





import numpy as np

from transformers import BatchFeature
from transformers.testing_utils import require_tf, require_torch

from .test_feature_extraction_common import FeatureExtractionSavingTestMixin
class 			UpperCamelCase_		(  _lowerCamelCase					):
					# to overwrite at feature extractactor specific tests
					lowerCAmelCase_							=	None
					lowerCAmelCase_							=	None




					@property
					def 	lowerCAmelCase			(		self  )		->							Union[str, Any]:
										return self.feat_extract_tester.prepare_feat_extract_dict()




					def 	lowerCAmelCase			(		self  )		->							Optional[int]:
										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										self.assertTrue(hasattr(lowerCAmelCase_				,						'feature_size'  )  )
										self.assertTrue(hasattr(lowerCAmelCase_				,						'sampling_rate'  )  )
										self.assertTrue(hasattr(lowerCAmelCase_				,						'padding_value'  )  )




					def 	lowerCAmelCase			(		self  )		->							Optional[int]:
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common()
										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )

										self.assertTrue(all(len(lowerCAmelCase_  ) == len(lowerCAmelCase_  ) for x, y in zip(lowerCAmelCase_				,						processed_features[input_name]  )  )  )

										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common(equal_length=lowerCAmelCase_  )
										_snake_case									=				BatchFeature({input_name: speech_inputs}				,						tensor_type='np'  )

										_snake_case									=				processed_features[input_name]

										if len(batch_features_input.shape  ) < 3:
															_snake_case									=				batch_features_input[:, :, None]

										self.assertTrue(
										    batch_features_input.shape
										    == (self.feat_extract_tester.batch_size, len(speech_inputs[0]  ), self.feat_extract_tester.feature_size)  )




					@require_torch
					def 	lowerCAmelCase			(		self  )		->							Union[str, Any]:
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common(equal_length=lowerCAmelCase_  )
										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}				,						tensor_type='pt'  )

										_snake_case									=				processed_features[input_name]

										if len(batch_features_input.shape  ) < 3:
															_snake_case									=				batch_features_input[:, :, None]

										self.assertTrue(
										    batch_features_input.shape
										    == (self.feat_extract_tester.batch_size, len(speech_inputs[0]  ), self.feat_extract_tester.feature_size)  )




					@require_tf
					def 	lowerCAmelCase			(		self  )		->							Optional[Any]:
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common(equal_length=lowerCAmelCase_  )
										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}				,						tensor_type='tf'  )

										_snake_case									=				processed_features[input_name]

										if len(batch_features_input.shape  ) < 3:
															_snake_case									=				batch_features_input[:, :, None]

										self.assertTrue(
										    batch_features_input.shape
										    == (self.feat_extract_tester.batch_size, len(speech_inputs[0]  ), self.feat_extract_tester.feature_size)  )




					def 	lowerCAmelCase			(		self				,						lowerCAmelCase_=False  )		->							List[Any]:
										def _inputs_have_equal_length(lowerCAmelCase_  ):
															_snake_case									=				len(input[0]  )
															for input_slice in input[1:]:
																				if len(lowerCAmelCase_  ) != length:
																									return False
															return True

										def _inputs_are_equal(lowerCAmelCase_				,						lowerCAmelCase_  ):
															if len(lowerCAmelCase_  ) != len(lowerCAmelCase_  ):
																				return False

															for input_slice_a, input_slice_a in zip(lowerCAmelCase_				,						lowerCAmelCase_  ):
																				if not np.allclose(np.asarray(lowerCAmelCase_  )				,						np.asarray(lowerCAmelCase_  )				,						atol=1E-3  ):
																									return False
															return True

										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common(numpify=lowerCAmelCase_  )
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )

										_snake_case									=				self.feat_extract_tester.seq_length_diff
										_snake_case									=				self.feat_extract_tester.max_seq_length + pad_diff
										_snake_case									=				self.feat_extract_tester.min_seq_length
										_snake_case									=				self.feat_extract_tester.batch_size
										_snake_case									=				self.feat_extract_tester.feature_size

										# test padding for List[int] + numpy
										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding=lowerCAmelCase_  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[-1]  )  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						return_tensors='np'  )
										_snake_case									=				input_a[input_name]

