
def 		UpperCamelCase     (       _UpperCAmelCase  :   int = 50  )   ->			int:






						'''simple docstring'''

						_lowercase       :	str           =   [1] * (length + 1)

						for row_length in range(length + 1  ):
												for tile_length in range(2 ,			5  ):
																		for tile_start in range(row_length - tile_length + 1  ):
																								ways_number[row_length] += ways_number[
																								    row_length - tile_start - tile_length
																								]

						return ways_number[length]


if __name__ == "__main__":
							print(f'''{solution() = }''')






from __future__ import annotations

import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf, slow

from ...test_configuration_common import ConfigTester
from ...test_modeling_tf_common import TFModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_tf_available():
							import numpy
							import tensorflow as tf

							from transformers import (
							    TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
							    TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
							    TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
							    BertConfig,
							    DPRConfig,
							    TFDPRContextEncoder,
							    TFDPRQuestionEncoder,
							    TFDPRReader,
							)




class   __lowercase						:






	def __init__(self				: Dict      ,	snake_case				: Dict      ,	snake_case				: List[Any]=13      ,	snake_case				: int=7      ,	snake_case				: List[str]=True      ,	snake_case				: List[Any]=True      ,	snake_case				: Union[str, Any]=True      ,	snake_case				: Dict=True      ,	snake_case				: Optional[Any]=99      ,	snake_case				: str=32      ,	snake_case				: Any=2      ,	snake_case				: Optional[Any]=4      ,	snake_case				: int=37      ,	snake_case				: Dict="gelu"      ,	snake_case				: Dict=0.1      ,	snake_case				: Dict=0.1      ,	snake_case				: Optional[int]=512      ,	snake_case				: Dict=16      ,	snake_case				: Union[str, Any]=2      ,	snake_case				: Dict=0.02      ,	snake_case				: str=3      ,	snake_case				: str=4      ,	snake_case				: Optional[Any]=None      ,	snake_case				: str=0      ,	) ->			Optional[Any]:
							_lowercase       :	int           =   parent
							_lowercase       :	Tuple           =   batch_size
							_lowercase       :	str           =   seq_length
							_lowercase       :	Optional[Any]           =   is_training
							_lowercase       :	List[Any]           =   use_input_mask
							_lowercase       :	Tuple           =   use_token_type_ids
							_lowercase       :	List[Any]           =   use_labels
							_lowercase       :	List[str]           =   vocab_size
							_lowercase       :	Dict           =   hidden_size
							_lowercase       :	str           =   num_hidden_layers
							_lowercase       :	Tuple           =   num_attention_heads
							_lowercase       :	Dict           =   intermediate_size
							_lowercase       :	List[Any]           =   hidden_act
							_lowercase       :	Optional[Any]           =   hidden_dropout_prob
							_lowercase       :	Dict           =   attention_probs_dropout_prob
							_lowercase       :	int           =   max_position_embeddings
							_lowercase       :	Tuple           =   type_vocab_size
							_lowercase       :	List[str]           =   type_sequence_label_size
							_lowercase       :	str           =   initializer_range
							_lowercase       :	Tuple           =   num_labels
							_lowercase       :	List[Any]           =   num_choices
							_lowercase       :	Dict           =   scope
							_lowercase       :	Optional[Any]           =   projection_dim






	def       _a(self				: Tuple    ) ->			List[str]:
							_lowercase       :	Optional[int]           =   ids_tensor([self.batch_size, self.seq_length]      ,	self.vocab_size    )

							_lowercase       :	Optional[int]           =   None
							if self.use_input_mask:
													# follow test_modeling_tf_ctrl.py
													_lowercase       :	List[Any]           =   random_attention_mask([self.batch_size, self.seq_length]    )

							_lowercase       :	List[Any]           =   None
							if self.use_token_type_ids:
													_lowercase       :	List[Any]           =   ids_tensor([self.batch_size, self.seq_length]      ,	self.type_vocab_size    )

