





import itertools
import random
import unittest

import numpy as np

from transformers import EncodecFeatureExtractor
from transformers.testing_utils import require_torch
from transformers.utils.import_utils import is_torch_available

from ...test_sequence_feature_extraction_common import SequenceFeatureExtractionTestMixin


if is_torch_available():
				import torch


SCREAMING_SNAKE_CASE_      :			Optional[int]		  =      random.Random()



def    SCREAMING_SNAKE_CASE							(			snake_case	,      snake_case=1.0	,      snake_case=None	,      snake_case=None       )		->						Dict:
		if rng is None:
				__lowercase					=    global_rng

		__lowercase					=    []
		for batch_idx in range(shape[0]       ):
				values.append([]       )
				for _ in range(shape[1]       ):
						values[-1].append(rng.random() * scale       )

		return values

@require_torch
class 		snake_case_      (       unittest.TestCase	):







	'''simple docstring'''




	def __init__(	self       :    List[Any]				,			__lowerCamelCase       :    Optional[int]				,			__lowerCamelCase       :    Any=7				,			__lowerCamelCase       :    str=400				,			__lowerCamelCase       :    str=2_000				,			__lowerCamelCase       :    Optional[int]=1				,			__lowerCamelCase       :    List[str]=0.0				,			__lowerCamelCase       :    Tuple=24_000				,			__lowerCamelCase       :    Any=True				,			)					->   List[str]:

			'''simple docstring'''




			__lowercase					=    parent
			__lowercase					=    batch_size
			__lowercase					=    min_seq_length
			__lowercase					=    max_seq_length
			__lowercase					=    (self.max_seq_length - self.min_seq_length) // (self.batch_size - 1)
			__lowercase					=    feature_size
			__lowercase					=    padding_value
			__lowercase					=    sampling_rate
			__lowercase					=    return_attention_mask




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

			'''simple docstring'''




			return {
			    "feature_size": self.feature_size,
			    "padding_value": self.padding_value,
			    "sampling_rate": self.sampling_rate,
			    "return_attention_mask": self.return_attention_mask,
			}






	def       UpperCAmelCase (	self       :    Optional[int]				,			__lowerCamelCase       :    Optional[Any]=False				,			__lowerCamelCase       :    Union[str, Any]=False      )					->   Optional[int]:

			'''simple docstring'''




			def _flatten(__lowerCamelCase       :    List[Any]      ):
					return list(itertools.chain(*__lowerCamelCase      )      )

			if equal_length:
					__lowercase					=    floats_list((self.batch_size, self.max_seq_length)      )
			else:
					# make sure that inputs increase in size
					__lowercase					=    [
					    _flatten(floats_list((x, self.feature_size)      )      )
					    for x in range(self.min_seq_length				,			self.max_seq_length				,			self.seq_length_diff      )
					]

			if numpify:
					__lowercase					=    [np.asarray(__lowerCamelCase      ) for x in audio_inputs]

			return audio_inputs





@require_torch
class 		snake_case_      (       UpperCAmelCase_    ,    unittest.TestCase	):







	'''simple docstring'''
	__UpperCamelCase        =		EncodecFeatureExtractor




	def       UpperCAmelCase (	self       :    Optional[Any]      )					->   str:

			'''simple docstring'''




			__lowercase					=    EnCodecFeatureExtractionTester(self      )




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

			'''simple docstring'''




			__lowercase					=    self.feature_extraction_class(**self.feat_extract_tester.prepare_feat_extract_dict()      )
			# create three inputs of length 800, 1000, and 1200
			__lowercase					=    [floats_list((1, x)      )[0] for x in range(800				,			1_400				,			200      )]
			__lowercase					=    [np.asarray(__lowerCamelCase      ) for audio_input in audio_inputs]

			# Test not batched input
			__lowercase					=    feat_extract(audio_inputs[0]				,			return_tensors='np'      ).input_values
			__lowercase					=    feat_extract(np_audio_inputs[0]				,			return_tensors='np'      ).input_values
			self.assertTrue(np.allclose(__lowerCamelCase				,			__lowerCamelCase				,			atol=1E-3      )      )

			# Test batched
			__lowercase					=    feat_extract(__lowerCamelCase				,			padding=__lowerCamelCase				,			return_tensors='np'      ).input_values
			__lowercase					=    feat_extract(__lowerCamelCase				,			padding=__lowerCamelCase				,			return_tensors='np'      ).input_values
			for enc_seq_a, enc_seq_a in zip(__lowerCamelCase				,			__lowerCamelCase      ):
					self.assertTrue(np.allclose(__lowerCamelCase				,			__lowerCamelCase				,			atol=1E-3      )      )




	def       UpperCAmelCase (	self       :    Dict      )					->   int:

