import collections
import tempfile
import unittest

import numpy as np

from transformers.testing_utils import (
    is_pt_flax_cross_test,
    require_flax,
    require_torch,
    require_vision,
    slow,
    torch_device,
)
from transformers.utils import is_flax_available, is_torch_available, is_vision_available

from ...test_modeling_flax_common import floats_tensor, ids_tensor, random_attention_mask
from ..bert.test_modeling_flax_bert import FlaxBertModelTester
from ..clip.test_modeling_flax_clip import FlaxCLIPVisionModelTester
from ..vit.test_modeling_flax_vit import FlaxViTModelTester


if is_flax_available():
      from transformers import (
          FlaxBertModel,
          FlaxCLIPVisionModel,
          FlaxVisionTextDualEncoderModel,
          FlaxViTModel,
          VisionTextDualEncoderConfig,
          VisionTextDualEncoderProcessor,
      )
      from transformers.modeling_flax_pytorch_utils import (
          convert_pytorch_state_dict_to_flax,
          load_flax_weights_in_pytorch_model,
      )


if is_torch_available():
      import torch

      from transformers import VisionTextDualEncoderModel

if is_vision_available():
      from PIL import Image







def     _a				(      lowercase__  :			Optional[Any] ):







     '''simple docstring'''


     if isinstance(lowercase__     ,  collections.abc.Iterable ):
          return x
     return (x, x)

@require_flax
class       snake_case					:




  def 	__lowercase(      self     :	Union[str, Any]     , a_     :	Optional[Any]     , a_     :	str				)->       Tuple:




       """simple docstring"""
       pass




  def 	__lowercase(      self     :	List[Any]				)->       Optional[Any]:




       """simple docstring"""
       pass




  def 	__lowercase(      self     :	str				)->       Tuple:




       """simple docstring"""
       pass




  def 	__lowercase(      self     :	int     , a_     :	np.ndarray     , a_     :	np.ndarray     , a_     :	float				)->       List[Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		np.abs((a - b)				).max()
       self.assertLessEqual(a_     , a_     , F'''Difference between torch and flax is {diff} (>= {tol}).'''				)




  def 	__lowercase(      self     :	Union[str, Any]     , a_     :	str     , a_     :	Union[str, Any]     , a_     :	Optional[int]     , a_     :	Any     , a_     :	str=None     , **a_     :	List[str]				)->       str:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		VisionTextDualEncoderConfig.from_vision_text_configs(a_     , a_				)

       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		FlaxVisionTextDualEncoderModel(a_				)

       SCREAMING_SNAKE_CASE__				:				str			=		model(input_ids=a_     , pixel_values=a_     , attention_mask=a_				)

       self.assertEqual(output['text_embeds'].shape     , (input_ids.shape[0], config.projection_dim)				)
       self.assertEqual(output['image_embeds'].shape     , (pixel_values.shape[0], config.projection_dim)				)




  def 	__lowercase(      self     :	Any     , a_     :	Any     , a_     :	str     , a_     :	Union[str, Any]     , a_     :	List[str]     , a_     :	Optional[Any]=None     , **a_     :	Optional[int]				)->       str:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				List[str]			=		self.get_vision_text_model(a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				Dict			=		{'vision_model': vision_model, 'text_model': text_model}
       SCREAMING_SNAKE_CASE__				:				List[str]			=		FlaxVisionTextDualEncoderModel.from_vision_text_pretrained(**a_				)

       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		model(input_ids=a_     , pixel_values=a_     , attention_mask=a_				)

       self.assertEqual(output['text_embeds'].shape     , (input_ids.shape[0], model.config.projection_dim)				)
       self.assertEqual(output['image_embeds'].shape     , (pixel_values.shape[0], model.config.projection_dim)				)




  def 	__lowercase(      self     :	Union[str, Any]     , a_     :	int     , a_     :	Any     , a_     :	Optional[int]     , a_     :	Union[str, Any]     , a_     :	Any=None     , **a_     :	str				)->       List[Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				Dict			=		self.get_vision_text_model(a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				str			=		{'vision_model': vision_model, 'text_model': text_model}
       SCREAMING_SNAKE_CASE__				:				Dict			=		FlaxVisionTextDualEncoderModel.from_vision_text_pretrained(**a_				)

