



"""simple docstring"""
import math





def  lowerCamelCase_						(UpperCamelCase__		:		int							):
    _UpperCAmelCase							:  Dict											=    math.loga(math.sqrt(4 * positive_integer + 1							) / 2 + 1 / 2							)

    return exponent == int(UpperCamelCase__							)





def  lowerCamelCase_						(UpperCamelCase__		:		float = 1 / 1_2345							):
    _UpperCAmelCase							:  Optional[Any]											=    0
    _UpperCAmelCase							:  int											=    0

    _UpperCAmelCase							:  int											=    3
    while True:
        _UpperCAmelCase							:  Optional[int]											=    (integer**2 - 1) / 4
        # if candidate is an integer, then there is a partition for k
        if partition_candidate == int(UpperCamelCase__							):
            _UpperCAmelCase							:  Any											=    int(UpperCamelCase__							)
            total_partitions += 1
            if check_partition_perfect(UpperCamelCase__							):
                perfect_partitions += 1
        if perfect_partitions > 0:
            if perfect_partitions / total_partitions < max_proportion:
                return int(UpperCamelCase__							)
        integer += 1


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







"""simple docstring"""
from ...configuration_utils import PretrainedConfig
from ...utils import logging


_lowerCAmelCase    :List[str]     =					logging.get_logger(__name__)

_lowerCAmelCase    :Any     =					{
    'tiiuae/falcon-40b': 'https://huggingface.co/tiiuae/falcon-40b/resolve/main/config.json',
    'tiiuae/falcon-7b': 'https://huggingface.co/tiiuae/falcon-7b/resolve/main/config.json',
}
class 							_UpperCAmelCase							( a      ):





     '''simple docstring'''



     a__									='''falcon'''
     a__									=['''past_key_values''']





     def __init__(					self       ,	A=6_5_0_2_4       ,	A=4_5_4_4       ,	A=3_2       ,	A=7_1       ,	A=1E-5       ,	A=0.02       ,	A=True       ,	A=0.0       ,	A=0.0       ,	A=None       ,	A=False       ,	A=False       ,	A=True       ,	A=True       ,	A=False       ,	A=1_1       ,	A=1_1       ,	**A       ,	)							->					Any:
         _UpperCAmelCase							:  int											=    vocab_size
         # Backward compatibility with n_embed kwarg
         _UpperCAmelCase							:  Optional[Any]											=    kwargs.pop('''n_embed'''       ,	A		)
         _UpperCAmelCase							:  int											=    hidden_size if n_embed is None else n_embed
         _UpperCAmelCase							:  List[str]											=    num_hidden_layers
         _UpperCAmelCase							:  Tuple											=    num_attention_heads
         _UpperCAmelCase							:  Optional[int]											=    layer_norm_epsilon
         _UpperCAmelCase							:  Tuple											=    initializer_range
         _UpperCAmelCase							:  Optional[int]											=    use_cache
         _UpperCAmelCase							:  Any											=    hidden_dropout
         _UpperCAmelCase							:  Dict											=    attention_dropout

         _UpperCAmelCase							:  Any											=    bos_token_id
         _UpperCAmelCase							:  List[Any]											=    eos_token_id
         _UpperCAmelCase							:  Tuple											=    num_attention_heads if num_kv_heads is None else num_kv_heads
         _UpperCAmelCase							:  Dict											=    alibi
         _UpperCAmelCase							:  Optional[int]											=    new_decoder_architecture
         _UpperCAmelCase							:  str											=    multi_query  # Ignored when new_decoder_architecture is True
         _UpperCAmelCase							:  Optional[int]											=    parallel_attn
         _UpperCAmelCase							:  Optional[int]											=    bias

         super().__init__(bos_token_id=A       ,	eos_token_id=A       ,	**A		)





     @property
     def  __lowerCAmelCase	(					self		)							->					List[str]:
         return self.hidden_size // self.num_attention_heads





     @property
     def  __lowerCAmelCase	(					self		)							->					List[Any]:
         return not self.alibi