										# max_length parameter has to be provided when setting `padding="max_length"`
										with self.assertRaises(lowerCAmelCase_  ):
															feat_extract.pad(lowerCAmelCase_				,						padding='max_length'  )[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=lowerCAmelCase_				,						return_tensors='np'  )
										_snake_case									=				input_a[input_name]

										self.assertFalse(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(_inputs_are_equal(lowerCAmelCase_				,						lowerCAmelCase_  )  )
										self.assertTrue(len(input_a[0]  ) == pad_min_length  )
										self.assertTrue(len(input_a[1]  ) == pad_min_length + pad_diff  )
										self.assertTrue(input_a.shape[:2] == (batch_size, len(input_a[0]  ))  )
										self.assertTrue(input_a.shape[:2] == (batch_size, pad_max_length)  )

										if feature_size > 1:
															self.assertTrue(input_a.shape[2] == input_a.shape[2] == feature_size  )

										# test padding for `pad_to_multiple_of` for List[int] + numpy
										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						pad_to_multiple_of=10  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						pad_to_multiple_of=10  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						pad_to_multiple_of=10				,						max_length=lowerCAmelCase_  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						pad_to_multiple_of=10				,						max_length=lowerCAmelCase_				,						return_tensors='np'				,						)
										_snake_case									=				input_a[input_name]

										self.assertTrue(all(len(lowerCAmelCase_  ) % 10 == 0 for x in input_a  )  )
										self.assertTrue(_inputs_are_equal(lowerCAmelCase_				,						lowerCAmelCase_  )  )

										_snake_case									=				pad_max_length if pad_max_length % 10 == 0 else (pad_max_length // 10 + 1) * 10
										self.assertTrue(all(len(lowerCAmelCase_  ) == expected_mult_pad_length for x in input_a  )  )
										self.assertEqual(input_a.shape[:2]				,						(batch_size, expected_mult_pad_length)  )

										if feature_size > 1:
															self.assertTrue(input_a.shape[2] == feature_size  )

										# Check padding value is correct
										_snake_case									=				(np.ones(self.feat_extract_tester.feature_size  ) * feat_extract.padding_value).sum()
										self.assertTrue(
										    abs(np.asarray(input_a[0]  )[pad_min_length:].sum() - padding_vector_sum * (pad_max_length - pad_min_length)  )
										    < 1E-3  )
										self.assertTrue(
										    abs(
										        np.asarray(input_a[1]  )[pad_min_length + pad_diff :].sum()
										        - padding_vector_sum * (pad_max_length - pad_min_length - pad_diff)  )
										    < 1E-3  )
										self.assertTrue(
										    abs(
										        np.asarray(input_a[2]  )[pad_min_length + 2 * pad_diff :].sum()
										        - padding_vector_sum * (pad_max_length - pad_min_length - 2 * pad_diff)  )
										    < 1E-3  )
										self.assertTrue(
										    abs(input_a[0, pad_min_length:].sum() - padding_vector_sum * (pad_max_length - pad_min_length)  ) < 1E-3  )
										self.assertTrue(
										    abs(input_a[0, pad_min_length:].sum() - padding_vector_sum * (expected_mult_pad_length - pad_min_length)  )
										    < 1E-3  )




					def 	lowerCAmelCase			(		self				,						lowerCAmelCase_=False  )		->							Union[str, Any]:
										def _inputs_have_equal_length(lowerCAmelCase_  ):
															_snake_case									=				len(input[0]  )
															for input_slice in input[1:]:
																				if len(lowerCAmelCase_  ) != length:
																									return False
															return True

										def _inputs_are_equal(lowerCAmelCase_				,						lowerCAmelCase_  ):
															if len(lowerCAmelCase_  ) != len(lowerCAmelCase_  ):
																				return False

															for input_slice_a, input_slice_a in zip(lowerCAmelCase_				,						lowerCAmelCase_  ):
																				if not np.allclose(np.asarray(lowerCAmelCase_  )				,						np.asarray(lowerCAmelCase_  )				,						atol=1E-3  ):
																									return False
															return True

