


'''simple docstring'''
class 					_A						:



   '''simple docstring'''






   def __init__(	self	:					int					, lowerCamelCase	:					List[Any]						)->	Any:
          snake_case__					:	Dict          =					val
          # Number of nodes in left subtree
          snake_case__					:	Optional[int]          =					0
          snake_case__					:	int          =					None
          snake_case__					:	List[Any]          =					None
          snake_case__					:	int          =					None




   def   __lowerCAmelCase						(	self	:					List[Any]					, lowerCamelCase	:					Union[str, Any]						)->	Tuple:
          assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

          if self.val < other.val:
                 snake_case__					:	List[str]          =					self.right
                 snake_case__					:	int          =					None
                 if self.right:
                        snake_case__					:	Tuple          =					other
                 snake_case__					:	Optional[Any]          =					other
                 snake_case__					:	Optional[Any]          =					self.left_tree_size * 2 + 1
                 return self
          else:
                 snake_case__					:	List[Any]          =					other.right
                 snake_case__					:	str          =					None
                 if other.right:
                        snake_case__					:	Optional[Any]          =					self
                 snake_case__					:	Optional[int]          =					self
                 snake_case__					:	List[str]          =					other.left_tree_size * 2 + 1
                 return other







class 					_A						:



   '''simple docstring'''






   def __init__(	self	:					Tuple					, lowerCamelCase	:					List[Any]=None					, lowerCamelCase	:					Optional[int]=None					, lowerCamelCase	:					str=0						)->	Any:
          snake_case__					:	List[str]          =					heap_size
          snake_case__					:	List[str]          =					bottom_root
          snake_case__					:	List[Any]          =					min_node




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

          # Empty heaps corner cases
          if other.size == 0:
                 return None
          if self.size == 0:
                 snake_case__					:	List[str]          =					other.size
                 snake_case__					:	Tuple          =					other.bottom_root
                 snake_case__					:	Tuple          =					other.min_node
                 return None
          # Update size
          snake_case__					:	Any          =					self.size + other.size

          # Update min.node
          if self.min_node.val > other.min_node.val:
                 snake_case__					:	Tuple          =					other.min_node
          # Merge

          # Order roots by left_subtree_size
          snake_case__					:	Dict          =					[]
          snake_case__       ,   snake_case__					:	str          =					self.bottom_root, other.bottom_root
          while i or j:
                 if i and ((not j) or i.left_tree_size < j.left_tree_size):
                        combined_roots_list.append((i, True)						)
                        snake_case__					:	Any          =					i.parent
                 else:
                        combined_roots_list.append((j, False)						)
                        snake_case__					:	List[str]          =					j.parent
        # Insert links between them
          for i in range(len(lowerCamelCase						) - 1						):
                 if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                        snake_case__					:	Dict          =					combined_roots_list[i + 1][0]
                        snake_case__					:	str          =					combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
          snake_case__					:	List[str]          =					combined_roots_list[0][0]
          while i.parent:
                 if (
                     (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
                 ) or (
                     i.left_tree_size == i.parent.left_tree_size
                     and i.left_tree_size != i.parent.parent.left_tree_size
                 ):
                        # Neighbouring Nodes
                        snake_case__					:	str          =					i.left
                        snake_case__					:	List[str]          =					i.parent.parent

                        # Merging trees
                        snake_case__					:	Optional[int]          =					i.merge_trees(i.parent						)

                        # Updating links
                        snake_case__					:	Optional[int]          =					previous_node
                        snake_case__					:	Union[str, Any]          =					next_node
                        if previous_node:
                               snake_case__					:	Any          =					i
                        if next_node:
                               snake_case__					:	List[str]          =					i
                 else:
                        snake_case__					:	Optional[int]          =					i.parent
        # Updating self.bottom_root
          while i.left:
                 snake_case__					:	List[Any]          =					i.left
          snake_case__					:	Union[str, Any]          =					i