							_lowercase       :	Tuple           =   None
							_lowercase       :	Optional[Any]           =   None
							_lowercase       :	Optional[Any]           =   None
							if self.use_labels:
													_lowercase       :	Optional[Any]           =   ids_tensor([self.batch_size]      ,	self.type_sequence_label_size    )
													_lowercase       :	Union[str, Any]           =   ids_tensor([self.batch_size, self.seq_length]      ,	self.num_labels    )
													_lowercase       :	List[str]           =   ids_tensor([self.batch_size]      ,	self.num_choices    )

							_lowercase       :	Union[str, Any]           =   BertConfig(
							    vocab_size=self.vocab_size      ,	hidden_size=self.hidden_size      ,	num_hidden_layers=self.num_hidden_layers      ,	num_attention_heads=self.num_attention_heads      ,	intermediate_size=self.intermediate_size      ,	hidden_act=self.hidden_act      ,	hidden_dropout_prob=self.hidden_dropout_prob      ,	attention_probs_dropout_prob=self.attention_probs_dropout_prob      ,	max_position_embeddings=self.max_position_embeddings      ,	type_vocab_size=self.type_vocab_size      ,	is_decoder=snake_case      ,	initializer_range=self.initializer_range      ,	)
							_lowercase       :	Any           =   DPRConfig(projection_dim=self.projection_dim      ,	**config.to_dict()    )

							return config, input_ids, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels






	def       _a(self				: Union[str, Any]      ,	snake_case				: Any      ,	snake_case				: Tuple      ,	snake_case				: str      ,	snake_case				: str      ,	snake_case				: Union[str, Any]      ,	snake_case				: Tuple      ,	snake_case				: str    ) ->			List[str]:
							_lowercase       :	List[Any]           =   TFDPRContextEncoder(config=snake_case    )
							_lowercase       :	Dict           =   model(snake_case      ,	attention_mask=snake_case      ,	token_type_ids=snake_case    )
							_lowercase       :	Optional[int]           =   model(snake_case      ,	token_type_ids=snake_case    )
							_lowercase       :	Union[str, Any]           =   model(snake_case    )
							self.parent.assertEqual(result.pooler_output.shape      ,	(self.batch_size, self.projection_dim or self.hidden_size)    )






	def       _a(self				: List[Any]      ,	snake_case				: List[str]      ,	snake_case				: Tuple      ,	snake_case				: Any      ,	snake_case				: int      ,	snake_case				: Optional[int]      ,	snake_case				: Any      ,	snake_case				: Union[str, Any]    ) ->			int:
							_lowercase       :	Optional[Any]           =   TFDPRQuestionEncoder(config=snake_case    )
							_lowercase       :	int           =   model(snake_case      ,	attention_mask=snake_case      ,	token_type_ids=snake_case    )
							_lowercase       :	str           =   model(snake_case      ,	token_type_ids=snake_case    )
							_lowercase       :	str           =   model(snake_case    )
							self.parent.assertEqual(result.pooler_output.shape      ,	(self.batch_size, self.projection_dim or self.hidden_size)    )






	def       _a(self				: Union[str, Any]      ,	snake_case				: Any      ,	snake_case				: int      ,	snake_case				: List[str]      ,	snake_case				: Union[str, Any]      ,	snake_case				: Tuple      ,	snake_case				: Optional[Any]      ,	snake_case				: Union[str, Any]    ) ->			Any:
							_lowercase       :	Any           =   TFDPRReader(config=snake_case    )
							_lowercase       :	Optional[Any]           =   model(snake_case      ,	attention_mask=snake_case    )

							self.parent.assertEqual(result.start_logits.shape      ,	(self.batch_size, self.seq_length)    )
							self.parent.assertEqual(result.end_logits.shape      ,	(self.batch_size, self.seq_length)    )
							self.parent.assertEqual(result.relevance_logits.shape      ,	(self.batch_size,)    )






	def       _a(self				: int    ) ->			Optional[Any]:
							_lowercase       :	Union[str, Any]           =   self.prepare_config_and_inputs()
							(
							    (
							    _lowercase
							)      ,    (
							    _lowercase
							)      ,    (
							    _lowercase
							)      ,    (
							    _lowercase
							)      ,    (
							    _lowercase
							)      ,    (
							    _lowercase
							)      ,    (
							    _lowercase
							)      ,    
							)       :	int           =   config_and_inputs
							_lowercase       :	int           =   {"input_ids": input_ids}
							return config, inputs_dict




