


def     lowerCAmelCase_					( ):
							for n in range(1							,     1_0_0_0_0_0_0     ):
														yield n * (n + 1) // 2







def     lowerCAmelCase_					( __lowerCamelCase     ):
							__snake_case		:      List[Any]										=       1
							__snake_case		:      int										=       2
							while i * i <= n:
														__snake_case		:      Dict										=       0
														while n % i == 0:
																					n //= i
																					multiplicity += 1
														divisors_count *= multiplicity + 1
														i += 1
							if n > 1:
														divisors_count *= 2
							return divisors_count







def     lowerCAmelCase_					( ):
							return next(i for i in triangle_number_generator() if count_divisors(__lowerCamelCase     ) > 5_0_0     )


if __name__ == "__main__":
			print(solution())





import math
from typing import Optional

import numpy as np

from ...configuration_utils import PretrainedConfig
from ...utils import logging


_snake_case					:		Union[str, Any]      =    logging.get_logger(__name__)

_snake_case					:		List[str]      =    {
    "facebook/encodec_24khz": "https://huggingface.co/facebook/encodec_24khz/resolve/main/config.json",
    "facebook/encodec_48khz": "https://huggingface.co/facebook/encodec_48khz/resolve/main/config.json",
}

class     a		(_lowerCAmelCase				):




							"""simple docstring"""


							__UpperCAmelCase   :							Tuple					  =  "encodec"

							def __init__(							self	:  Any   ,     lowerCamelCase	:  Optional[int]=[1.5, 3.0, 6.0, 12.0, 24.0]   ,     lowerCamelCase	:  List[str]=24000   ,     lowerCamelCase	:  int=1   ,     lowerCamelCase	:  Optional[int]=False   ,     lowerCamelCase	:  Dict=None   ,     lowerCamelCase	:  Tuple=None   ,     lowerCamelCase	:  Optional[int]=128   ,     lowerCamelCase	:  Optional[int]=32   ,     lowerCamelCase	:  List[str]=1   ,     lowerCamelCase	:  str=[8, 5, 4, 2]   ,     lowerCamelCase	:  List[str]="weight_norm"   ,     lowerCamelCase	:  Any=7   ,     lowerCamelCase	:  Tuple=7   ,     lowerCamelCase	:  int=3   ,     lowerCamelCase	:  int=2   ,     lowerCamelCase	:  Union[str, Any]=True   ,     lowerCamelCase	:  List[Any]="reflect"   ,     lowerCamelCase	:  Union[str, Any]=2   ,     lowerCamelCase	:  Optional[int]=2   ,     lowerCamelCase	:  int=1.0   ,     lowerCamelCase	:  Optional[Any]=1024   ,     lowerCamelCase	:  Optional[Any]=None   ,     lowerCamelCase	:  str=True   ,     **lowerCamelCase	:  Dict   ,     )     ->   Any:
														__snake_case		:      Tuple										=       target_bandwidths
														__snake_case		:      Union[str, Any]										=       sampling_rate
														__snake_case		:      Union[str, Any]										=       audio_channels
														__snake_case		:      Dict										=       normalize
														__snake_case		:      List[Any]										=       chunk_length_s
														__snake_case		:      Tuple										=       overlap
														__snake_case		:      Optional[int]										=       hidden_size
														__snake_case		:      List[Any]										=       num_filters
														__snake_case		:      Union[str, Any]										=       num_residual_layers
														__snake_case		:      Optional[int]										=       upsampling_ratios
														__snake_case		:      List[str]										=       norm_type
														__snake_case		:      Optional[int]										=       kernel_size
														__snake_case		:      Dict										=       last_kernel_size
														__snake_case		:      Tuple										=       residual_kernel_size
														__snake_case		:      List[Any]										=       dilation_growth_rate
														__snake_case		:      Optional[int]										=       use_causal_conv
														__snake_case		:      Tuple										=       pad_mode
														__snake_case		:      Union[str, Any]										=       compress
														__snake_case		:      Union[str, Any]										=       num_lstm_layers
														__snake_case		:      int										=       trim_right_ratio
														__snake_case		:      Tuple										=       codebook_size
														__snake_case		:      Optional[Any]										=       codebook_dim if codebook_dim is not None else hidden_size
														__snake_case		:      int										=       use_conv_shortcut

														if self.norm_type not in ["weight_norm", "time_group_norm"]:
																					raise ValueError(
																					    F'self.norm_type must be one of `"weight_norm"`, `"time_group_norm"`), got {self.norm_type}'    )

														super().__init__(**lowerCamelCase    )

							@property
							def    __snake_case (							self	:  int    )     ->   Optional[int]:
														if self.chunk_length_s is None:
																					return None
														else:
																					return int(self.chunk_length_s * self.sampling_rate    )

							@property
							def    __snake_case (							self	:  Union[str, Any]    )     ->   Optional[int]:
														if self.chunk_length_s is None or self.overlap is None:
																					return None
														else:
																					return max(1   ,     int((1.0 - self.overlap) * self.chunk_length    )    )

							@property
							def    __snake_case (							self	:  Optional[Any]    )     ->   int:
														__snake_case		:      Union[str, Any]										=       np.prod(self.upsampling_ratios    )
														return math.ceil(self.sampling_rate / hop_length    )






							@property
							def    __snake_case (							self	:  Optional[Any]    )     ->   int:
														return int(1000 * self.target_bandwidths[-1] // (self.frame_rate * 10)    )