          # Update other
          snake_case__					:	List[str]          =					self.size
          snake_case__					:	Dict          =					self.bottom_root
          snake_case__					:	int          =					self.min_node

          # Return the merged heap
          return self




   def   __lowerCAmelCase						(	self	:					Optional[int]					, lowerCamelCase	:					Any						)->	List[str]:
          if self.size == 0:
                 snake_case__					:	Dict          =					Node(lowerCamelCase						)
                 snake_case__					:	List[Any]          =					1
                 snake_case__					:	str          =					self.bottom_root
          else:
                 # Create new node
                 snake_case__					:	Tuple          =					Node(lowerCamelCase						)

                 # Update size
                 self.size += 1

                 # update min_node
                 if val < self.min_node.val:
                        snake_case__					:	Any          =					new_node
                 # Put new_node as a bottom_root in heap
                 snake_case__					:	str          =					new_node
                 snake_case__					:	Union[str, Any]          =					self.bottom_root
                 snake_case__					:	Optional[int]          =					new_node

                 # Consecutively merge roots with same left_tree_size
                 while (
                     self.bottom_root.parent
                     and self.bottom_root.left_tree_size
                     == self.bottom_root.parent.left_tree_size
                 ):
                        # Next node
                        snake_case__					:	str          =					self.bottom_root.parent.parent

                        # Merge
                        snake_case__					:	List[Any]          =					self.bottom_root.merge_trees(self.bottom_root.parent						)

                        # Update Links
                        snake_case__					:	List[Any]          =					next_node
                        snake_case__					:	Dict          =					None
                        if next_node:
                               snake_case__					:	List[str]          =					self.bottom_root




   def   __lowerCAmelCase						(	self	:					Optional[Any]						)->	str:
          return self.min_node.val




   def   __lowerCAmelCase						(	self	:					int						)->	List[Any]:
          return self.size == 0




   def   __lowerCAmelCase						(	self	:					Optional[int]						)->	Any:
          snake_case__					:	Optional[Any]          =					self.min_node.val

          # Last element in heap corner case
          if self.size == 1:
                 # Update size
                 snake_case__					:	Dict          =					0

                 # Update bottom root
                 snake_case__					:	int          =					None

                 # Update min_node
                 snake_case__					:	Union[str, Any]          =					None

                 return min_value
          # No right subtree corner case
          # The structure of the tree implies that this should be the bottom root
          # and there is at least one other root
          if self.min_node.right is None:
                 # Update size
                 self.size -= 1

                 # Update bottom root
                 snake_case__					:	Optional[int]          =					self.bottom_root.parent
                 snake_case__					:	List[str]          =					None

                 # Update min_node
                 snake_case__					:	Dict          =					self.bottom_root
                 snake_case__					:	Union[str, Any]          =					self.bottom_root.parent
                 while i:
                        if i.val < self.min_node.val:
                               snake_case__					:	str          =					i
                        snake_case__					:	Union[str, Any]          =					i.parent
                 return min_value
          # General case
          # Find the BinomialHeap of the right subtree of min_node
          snake_case__					:	List[Any]          =					self.min_node.right
          snake_case__					:	Union[str, Any]          =					None
          snake_case__					:	List[Any]          =					bottom_of_new
          snake_case__					:	List[Any]          =					1

          # Size, min_node and bottom_root
          while bottom_of_new.left:
                 snake_case__					:	Optional[Any]          =					size_of_new * 2 + 1
                 snake_case__					:	List[str]          =					bottom_of_new.left
                 if bottom_of_new.val < min_of_new.val:
                        snake_case__					:	Dict          =					bottom_of_new
        # Corner case of single root on top left path
          if (not self.min_node.left) and (not self.min_node.parent):
                 snake_case__					:	int          =					size_of_new
                 snake_case__					:	Optional[int]          =					bottom_of_new
                 snake_case__					:	Any          =					min_of_new
                 # print("Single root, multiple nodes case")
                 return min_value
          # Remaining cases
          # Construct heap of right subtree
          snake_case__					:	Tuple          =					BinomialHeap(
              bottom_root=lowerCamelCase					, min_node=lowerCamelCase					, heap_size=lowerCamelCase						)