			'''simple docstring'''




			__lowercase					=    self.feature_extraction_class(**self.feat_extract_tester.prepare_feat_extract_dict()      )
			__lowercase					=    np.random.rand(100      ).astype(np.floataa      )
			__lowercase					=    np_audio_inputs.tolist()

			for inputs in [py_audio_inputs, np_audio_inputs]:
					__lowercase					=    feature_extractor.pad([{'input_values': inputs}]				,			return_tensors='np'      )
					self.assertTrue(np_processed.input_values.dtype == np.floataa      )
					__lowercase					=    feature_extractor.pad([{'input_values': inputs}]				,			return_tensors='pt'      )
					self.assertTrue(pt_processed.input_values.dtype == torch.floataa      )




	def       UpperCAmelCase (	self       :    Tuple				,			__lowerCamelCase       :    Any      )					->   Tuple:

			'''simple docstring'''




			from datasets import load_dataset

			__lowercase					=    load_dataset('hf-internal-testing/librispeech_asr_dummy'				,			'clean'				,			split='validation'      )
			# automatic decoding with librispeech
			__lowercase					=    ds.sort('id'      ).select(range(__lowerCamelCase      )      )[:num_samples]['audio']

			return [x["array"] for x in audio_samples]




	def       UpperCAmelCase (	self       :    List[str]      )					->   str:

			'''simple docstring'''




			__lowercase					=    torch.tensor(
			    [2.3_8_0_4E-0_3, 2.0_7_5_2E-0_3, 1.9_8_3_6E-0_3, 2.1_0_5_7E-0_3, 1.6_1_7_4E-0_3,
			     3.0_5_1_8E-0_4, 9.1_5_5_3E-0_5, 3.3_5_6_9E-0_4, 9.7_6_5_6E-0_4, 1.8_3_1_1E-0_3,
			     2.0_1_4_2E-0_3, 2.1_0_5_7E-0_3, 1.7_3_9_5E-0_3, 4.5_7_7_6E-0_4, -3.9_6_7_3E-0_4,
			     4.5_7_7_6E-0_4, 1.0_0_7_1E-0_3, 9.1_5_5_3E-0_5, 4.8_8_2_8E-0_4, 1.1_5_9_7E-0_3,
			     7.3_2_4_2E-0_4, 9.4_6_0_4E-0_4, 1.8_0_0_5E-0_3, 1.8_3_1_1E-0_3, 8.8_5_0_1E-0_4,
			     4.2_7_2_5E-0_4, 4.8_8_2_8E-0_4, 7.3_2_4_2E-0_4, 1.0_9_8_6E-0_3, 2.1_0_5_7E-0_3]      )
			# fmt: on
			__lowercase					=    self._load_datasamples(1      )
			__lowercase					=    EncodecFeatureExtractor()
			__lowercase					=    feature_extractor(__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(input_values.shape				,			(1, 1, 93_680)      )
			self.assertTrue(torch.allclose(input_values[0, 0, :30]				,			__lowerCamelCase				,			atol=1E-6      )      )




	def       UpperCAmelCase (	self       :    str      )					->   str:

			'''simple docstring'''




			__lowercase					=    torch.tensor(
			    [2.3_8_0_4E-0_3, 2.0_7_5_2E-0_3, 1.9_8_3_6E-0_3, 2.1_0_5_7E-0_3, 1.6_1_7_4E-0_3,
			     3.0_5_1_8E-0_4, 9.1_5_5_3E-0_5, 3.3_5_6_9E-0_4, 9.7_6_5_6E-0_4, 1.8_3_1_1E-0_3,
			     2.0_1_4_2E-0_3, 2.1_0_5_7E-0_3, 1.7_3_9_5E-0_3, 4.5_7_7_6E-0_4, -3.9_6_7_3E-0_4,
			     4.5_7_7_6E-0_4, 1.0_0_7_1E-0_3, 9.1_5_5_3E-0_5, 4.8_8_2_8E-0_4, 1.1_5_9_7E-0_3,
			     7.3_2_4_2E-0_4, 9.4_6_0_4E-0_4, 1.8_0_0_5E-0_3, 1.8_3_1_1E-0_3, 8.8_5_0_1E-0_4,
			     4.2_7_2_5E-0_4, 4.8_8_2_8E-0_4, 7.3_2_4_2E-0_4, 1.0_9_8_6E-0_3, 2.1_0_5_7E-0_3]      )
			# fmt: on
			__lowercase					=    self._load_datasamples(1      )
			__lowercase					=    [np.tile(input_audio[0][None]				,			reps=(2, 1)      )]
			input_audio[0][1] *= 0.5
			__lowercase					=    EncodecFeatureExtractor(feature_size=2      )
			__lowercase					=    feature_extractor(__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(input_values.shape				,			(1, 2, 93_680)      )
			self.assertTrue(torch.allclose(input_values[0, 0, :30]				,			__lowerCamelCase				,			atol=1E-6      )      )
			self.assertTrue(torch.allclose(input_values[0, 1, :30]				,			EXPECTED_INPUT_VALUES * 0.5				,			atol=1E-6      )      )