										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common(numpify=lowerCAmelCase_  )
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )

										# truncate to smallest
										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[0]  )				,						truncation=lowerCAmelCase_  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[0]  )  )
										_snake_case									=				input_a[input_name]

										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertFalse(_inputs_have_equal_length(lowerCAmelCase_  )  )

										# truncate to smallest with np
										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[0]  )				,						return_tensors='np'				,						truncation=lowerCAmelCase_				,						)
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[0]  )				,						return_tensors='np'  )
										_snake_case									=				input_a[input_name]

										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(input_a.shape[1] == len(speech_inputs[0]  )  )

										# since truncation forces padding to be smaller than longest input
										# function can't return `np.ndarray`, but has to return list
										self.assertFalse(_inputs_have_equal_length(lowerCAmelCase_  )  )

										# truncate to middle
										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[1]  )				,						truncation=lowerCAmelCase_				,						return_tensors='np'				,						)
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[1]  )				,						truncation=lowerCAmelCase_  )
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[1]  )				,						return_tensors='np'  )
										_snake_case									=				input_a[input_name]

										self.assertTrue(input_a.shape[1] == len(speech_inputs[1]  )  )
										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(_inputs_are_equal(lowerCAmelCase_				,						lowerCAmelCase_  )  )

										# since truncation forces padding to be smaller than longest input
										# function can't return `np.ndarray`, but has to return list
										self.assertFalse(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertTrue(len(input_a[-1]  ) == len(speech_inputs[-1]  )  )

										# padding has to be max_length when setting `truncation=True`
										with self.assertRaises(lowerCAmelCase_  ):
															feat_extract.pad(lowerCAmelCase_				,						truncation=lowerCAmelCase_  )[input_name]

										# padding has to be max_length when setting `truncation=True`
										with self.assertRaises(lowerCAmelCase_  ):
															feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						truncation=lowerCAmelCase_  )[input_name]

										# padding has to be max_length when setting `truncation=True`
										with self.assertRaises(lowerCAmelCase_  ):
															feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						truncation=lowerCAmelCase_  )[input_name]

										# max_length parameter has to be provided when setting `truncation=True` and padding="max_length"
										with self.assertRaises(lowerCAmelCase_  ):
															feat_extract.pad(lowerCAmelCase_				,						padding='max_length'				,						truncation=lowerCAmelCase_  )[input_name]

										# test truncation for `pad_to_multiple_of` for List[int] + numpy
										_snake_case									=				12
										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[0]  )				,						pad_to_multiple_of=lowerCAmelCase_				,						truncation=lowerCAmelCase_				,						)
										_snake_case									=				input_a[input_name]

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=len(speech_inputs[0]  )				,						pad_to_multiple_of=lowerCAmelCase_				,						)
										_snake_case									=				input_a[input_name]

										# retrieve expected_length as multiple of pad_to_multiple_of
										_snake_case									=				len(speech_inputs[0]  )
										if expected_length % pad_to_multiple_of != 0:
															_snake_case									=				((len(speech_inputs[0]  ) // pad_to_multiple_of) + 1) * pad_to_multiple_of

										self.assertTrue(len(input_a[0]  ) == expected_length  )
										self.assertTrue(_inputs_have_equal_length(lowerCAmelCase_  )  )
										self.assertFalse(_inputs_have_equal_length(lowerCAmelCase_  )  )




					def 	lowerCAmelCase			(		self  )		->							Tuple:
										self._check_padding(numpify=lowerCAmelCase_  )




					def 	lowerCAmelCase			(		self  )		->							List[str]:
										self._check_padding(numpify=lowerCAmelCase_  )




					def 	lowerCAmelCase			(		self  )		->							List[str]:
										self._check_truncation(numpify=lowerCAmelCase_  )




					def 	lowerCAmelCase			(		self  )		->							List[str]:
										self._check_truncation(numpify=lowerCAmelCase_  )




					@require_torch
					def 	lowerCAmelCase			(		self  )		->							str:
										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common()
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						return_tensors='np'  )[input_name]
										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						return_tensors='pt'  )[input_name]

										self.assertTrue(abs(input_np.astype(np.floataa  ).sum() - input_pt.numpy().astype(np.floataa  ).sum()  ) < 1E-2  )