          # Update size
          snake_case__					:	Any          =					self.size - 1 - size_of_new

          # Neighbour nodes
          snake_case__					:	Dict          =					self.min_node.left
          snake_case__					:	int          =					self.min_node.parent

          # Initialize new bottom_root and min_node
          snake_case__					:	Optional[int]          =					previous_node or next_node
          snake_case__					:	Tuple          =					next_node

          # Update links of previous_node and search below for new min_node and
          # bottom_root
          if previous_node:
                 snake_case__					:	Dict          =					next_node

                 # Update bottom_root and search for min_node below
                 snake_case__					:	Optional[int]          =					previous_node
                 snake_case__					:	Dict          =					previous_node
                 while self.bottom_root.left:
                        snake_case__					:	str          =					self.bottom_root.left
                        if self.bottom_root.val < self.min_node.val:
                               snake_case__					:	str          =					self.bottom_root
          if next_node:
                 snake_case__					:	Union[str, Any]          =					previous_node

                 # Search for new min_node above min_node
                 snake_case__					:	int          =					next_node
                 while i:
                        if i.val < self.min_node.val:
                               snake_case__					:	Any          =					i
                        snake_case__					:	List[str]          =					i.parent
        # Merge heaps
          self.merge_heaps(lowerCamelCase						)

          return min_value




   def   __lowerCAmelCase						(	self	:					List[Any]						)->	Tuple:
          snake_case__					:	List[Any]          =					self.bottom_root
          while top_root.parent:
                 snake_case__					:	Optional[Any]          =					top_root.parent
          # preorder
          snake_case__					:	Dict          =					[]
          self.__traversal(lowerCamelCase					, lowerCamelCase						)
          return heap_pre_order




   def   __lowerCAmelCase						(	self	:					List[Any]					, lowerCamelCase	:					Dict					, lowerCamelCase	:					int					, lowerCamelCase	:					Optional[Any]=0						)->	List[Any]:
          if curr_node:
                 preorder.append((curr_node.val, level)						)
                 self.__traversal(curr_node.left					, lowerCamelCase					, level + 1						)
                 self.__traversal(curr_node.right					, lowerCamelCase					, level + 1						)
          else:
                 preorder.append(("""#""", level)						)




   def __str__(	self	:					Optional[Any]						)->	List[Any]:
          if self.is_empty():
                 return ""
          snake_case__					:	int          =					self.pre_order()

          return "\n".join(("""-""" * level + str(lowerCamelCase						)) for value, level in preorder_heap						)


# Unit Tests
if __name__ == "__main__":
     import doctest

     doctest.testmod()








'''simple docstring'''
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device


if is_torch_available():
     import torch

     from transformers import XLMProphetNetForConditionalGeneration, XLMProphetNetTokenizer







@require_torch
class 					_A						(						unittest.TestCase							):



   '''simple docstring'''






   @slow
   def   __lowerCAmelCase						(	self	:					Tuple						)->	Optional[int]:
          snake_case__					:	Any          =					XLMProphetNetForConditionalGeneration.from_pretrained("""microsoft/xprophetnet-large-wiki100-cased"""						)
          model.to(lowerCamelCase						)