       SCREAMING_SNAKE_CASE__				:				List[Any]			=		model(input_ids=a_     , pixel_values=a_     , attention_mask=a_				)
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		output[0]

       with tempfile.TemporaryDirectory() as tmpdirname:
            model.save_pretrained(a_				)
            SCREAMING_SNAKE_CASE__				:				List[str]			=		FlaxVisionTextDualEncoderModel.from_pretrained(a_				)

            SCREAMING_SNAKE_CASE__				:				Optional[int]			=		model(input_ids=a_     , pixel_values=a_     , attention_mask=a_				)
            SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		after_output[0]
            SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		np.amax(np.abs(out_a - out_a				)				)
            self.assertLessEqual(a_     , 1e-3				)




  def 	__lowercase(      self     :	List[Any]     , a_     :	int     , a_     :	Dict     , a_     :	str     , a_     :	Tuple     , a_     :	Any=None     , **a_     :	int				)->       int:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				Dict			=		self.get_vision_text_model(a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		{'vision_model': vision_model, 'text_model': text_model}
       SCREAMING_SNAKE_CASE__				:				int			=		FlaxVisionTextDualEncoderModel.from_vision_text_pretrained(**a_				)

       SCREAMING_SNAKE_CASE__				:				int			=		model(
           input_ids=a_     , pixel_values=a_     , attention_mask=a_     , output_attentions=a_				)

       SCREAMING_SNAKE_CASE__				:				str			=		output.vision_model_output.attentions
       self.assertEqual(len(a_				)     , vision_config.num_hidden_layers				)

       # in ViT, the seq_len equals the number of patches + 1 (we add 1 for the [CLS] token)
       SCREAMING_SNAKE_CASE__				:				int			=		to_atuple(vision_model.config.image_size				)
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		to_atuple(vision_model.config.patch_size				)
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		(image_size[1] // patch_size[1]) * (image_size[0] // patch_size[0])
       SCREAMING_SNAKE_CASE__				:				List[str]			=		num_patches + 1
       self.assertEqual(vision_attentions[0].shape[-3:]     , (vision_config.num_attention_heads, seq_len, seq_len)				)

       SCREAMING_SNAKE_CASE__				:				Dict			=		output.text_model_output.attentions
       self.assertEqual(len(a_				)     , text_config.num_hidden_layers				)

       self.assertEqual(
           text_attentions[0].shape[-3:]     , (text_config.num_attention_heads, input_ids.shape[-1], input_ids.shape[-1])     , )




  def 	__lowercase(      self     :	List[Any]     , a_     :	Tuple     , a_     :	List[Any]     , a_     :	Optional[int]				)->       Tuple:




       """simple docstring"""
       pt_model.to(a_				)
       pt_model.eval()

       # prepare inputs
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		inputs_dict
       SCREAMING_SNAKE_CASE__				:				str			=		{k: torch.tensor(v.tolist()				) for k, v in flax_inputs.items()}

       with torch.no_grad():
            SCREAMING_SNAKE_CASE__				:				int			=		pt_model(**a_				).to_tuple()

       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		fx_model(**a_				).to_tuple()
       self.assertEqual(len(a_				)     , len(a_				)     , 'Output lengths differ between Flax and PyTorch'				)
       for fx_output, pt_output in zip(fx_outputs[:4]     , pt_outputs[:4]				):
            self.assert_almost_equals(a_     , pt_output.numpy()     , 4e-2				)

       # PT -> Flax
       with tempfile.TemporaryDirectory() as tmpdirname:
            pt_model.save_pretrained(a_				)
            SCREAMING_SNAKE_CASE__				:				int			=		FlaxVisionTextDualEncoderModel.from_pretrained(a_     , from_pt=a_				)

       SCREAMING_SNAKE_CASE__				:				str			=		fx_model_loaded(**a_				).to_tuple()
       self.assertEqual(len(a_				)     , len(a_				)     , 'Output lengths differ between Flax and PyTorch'				)
       for fx_output_loaded, pt_output in zip(fx_outputs_loaded[:4]     , pt_outputs[:4]				):
            self.assert_almost_equals(a_     , pt_output.numpy()     , 4e-2				)