					@require_tf
					def 	lowerCAmelCase			(		self  )		->							List[str]:
										_snake_case									=				self.feature_extraction_class(**self.feat_extract_dict  )
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common()
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						return_tensors='np'  )[input_name]
										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						return_tensors='tf'  )[input_name]

										self.assertTrue(abs(input_np.astype(np.floataa  ).sum() - input_tf.numpy().astype(np.floataa  ).sum()  ) < 1E-2  )




					def 	lowerCAmelCase			(		self  )		->							List[str]:
										_snake_case									=				self.feat_extract_dict
										_snake_case									=				True
										_snake_case									=				self.feature_extraction_class(**lowerCAmelCase_  )
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common()
										_snake_case									=				[len(lowerCAmelCase_  ) for x in speech_inputs]
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )

										_snake_case									=				feat_extract.pad(lowerCAmelCase_				,						padding='longest'				,						return_tensors='np'  )
										self.assertIn('attention_mask'				,						lowerCAmelCase_  )
										self.assertListEqual(list(processed.attention_mask.shape  )				,						list(processed[input_name].shape[:2]  )  )
										self.assertListEqual(processed.attention_mask.sum(-1  ).tolist()				,						lowerCAmelCase_  )






					def 	lowerCAmelCase			(		self  )		->							List[str]:
										_snake_case									=				self.feat_extract_dict
										_snake_case									=				True
										_snake_case									=				self.feature_extraction_class(**lowerCAmelCase_  )
										_snake_case									=				self.feat_extract_tester.prepare_inputs_for_common()
										_snake_case									=				[len(lowerCAmelCase_  ) for x in speech_inputs]
										_snake_case									=				feat_extract.model_input_names[0]

										_snake_case									=				BatchFeature({input_name: speech_inputs}  )
										_snake_case									=				min(lowerCAmelCase_  )

										_snake_case									=				feat_extract.pad(
										    lowerCAmelCase_				,						padding='max_length'				,						max_length=lowerCAmelCase_				,						truncation=lowerCAmelCase_				,						return_tensors='np'  )
										self.assertIn('attention_mask'				,						lowerCAmelCase_  )
										self.assertListEqual(
										    list(processed_pad.attention_mask.shape  )				,						[processed_pad[input_name].shape[0], max_length]  )
										self.assertListEqual(
										    processed_pad.attention_mask[:, :max_length].sum(-1  ).tolist()				,						[max_length for x in speech_inputs]  )










UpperCAmelCase_      							=     range(2, 20 + 1)
UpperCAmelCase_      							=     [10**k for k in range(ks[-1] + 1)]
UpperCAmelCase_      							=     {}





def 						lowerCamelCase__     (     UpperCamelCase__			:       Optional[Any]       ,    UpperCamelCase__			:       List[Any]       ,    UpperCamelCase__			:       Union[str, Any]       ,    UpperCamelCase__			:       str						)			-> List[str]:



					'''simple docstring'''




					_snake_case									=				sum(a_i[j] for j in range(UpperCamelCase__       ,    len(UpperCamelCase__						)						)						)
					_snake_case									=				sum(a_i[j] * base[j] for j in range(min(len(UpperCamelCase__						)       ,    UpperCamelCase__						)						)						)

					_snake_case							,     _snake_case									=				0, 0
					_snake_case									=				n - i

					_snake_case									=				memo.get(UpperCamelCase__						)

					if sub_memo is not None:
										_snake_case									=				sub_memo.get(UpperCamelCase__						)

										if jumps is not None and len(UpperCamelCase__						) > 0:
															# find and make the largest jump without going over
															_snake_case									=				-1
															for _k in range(len(UpperCamelCase__						) - 1       ,    -1       ,    -1						):
																				if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																									_snake_case									=				_k
																									break

															if max_jump >= 0:
																				_snake_case							,     _snake_case							,     _snake_case									=				jumps[max_jump]
																				# since the difference between jumps is cached, add c
																				_snake_case									=				diff + c
																				for j in range(min(UpperCamelCase__       ,    len(UpperCamelCase__						)						)						):
																									_snake_case							,     _snake_case									=				divmod(UpperCamelCase__       ,    10						)
																				if new_c > 0:
																									add(UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__						)