          # encoder-decoder outputs
          snake_case__					:	Optional[int]          =					torch.tensor([[17, 96_208, 103_471, 2]]						).to(lowerCamelCase						)
          snake_case__					:	Optional[Any]          =					torch.tensor(
              [[2, 250, 9_953, 34, 69_489, 1_620, 32, 118_424, 624, 210, 105, 2_913, 1_032, 351]]						).to(lowerCamelCase						)
          snake_case__					:	Optional[Any]          =					model(
              input_ids=lowerCamelCase					, attention_mask=lowerCamelCase					, encoder_outputs=lowerCamelCase					, decoder_input_ids=lowerCamelCase						)
          snake_case__					:	List[Any]          =					output[0]
          snake_case__					:	Any          =					torch.Size((1, 14, 250_012)						)
          self.assertEqual(output_predited_logis.shape					, lowerCamelCase						)
          snake_case__					:	Optional[int]          =					torch.tensor(
              [[[-6.3_986, -8.2_391, 12.5_189], [-6.3_289, -8.0_864, 12.6_211], [-6.2_418, -8.0_445, 12.7_968]]]						).to(lowerCamelCase						)
          self.assertTrue(torch.allclose(output_predited_logis[:, :3, :3]					, lowerCamelCase					, atol=1e-4						)						)

          # encoder outputs
          snake_case__					:	Dict          =					model.prophetnet.encoder(lowerCamelCase						)[0]
          snake_case__					:	Optional[Any]          =					torch.tensor(
              [[[-1.4_260, -0.7_628, 0.8_453], [-1.4_719, -0.1_391, 0.7_807], [-1.7_678, 0.0_114, 0.4_646]]]						).to(lowerCamelCase						)
          snake_case__					:	str          =					torch.Size((1, 4, 1_024)						)
          self.assertEqual(encoder_outputs.shape					, lowerCamelCase						)
          self.assertTrue(torch.allclose(encoder_outputs[:, :3, :3]					, lowerCamelCase					, atol=1e-4						)						)

          # decoder outputs
          snake_case__					:	int          =					model.prophetnet.decoder(
              lowerCamelCase					, encoder_hidden_states=lowerCamelCase					, )
          snake_case__					:	Any          =					decoder_outputs[1].view(1					, model.config.ngram					, 14					, -1						)
          snake_case__					:	Optional[Any]          =					model.lm_head(lowerCamelCase						)
          snake_case__					:	str          =					predicting_streams_logits[:, 0]
          self.assertTrue(torch.allclose(next_first_stream_logits[:, :3, :3]					, lowerCamelCase					, atol=1e-4						)						)




   @slow
   def   __lowerCAmelCase						(	self	:					Union[str, Any]						)->	Optional[Any]:
          snake_case__					:	Tuple          =					XLMProphetNetForConditionalGeneration.from_pretrained(
              """microsoft/xprophetnet-large-wiki100-cased-xglue-ntg"""						)
          model.to(lowerCamelCase						)

          snake_case__					:	str          =					torch.tensor([[17, 96_208, 103_471, 2]]						).to(lowerCamelCase						)
          snake_case__					:	Union[str, Any]          =					torch.tensor(
              [[2, 250, 9_953, 34, 69_489, 1_620, 32, 118_424, 624, 210, 105, 2_913, 1_032, 351]]						).to(lowerCamelCase						)
          snake_case__					:	List[Any]          =					model(
              input_ids=lowerCamelCase					, attention_mask=lowerCamelCase					, encoder_outputs=lowerCamelCase					, decoder_input_ids=lowerCamelCase						)
          snake_case__					:	List[str]          =					output[0]
          snake_case__					:	Any          =					torch.Size((1, 14, 250_012)						)
          self.assertEqual(output_predited_logis.shape					, lowerCamelCase						)
          # compare the actual values for a slice.
          snake_case__					:	List[str]          =					torch.tensor(
              [[[-9.2_253, -9.7_173, -6.3_529], [-7.6_701, -9.0_145, -1.9_382], [-8.0_195, -7.0_004, -0.1_523]]]						).to(lowerCamelCase						)

          self.assertTrue(torch.allclose(output_predited_logis[:, :3, :3]					, lowerCamelCase					, atol=1e-4						)						)




