD(new_size[1],	new_size[0]     ).to(layer.weight.device     )
					SCREAMING_SNAKE_CASE           =      False
					new_layer.weight.copy_(W.contiguous()     )
					SCREAMING_SNAKE_CASE           =      True
					SCREAMING_SNAKE_CASE           =      False
					new_layer.bias.copy_(b.contiguous()     )
					SCREAMING_SNAKE_CASE           =      True
					return new_layer

def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_ = None     ):
					if isinstance(SCREAMING_SNAKE_CASE_,	nn.Linear     ):
										return prune_linear_layer(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	dim=0 if dim is None else dim     )
					elif isinstance(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_     ):
										return prune_convad_layer(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	dim=1 if dim is None else dim     )
					else:
										raise ValueError(f'''Can\'t prune layer of class {layer.__class__}'''     )

def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	*SCREAMING_SNAKE_CASE_     ):
					assert len(SCREAMING_SNAKE_CASE_     ) > 0, f'''{input_tensors} has to be a tuple/list of tensors'''

					# inspect.signature exist since python 3.5 and is a python method -> no problem with backward compatibility
					SCREAMING_SNAKE_CASE           =      len(inspect.signature(SCREAMING_SNAKE_CASE_     ).parameters     )
					if num_args_in_forward_chunk_fn != len(SCREAMING_SNAKE_CASE_     ):
										raise ValueError(
										    f'''forward_chunk_fn expects {num_args_in_forward_chunk_fn} arguments, but only {len(SCREAMING_SNAKE_CASE_     )} input '''
										    'tensors are given'     )

					if chunk_size > 0:
										SCREAMING_SNAKE_CASE           =      input_tensors[0].shape[chunk_dim]
										for input_tensor in input_tensors:
															if input_tensor.shape[chunk_dim] != tensor_shape:
																				raise ValueError(
																				    f'''All input tenors have to be of the same shape: {tensor_shape}, '''
																				    f'''found shape {input_tensor.shape[chunk_dim]}'''     )

										if input_tensors[0].shape[chunk_dim] % chunk_size != 0:
															raise ValueError(
															    f'''The dimension to be chunked {input_tensors[0].shape[chunk_dim]} has to be a multiple of the chunk '''
															    f'''size {chunk_size}'''     )

										SCREAMING_SNAKE_CASE           =      input_tensors[0].shape[chunk_dim] // chunk_size

										# chunk input tensor into tuples
										SCREAMING_SNAKE_CASE           =      tuple(input_tensor.chunk(SCREAMING_SNAKE_CASE_,	dim=SCREAMING_SNAKE_CASE_     ) for input_tensor in input_tensors     )
										# apply forward fn to every tuple
										SCREAMING_SNAKE_CASE           =      tuple(forward_fn(*SCREAMING_SNAKE_CASE_     ) for input_tensors_chunk in zip(*SCREAMING_SNAKE_CASE_     )     )
										# concatenate output at same dimension
										return torch.cat(SCREAMING_SNAKE_CASE_,	dim=SCREAMING_SNAKE_CASE_     )

					return forward_fn(*SCREAMING_SNAKE_CASE_     )

def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_     ):
					SCREAMING_SNAKE_CASE           =      torch.ones(SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_     )
					SCREAMING_SNAKE_CASE           =      set(SCREAMING_SNAKE_CASE_     ) - already_pruned_heads  # Convert to set and remove already pruned heads
					for head in heads:
										# Compute how many pruned heads are before the head and move the index accordingly
										SCREAMING_SNAKE_CASE           =      head - sum(1 if h < head else 0 for h in already_pruned_heads     )
										SCREAMING_SNAKE_CASE           =      0
					SCREAMING_SNAKE_CASE           =      mask.view(-1     ).contiguous().eq(1     )
					SCREAMING_SNAKE_CASE           =      torch.arange(len(SCREAMING_SNAKE_CASE_     )     )[mask].long()
					return heads, index

def     UpperCamelCase_    (						*SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_ = None     ):
					return torch.meshgrid(*SCREAMING_SNAKE_CASE_,	indexing=SCREAMING_SNAKE_CASE_     )



def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_     ):
					return tensor.device, storage_ptr(SCREAMING_SNAKE_CASE_     ), storage_size(SCREAMING_SNAKE_CASE_     )