       # Flax -> PT
       with tempfile.TemporaryDirectory() as tmpdirname:
            fx_model.save_pretrained(a_				)
            SCREAMING_SNAKE_CASE__				:				List[Any]			=		VisionTextDualEncoderModel.from_pretrained(a_     , from_flax=a_				)

       pt_model_loaded.to(a_				)
       pt_model_loaded.eval()

       with torch.no_grad():
            SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		pt_model_loaded(**a_				).to_tuple()

       self.assertEqual(len(a_				)     , len(a_				)     , 'Output lengths differ between Flax and PyTorch'				)
       for fx_output, pt_output_loaded in zip(fx_outputs[:4]     , pt_outputs_loaded[:4]				):
            self.assert_almost_equals(a_     , pt_output_loaded.numpy()     , 4e-2				)




  def 	__lowercase(      self     :	Optional[int]     , a_     :	int     , a_     :	int     , a_     :	Dict				)->       Union[str, Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		VisionTextDualEncoderConfig.from_vision_text_configs(a_     , a_				)

       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		VisionTextDualEncoderModel(a_				)
       SCREAMING_SNAKE_CASE__				:				List[str]			=		FlaxVisionTextDualEncoderModel(a_				)

       SCREAMING_SNAKE_CASE__				:				str			=		convert_pytorch_state_dict_to_flax(pt_model.state_dict()     , a_				)
       SCREAMING_SNAKE_CASE__				:				str			=		fx_state

       self.check_pt_flax_equivalence(a_     , a_     , a_				)




  def 	__lowercase(      self     :	List[str]     , a_     :	Union[str, Any]     , a_     :	str     , a_     :	Any				)->       int:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		VisionTextDualEncoderConfig.from_vision_text_configs(a_     , a_				)

       SCREAMING_SNAKE_CASE__				:				int			=		VisionTextDualEncoderModel(a_				)
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		FlaxVisionTextDualEncoderModel(a_				)

       SCREAMING_SNAKE_CASE__				:				List[Any]			=		load_flax_weights_in_pytorch_model(a_     , fx_model.params				)

       self.check_pt_flax_equivalence(a_     , a_     , a_				)




  def 	__lowercase(      self     :	List[Any]				)->       List[Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		self.prepare_config_and_inputs()
       self.check_model_from_pretrained_configs(**a_				)




  def 	__lowercase(      self     :	Union[str, Any]				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				str			=		self.prepare_config_and_inputs()
       self.check_vision_text_dual_encoder_from_pretrained(**a_				)




  def 	__lowercase(      self     :	str				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				int			=		self.prepare_config_and_inputs()
       self.check_save_load(**a_				)




  def 	__lowercase(      self     :	Optional[Any]				)->       Dict:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				int			=		self.prepare_config_and_inputs()
       self.check_vision_text_output_attention(**a_				)




  @is_pt_flax_cross_test
  def 	__lowercase(      self     :	Optional[Any]				)->       List[str]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		self.prepare_config_and_inputs()
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		config_inputs_dict.pop('vision_config'				)
       SCREAMING_SNAKE_CASE__				:				List[str]			=		config_inputs_dict.pop('text_config'				)

       SCREAMING_SNAKE_CASE__				:				List[Any]			=		config_inputs_dict

       self.check_equivalence_pt_to_flax(a_     , a_     , a_				)
       self.check_equivalence_flax_to_pt(a_     , a_     , a_				)




  @slow
  def 	__lowercase(      self     :	Union[str, Any]				)->       int:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				Dict			=		self.get_pretrained_model_and_inputs()

       SCREAMING_SNAKE_CASE__				:				Dict			=		model_a(**a_				)
       SCREAMING_SNAKE_CASE__				:				Tuple			=		outputs[0]

       with tempfile.TemporaryDirectory() as tmp_dirname:
            model_a.save_pretrained(a_				)
            SCREAMING_SNAKE_CASE__				:				List[Any]			=		FlaxVisionTextDualEncoderModel.from_pretrained(a_				)

            SCREAMING_SNAKE_CASE__				:				int			=		model_a(**a_				)
            SCREAMING_SNAKE_CASE__				:				Dict			=		after_outputs[0]
            SCREAMING_SNAKE_CASE__				:				int			=		np.amax(np.abs(out_a - out_a				)				)
            self.assertLessEqual(a_     , 1e-5				)