   @slow
   def   __lowerCAmelCase						(	self	:					str						)->	str:
          snake_case__					:	Dict          =					XLMProphetNetForConditionalGeneration.from_pretrained(
              """microsoft/xprophetnet-large-wiki100-cased-xglue-ntg"""						)
          model.to(lowerCamelCase						)
          snake_case__					:	Optional[int]          =					512

          snake_case__					:	Any          =					XLMProphetNetTokenizer.from_pretrained("""microsoft/xprophetnet-large-wiki100-cased-xglue-ntg"""						)

          snake_case__					:	Optional[int]          =					(
              """Microsoft Corporation intends to officially end free support for the Windows 7 operating system after"""
              """ January 14, 2020, according to the official portal of the organization. From that day, users of this"""
              """ system will not be able to receive security updates, which could make their computers vulnerable to"""
              """ cyber attacks."""
          )
          snake_case__					:	Union[str, Any]          =					(
              """орпорация Microsoft намерена официально прекратить бесплатную поддержку операционной системы Windows 7"""
              """ после 14 января 2020 года, сообщается на официальном портале организации . С указанного дня пользователи"""
              """ этой системы не смогут получать обновления безопасности, из-за чего их компьютеры могут стать уязвимыми"""
              """ к кибератакам."""
          )
          snake_case__					:	int          =					(
              """根据该组织的官方门户网站，微软公司打算在2020年1月14日之后正式终止对Windows 7操作系统的免费支持。从那时起，该系统的用户将无法接收安全更新，这可能会使他们的计算机容易受到网络攻击。"""
          )

          snake_case__					:	int          =					tokenizer(
              [EN_SENTENCE, RU_SENTENCE, ZH_SENTENCE]					, padding=lowerCamelCase					, max_length=255					, return_tensors="""pt"""						).input_ids
          snake_case__					:	Optional[int]          =					input_ids.to(lowerCamelCase						)

          snake_case__					:	Optional[Any]          =					model.generate(
              lowerCamelCase					, num_beams=10					, length_penalty=1.0					, no_repeat_ngram_size=3					, early_stopping=lowerCamelCase						)
          snake_case__					:	Union[str, Any]          =					[tokenizer.decode(lowerCamelCase					, skip_special_tokens=lowerCamelCase						) for g in summary_ids]
          snake_case__					:	Optional[Any]          =					"""Microsoft to end Windows 7 free support after January 14, 2020"""
          snake_case__					:	Dict          =					"""Microsoft намерена прекратить бесплатную поддержку Windows 7 после 14 января 2020 года"""
          snake_case__					:	Optional[int]          =					"""微软打算终止对Windows 7操作系统的免费支持"""
          self.assertListEqual(
              [EXPECTED_TITLE_EN, EXPECTED_TITLE_RU, EXPECTED_TITLE_ZH]					, lowerCamelCase					, )

          snake_case__					:	Optional[int]          =					model.generate(
              lowerCamelCase					, num_beams=1					, length_penalty=1.0					, no_repeat_ngram_size=3					, early_stopping=lowerCamelCase						)
          snake_case__					:	Tuple          =					[
              tokenizer.convert_ids_to_tokens(lowerCamelCase					, skip_special_tokens=lowerCamelCase						) for g in summary_ids_beama
          ]
          snake_case__					:	Any          =					"""▁Microsoft ▁to ▁end ▁free ▁support ▁for ▁Windows ▁7""".split(""" """						)
          snake_case__					:	Union[str, Any]          =					"""▁Microsoft ▁намерен а ▁прекрати ть ▁бес плат ную ▁поддержку ▁Windows ▁7 ▁после ▁14 ▁января ▁2020 ▁года""".split(
              """ """						)
          snake_case__					:	Tuple          =					"""微软 公司 打算 终止 对 Windows ▁7 操作 系统的 免费 支持""".split(""" """						)
          self.assertListEqual(
              [EXPECTED_TITLE_EN_BEAM1_TOK, EXPECTED_TITLE_RU_BEAM1_TOK, EXPECTED_TITLE_ZH_BEAM1_TOK]					, lowerCamelCase					, )