										else:
															_snake_case									=				[]
					else:
										_snake_case									=				{c: []}
										_snake_case									=				sub_memo

					if dn >= max_dn or c + diff >= base[k]:
										return diff, dn

					if k > ks[0]:
										while True:
															# keep doing smaller jumps
															_snake_case							,     _snake_case									=				next_term(UpperCamelCase__       ,    k - 1       ,    i + dn       ,    UpperCamelCase__						)
															diff += _diff
															dn += terms_jumped

															if dn >= max_dn or c + diff >= base[k]:
																				break
					else:
										# would be too small a jump, just compute sequential terms instead
										_snake_case							,     _snake_case									=				compute(UpperCamelCase__       ,    UpperCamelCase__       ,    i + dn       ,    UpperCamelCase__						)
										diff += _diff
										dn += terms_jumped

					_snake_case									=				sub_memo[c]

					# keep jumps sorted by # of terms skipped
					_snake_case									=				0
					while j < len(UpperCamelCase__						):
										if jumps[j][1] > dn:
															break
										j += 1

					# cache the jump for this value digitsum(b) and c
					sub_memo[c].insert(UpperCamelCase__       ,    (diff, dn, k)						)
					return (diff, dn)





def 						lowerCamelCase__     (     UpperCamelCase__			:       str       ,    UpperCamelCase__			:       str       ,    UpperCamelCase__			:       List[str]       ,    UpperCamelCase__			:       Union[str, Any]						)			-> Optional[Any]:



					'''simple docstring'''




					if i >= n:
										return 0, i
					if k > len(UpperCamelCase__						):
										a_i.extend([0 for _ in range(k - len(UpperCamelCase__						)						)]						)

					# note: a_i -> b * 10^k + c
					# ds_b -> digitsum(b)
					# ds_c -> digitsum(c)
					_snake_case									=				i
					_snake_case							,     _snake_case							,     _snake_case									=				0, 0, 0
					for j in range(len(UpperCamelCase__						)						):
										if j >= k:
															ds_b += a_i[j]
										else:
															ds_c += a_i[j]

					while i < n:
										i += 1
										_snake_case									=				ds_c + ds_b
										diff += addend
										_snake_case									=				0
										for j in range(UpperCamelCase__						):
															_snake_case									=				a_i[j] + addend
															_snake_case							,     _snake_case									=				divmod(UpperCamelCase__       ,    10						)

															ds_c += a_i[j]

										if addend > 0:
															break

					if addend > 0:
										add(UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__						)
					return diff, i - start_i





def 						lowerCamelCase__     (     UpperCamelCase__			:       Any       ,    UpperCamelCase__			:       Union[str, Any]       ,    UpperCamelCase__			:       Optional[Any]						)			-> Any:



					'''simple docstring'''




					for j in range(UpperCamelCase__       ,    len(UpperCamelCase__						)						):
										_snake_case									=				digits[j] + addend
										if s >= 10:
															_snake_case							,     _snake_case									=				divmod(UpperCamelCase__       ,    10						)
															_snake_case									=				addend // 10 + quotient
										else:
															_snake_case									=				s
															_snake_case									=				addend // 10

										if addend == 0:
															break

					while addend > 0:
										_snake_case							,     _snake_case									=				divmod(UpperCamelCase__       ,    10						)
										digits.append(UpperCamelCase__						)





def 						lowerCamelCase__     (     UpperCamelCase__			:       int = 10**15						)			-> int:



					'''simple docstring'''




					_snake_case									=				[1]
					_snake_case									=				1
					_snake_case									=				0
					while True:
										_snake_case							,     _snake_case									=				next_term(UpperCamelCase__       ,    20       ,    i + dn       ,    UpperCamelCase__						)
										dn += terms_jumped
										if dn == n - i:
															break

					_snake_case									=				0
					for j in range(len(UpperCamelCase__						)						):
										a_n += digits[j] * 10**j
					return a_n


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