@require_flax
class       snake_case					(      UpperCamelCase_   ,						unittest.TestCase						):




  def 	__lowercase(      self     :	List[Any]				)->       Union[str, Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		FlaxVisionTextDualEncoderModel.from_vision_text_pretrained(
           'hf-internal-testing/tiny-random-vit'     , 'hf-internal-testing/tiny-bert'     , vision_from_pt=a_     , text_from_pt=a_     , )
       SCREAMING_SNAKE_CASE__				:				Tuple			=		13
       SCREAMING_SNAKE_CASE__				:				Dict			=		floats_tensor(
           [
               batch_size,
               model.config.vision_config.num_channels,
               model.config.vision_config.image_size,
               model.config.vision_config.image_size,
           ]				)
       SCREAMING_SNAKE_CASE__				:				str			=		ids_tensor([batch_size, 4]     , model.config.text_config.vocab_size				)
       SCREAMING_SNAKE_CASE__				:				int			=		random_attention_mask([batch_size, 4]				)
       SCREAMING_SNAKE_CASE__				:				Dict			=		{'pixel_values': pixel_values, 'input_ids': input_ids, 'attention_mask': attention_mask}

       return model, inputs




  def 	__lowercase(      self     :	List[str]     , a_     :	Optional[Any]     , a_     :	Tuple				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Tuple			=		FlaxViTModel(a_				)
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		FlaxBertModel(a_				)
       return vision_model, text_model




  def 	__lowercase(      self     :	Any				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		FlaxViTModelTester(self				)
       SCREAMING_SNAKE_CASE__				:				int			=		FlaxBertModelTester(self				)
       SCREAMING_SNAKE_CASE__				:				Tuple			=		vit_model_tester.prepare_config_and_inputs()
       SCREAMING_SNAKE_CASE__				:				List[str]			=		bert_model_tester.prepare_config_and_inputs()

       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				Any			=		vision_config_and_inputs

       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				List[str]			=		text_config_and_inputs

       # make sure that cross attention layers are added
       return {
           "text_config": text_config,
           "vision_config": vision_config,
           "pixel_values": pixel_values,
           "attention_mask": attention_mask,
           "input_ids": input_ids,
           "token_type_ids": token_type_ids,
       }




@require_torch
class       snake_case					(      UpperCamelCase_   ,						unittest.TestCase						):




  def 	__lowercase(      self     :	Tuple				)->       List[Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		FlaxVisionTextDualEncoderModel.from_vision_text_pretrained(
           'hf-internal-testing/tiny-random-clip'     , 'hf-internal-testing/tiny-bert'     , vision_from_pt=a_     , text_from_pt=a_     , )
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		13
       SCREAMING_SNAKE_CASE__				:				List[str]			=		floats_tensor(
           [
               batch_size,
               model.config.vision_config.num_channels,
               model.config.vision_config.image_size,
               model.config.vision_config.image_size,
           ]				)
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		ids_tensor([batch_size, 4]     , model.config.text_config.vocab_size				)
       SCREAMING_SNAKE_CASE__				:				List[str]			=		random_attention_mask([batch_size, 4]				)
       SCREAMING_SNAKE_CASE__				:				int			=		{'pixel_values': pixel_values, 'input_ids': input_ids, 'attention_mask': attention_mask}

       return model, inputs




  def 	__lowercase(      self     :	Union[str, Any]     , a_     :	Tuple     , a_     :	Dict				)->       Tuple:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		FlaxCLIPVisionModel(a_				)
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		FlaxBertModel(a_				)
       return vision_model, text_model




  def 	__lowercase(      self     :	int				)->       Tuple:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		FlaxCLIPVisionModelTester(self				)
       SCREAMING_SNAKE_CASE__				:				Tuple			=		FlaxBertModelTester(self				)
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		clip_model_tester.prepare_config_and_inputs()
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		bert_model_tester.prepare_config_and_inputs()

       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				List[Any]			=		vision_config_and_inputs

       SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__			,							SCREAMING_SNAKE_CASE__				:				Dict			=		text_config_and_inputs

       # make sure that cross attention layers are added
       return {
           "text_config": text_config,
           "vision_config": vision_config,
           "pixel_values": pixel_values,
           "attention_mask": attention_mask,
           "input_ids": input_ids,
           "token_type_ids": token_type_ids,
       }




@require_flax
@require_vision
class       snake_case					(      unittest.TestCase						):




  @slow
  def 	__lowercase(      self     :	Optional[int]				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		FlaxVisionTextDualEncoderModel.from_pretrained('clip-italian/clip-italian'     , logit_scale_init_value=1.0				)
       SCREAMING_SNAKE_CASE__				:				Any			=		VisionTextDualEncoderProcessor.from_pretrained('clip-italian/clip-italian'				)