@require_tf
class   __lowercase						(						__snake_case   , __snake_case   , unittest.TestCase       ):
	_A       =   (
	    (
	        TFDPRContextEncoder,
	        TFDPRQuestionEncoder,
	        TFDPRReader,
	    )
	    if is_tf_available()
	    else ()
	)
	_A       =   {"feature-extraction": TFDPRQuestionEncoder} if is_tf_available() else {}

	_A       =   False
	_A       =   False
	_A       =   False
	_A       =   False
	_A       =   False






	def       _a(self				: str    ) ->			List[str]:
							_lowercase       :	List[Any]           =   TFDPRModelTester(self    )
							_lowercase       :	Any           =   ConfigTester(self      ,	config_class=snake_case      ,	hidden_size=37    )






	def       _a(self				: str    ) ->			Union[str, Any]:
							self.config_tester.run_common_tests()






	def       _a(self				: Any    ) ->			Tuple:
							_lowercase       :	List[str]           =   self.model_tester.prepare_config_and_inputs()
							self.model_tester.create_and_check_dpr_context_encoder(*snake_case    )






	def       _a(self				: Dict    ) ->			Optional[Any]:
							_lowercase       :	str           =   self.model_tester.prepare_config_and_inputs()
							self.model_tester.create_and_check_dpr_question_encoder(*snake_case    )






	def       _a(self				: List[Any]    ) ->			Any:
							_lowercase       :	Optional[Any]           =   self.model_tester.prepare_config_and_inputs()
							self.model_tester.create_and_check_dpr_reader(*snake_case    )






	@slow
	def       _a(self				: int    ) ->			str:
							for model_name in TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
													_lowercase       :	str           =   TFDPRContextEncoder.from_pretrained(snake_case    )
													self.assertIsNotNone(snake_case    )

							for model_name in TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
													_lowercase       :	List[str]           =   TFDPRContextEncoder.from_pretrained(snake_case    )
													self.assertIsNotNone(snake_case    )

							for model_name in TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
													_lowercase       :	int           =   TFDPRQuestionEncoder.from_pretrained(snake_case    )
													self.assertIsNotNone(snake_case    )

							for model_name in TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
													_lowercase       :	Any           =   TFDPRReader.from_pretrained(snake_case    )
													self.assertIsNotNone(snake_case    )




@require_tf
class   __lowercase						(						unittest.TestCase       ):






	@slow
	def       _a(self				: Dict    ) ->			Any:
							_lowercase       :	Any           =   TFDPRQuestionEncoder.from_pretrained("facebook/dpr-question_encoder-single-nq-base"    )

							_lowercase       :	Optional[int]           =   tf.constant(
							    [[101, 7592, 1010, 2003, 2026, 3899, 1_0140, 1029, 102]]    )  # [CLS] hello, is my dog cute? [SEP]
							_lowercase       :	List[Any]           =   model(snake_case    )[0]  # embedding shape = (1, 768)
							# compare the actual values for a slice.
							_lowercase       :	Optional[Any]           =   tf.constant(
							    [
							        [
							            0.03_23_62_53,
							            0.12_75_33_35,
							            0.16_81_85_09,
							            0.00_27_97_86,
							            0.3_89_69_33,
							            0.24_26_49_45,
							            0.2_17_89_71,
							            -0.02_33_52_27,
							            -0.08_48_19_59,
							            -0.14_32_41_17,
							        ]
							    ]    )
							self.assertTrue(numpy.allclose(output[:, :10].numpy()      ,	expected_slice.numpy()      ,	atol=1e-4    )    )