	def       UpperCAmelCase (	self       :    Dict      )					->   Union[str, Any]:

			'''simple docstring'''




			__lowercase					=    self._load_datasamples(2      )
			# would be easier if the stride was like
			__lowercase					=    EncodecFeatureExtractor(feature_size=1				,			chunk_length_s=1				,			overlap=0.01      )

			# pad and trunc raise an error ?
			with self.assertRaisesRegex(
			    __lowerCamelCase				,			'^Both padding and truncation were set. Make sure you only set one.$'				,			):
					__lowercase					=    feature_extractor(
					    __lowerCamelCase				,			padding='max_length'				,			truncation=__lowerCamelCase				,			return_tensors='pt'      ).input_values

			# truncate to chunk
			__lowercase					=    feature_extractor(__lowerCamelCase				,			truncation=__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(2, 1, 71_520)      )  # 2 chunks

			# force truncate to max_length
			__lowercase					=    feature_extractor(
			    __lowerCamelCase				,			truncation=__lowerCamelCase				,			max_length=48_000				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(2, 1, 48_000)      )

			# pad to chunk
			__lowercase					=    feature_extractor(__lowerCamelCase				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(padded_outputs.shape				,			(2, 1, 95_280)      )

			# pad to chunk
			__lowercase					=    feature_extractor(__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(2, 1, 95_280)      )

			# force pad to max length
			__lowercase					=    feature_extractor(
			    __lowerCamelCase				,			padding='max_length'				,			max_length=100_000				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(2, 1, 100_000)      )

			# force no pad
			with self.assertRaisesRegex(
			    __lowerCamelCase				,			'^Unable to create tensor, you should probably activate padding with \'padding=True\' to have batched tensors with the same length.$'				,			):
					__lowercase					=    feature_extractor(__lowerCamelCase				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values

			__lowercase					=    feature_extractor(input_audio[0]				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(1, 1, 93_680)      )

			# no pad if no chunk_length_s
			__lowercase					=    None
			with self.assertRaisesRegex(
			    __lowerCamelCase				,			'^Unable to create tensor, you should probably activate padding with \'padding=True\' to have batched tensors with the same length.$'				,			):
					__lowercase					=    feature_extractor(__lowerCamelCase				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values

			__lowercase					=    feature_extractor(input_audio[0]				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(1, 1, 93_680)      )

			# no pad if no overlap
			__lowercase					=    2
			__lowercase					=    None
			with self.assertRaisesRegex(
			    __lowerCamelCase				,			'^Unable to create tensor, you should probably activate padding with \'padding=True\' to have batched tensors with the same length.$'				,			):
					__lowercase					=    feature_extractor(__lowerCamelCase				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values

			__lowercase					=    feature_extractor(input_audio[0]				,			padding=__lowerCamelCase				,			return_tensors='pt'      ).input_values
			self.assertEquals(truncated_outputs.shape				,			(1, 1, 93_680)      )











from math import floor, sqrt



def    SCREAMING_SNAKE_CASE							(			snake_case       )		->						int:
		__lowercase					=    0.0
		__lowercase					=    1.0
		__lowercase					=    int(sqrt(snake_case       )       )
		__lowercase					=    root
		__lowercase					=    0
		while integer_part != 2 * root:
				__lowercase					=    denominator * integer_part - numerator
				__lowercase					=    (n - numerator**2) / denominator
				__lowercase					=    int((root + numerator) / denominator       )
				period += 1
		return period



def    SCREAMING_SNAKE_CASE							(			snake_case = 10_000       )		->						int:
		__lowercase					=    0
		for i in range(2	,      n + 1       ):
				__lowercase					=    sqrt(snake_case       )
				if sr - floor(snake_case       ) != 0 and continuous_fraction_period(snake_case       ) % 2 == 1:
						count_odd_periods += 1
		return count_odd_periods


if __name__ == "__main__":
		print(F"""{solution(int(input().strip()))}""")