       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		Image.open('./tests/fixtures/tests_samples/COCO/000000039769.png'				)
       SCREAMING_SNAKE_CASE__				:				Any			=		processor(
           text=['una foto di un gatto', 'una foto di un cane']     , images=a_     , padding=a_     , return_tensors='np'				)

       SCREAMING_SNAKE_CASE__				:				str			=		model(**a_				)

       # verify the logits
       self.assertEqual(outputs.logits_per_image.shape     , (inputs.pixel_values.shape[0], inputs.input_ids.shape[0])				)
       self.assertEqual(
           outputs.logits_per_text.shape     , (inputs.input_ids.shape[0], inputs.pixel_values.shape[0])     , )

       SCREAMING_SNAKE_CASE__				:				List[str]			=		np.array([[1.228_4727, 0.310_4122]]				)

       self.assertTrue(np.allclose(outputs.logits_per_image     , a_     , atol=1e-3				)				)




import heapq as hq
import math
from collections.abc import Iterator

class       snake_case					:




  def __init__(      self     :	str     , a_     :	str				)->       Any:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		str(id_				)
       SCREAMING_SNAKE_CASE__				:				Any			=		None
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		None
       SCREAMING_SNAKE_CASE__				:				Any			=		[]
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		{}  # {vertex:distance}




  def __lt__(      self     :	int     , a_     :	Tuple				)->       Union[str, Any]:




       """simple docstring"""
       return self.key < other.key




  def __repr__(      self     :	Any				)->       Dict:




       """simple docstring"""
       return self.id




  def 	__lowercase(      self     :	Optional[Any]     , a_     :	int				)->       List[str]:




       """simple docstring"""
       self.neighbors.append(a_				)




  def 	__lowercase(      self     :	int     , a_     :	int     , a_     :	Optional[Any]				)->       Any:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Tuple			=		weight







def     _a				(      lowercase__  :			Optional[Any]     ,  lowercase__  :			Union[str, Any]     ,  lowercase__  :			Tuple     ,  lowercase__  :			Dict ):







     '''simple docstring'''


     graph[a - 1].add_neighbor(graph[b - 1] )
     graph[b - 1].add_neighbor(graph[a - 1] )
     # add the edges:
     graph[a - 1].add_edge(graph[b - 1]     ,  lowercase__ )
     graph[b - 1].add_edge(graph[a - 1]     ,  lowercase__ )







def     _a				(      lowercase__  :			list     ,  lowercase__  :			Vertex ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				Any			=		[]
     for u in graph:
          SCREAMING_SNAKE_CASE__				:				Dict			=		math.inf
          SCREAMING_SNAKE_CASE__				:				str			=		None
     SCREAMING_SNAKE_CASE__				:				List[str]			=		0
     SCREAMING_SNAKE_CASE__				:				int			=		graph[:]
     while q:
          SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		min(lowercase__ )
          q.remove(lowercase__ )
          for v in u.neighbors:
               if (v in q) and (u.edges[v.id] < v.key):
                    SCREAMING_SNAKE_CASE__				:				int			=		u
                    SCREAMING_SNAKE_CASE__				:				Any			=		u.edges[v.id]
     for i in range(1     ,  len(lowercase__ ) ):
          a.append((int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1) )
     return a







def     _a				(      lowercase__  :			list     ,  lowercase__  :			Vertex ):







     '''simple docstring'''


     for u in graph:
          SCREAMING_SNAKE_CASE__				:				List[str]			=		math.inf
          SCREAMING_SNAKE_CASE__				:				int			=		None
     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		0

     SCREAMING_SNAKE_CASE__				:				Tuple			=		list(lowercase__ )
     hq.heapify(lowercase__ )

     while h:
          SCREAMING_SNAKE_CASE__				:				Optional[int]			=		hq.heappop(lowercase__ )
          for v in u.neighbors:
               if (v in h) and (u.edges[v.id] < v.key):
                    SCREAMING_SNAKE_CASE__				:				List[str]			=		u
                    SCREAMING_SNAKE_CASE__				:				Dict			=		u.edges[v.id]
                    hq.heapify(lowercase__ )

     for i in range(1     ,  len(lowercase__ ) ):
          yield (int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1)







def     _a				(      ):







     '''simple docstring'''




if __name__ == "__main__":
      import doctest

      doctest.testmod()



