

from math import isclose, sqrt



def   __UpperCAmelCase					(      __a :     float						,__a :     float						,__a :     float      )     ->	tuple[float, float, float]:

					"""simple docstring"""

					_a      :       Any   =						point_y / 4 / point_x
					_a      :       Dict   =						2 * normal_gradient / (1 + normal_gradient * normal_gradient)
					_a      :       Optional[Any]   =						(1 - normal_gradient * normal_gradient) / (
					    1 + normal_gradient * normal_gradient
					)
					_a      :       Optional[Any]   =						(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

					# to find the next point, solve the simultaeneous equations:
					# y^2 + 4x^2 = 100
					# y - b = m * (x - a)
					# ==> A x^2 + B x + C = 0
					_a      :       List[Any]   =						outgoing_gradient**2 + 4
					_a      :       int   =						2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
					_a      :       Optional[int]   =						(point_y - outgoing_gradient * point_x) ** 2 - 100

					_a      :       List[str]   =						(
					    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term      )
					) / (2 * quadratic_term)
					_a      :       Dict   =						(
					    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term      )
					) / (2 * quadratic_term)

					# two solutions, one of which is our input point
					_a      :       Optional[Any]   =						x_minus if isclose(__a						,__a      ) else x_plus
					_a      :       Optional[Any]   =						point_y + outgoing_gradient * (next_x - point_x)

					return next_x, next_y, outgoing_gradient



def   __UpperCAmelCase					(      __a :     float = 1.4						,__a :     float = -9.6      )     ->	int:

					"""simple docstring"""

					_a      :       int   =						0
					_a      :       float   =						first_x_coord
					_a      :       float   =						first_y_coord
					_a      :       float   =						(10.1 - point_y) / (0.0 - point_x)

					while not (-0.01 <= point_x <= 0.01 and point_y > 0):
										_a ,   _a ,   _a      :       Dict   =						next_point(__a						,__a						,__a      )
										num_reflections += 1

					return num_reflections


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





import json
from typing import List, Optional, Tuple

from tokenizers import normalizers

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_funnel import FunnelTokenizer


__A							=logging.get_logger(__name__)

__A							={'''vocab_file''': '''vocab.txt''', '''tokenizer_file''': '''tokenizer.json'''}

__A							=[
    '''small''',
    '''small-base''',
    '''medium''',
    '''medium-base''',
    '''intermediate''',
    '''intermediate-base''',
    '''large''',
    '''large-base''',
    '''xlarge''',
    '''xlarge-base''',
]

__A							={
    '''vocab_file''': {
        '''funnel-transformer/small''': '''https://huggingface.co/funnel-transformer/small/resolve/main/vocab.txt''',
        '''funnel-transformer/small-base''': '''https://huggingface.co/funnel-transformer/small-base/resolve/main/vocab.txt''',
        '''funnel-transformer/medium''': '''https://huggingface.co/funnel-transformer/medium/resolve/main/vocab.txt''',
        '''funnel-transformer/medium-base''': (
            '''https://huggingface.co/funnel-transformer/medium-base/resolve/main/vocab.txt'''
        ),
        '''funnel-transformer/intermediate''': (
            '''https://huggingface.co/funnel-transformer/intermediate/resolve/main/vocab.txt'''
        ),
        '''funnel-transformer/intermediate-base''': (
            '''https://huggingface.co/funnel-transformer/intermediate-base/resolve/main/vocab.txt'''
        ),
        '''funnel-transformer/large''': '''https://huggingface.co/funnel-transformer/large/resolve/main/vocab.txt''',
        '''funnel-transformer/large-base''': '''https://huggingface.co/funnel-transformer/large-base/resolve/main/vocab.txt''',
        '''funnel-transformer/xlarge''': '''https://huggingface.co/funnel-transformer/xlarge/resolve/main/vocab.txt''',
        '''funnel-transformer/xlarge-base''': (
            '''https://huggingface.co/funnel-transformer/xlarge-base/resolve/main/vocab.txt'''
        ),
    },
    '''tokenizer_file''': {
        '''funnel-transformer/small''': '''https://huggingface.co/funnel-transformer/small/resolve/main/tokenizer.json''',
        '''funnel-transformer/small-base''': (
            '''https://huggingface.co/funnel-transformer/small-base/resolve/main/tokenizer.json'''
        ),
        '''funnel-transformer/medium''': '''https://huggingface.co/funnel-transformer/medium/resolve/main/tokenizer.json''',
        '''funnel-transformer/medium-base''': (
            '''https://huggingface.co/funnel-transformer/medium-base/resolve/main/tokenizer.json'''
        ),
        '''funnel-transformer/intermediate''': (
            '''https://huggingface.co/funnel-transformer/intermediate/resolve/main/tokenizer.json'''
        ),
        '''funnel-transformer/intermediate-base''': (
            '''https://huggingface.co/funnel-transformer/intermediate-base/resolve/main/tokenizer.json'''
        ),
        '''funnel-transformer/large''': '''https://huggingface.co/funnel-transformer/large/resolve/main/tokenizer.json''',
        '''funnel-transformer/large-base''': (
            '''https://huggingface.co/funnel-transformer/large-base/resolve/main/tokenizer.json'''
        ),
        '''funnel-transformer/xlarge''': '''https://huggingface.co/funnel-transformer/xlarge/resolve/main/tokenizer.json''',
        '''funnel-transformer/xlarge-base''': (
            '''https://huggingface.co/funnel-transformer/xlarge-base/resolve/main/tokenizer.json'''
        ),
    },
}
__A							={F"""funnel-transformer/{name}""": 5_1_2 for name in _model_names}
__A							={F"""funnel-transformer/{name}""": {'''do_lower_case''': True} for name in _model_names}




class        _SCREAMING_SNAKE_CASE	( snake_case_		):
	lowerCAmelCase__   =					VOCAB_FILES_NAMES
	lowerCAmelCase__   =					PRETRAINED_VOCAB_FILES_MAP
	lowerCAmelCase__   =					PRETRAINED_INIT_CONFIGURATION
	lowerCAmelCase__   =					FunnelTokenizer
	lowerCAmelCase__   =					PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
	lowerCAmelCase__   =					2



	def __init__(       self		,    lowercase=None		,    lowercase=None		,    lowercase=True		,    lowercase="<unk>"		,    lowercase="<sep>"		,    lowercase="<pad>"		,    lowercase="<cls>"		,    lowercase="<mask>"		,    lowercase="<s>"		,    lowercase="</s>"		,    lowercase=True		,    lowercase=True		,    lowercase=None		,    lowercase="##"		,    **lowercase		,    )							->			List[str]:
					super().__init__(
					    lowercase		,    tokenizer_file=lowercase		,    do_lower_case=lowercase		,    unk_token=lowercase		,    sep_token=lowercase		,    pad_token=lowercase		,    cls_token=lowercase		,    mask_token=lowercase		,    bos_token=lowercase		,    eos_token=lowercase		,    clean_text=lowercase		,    tokenize_chinese_chars=lowercase		,    strip_accents=lowercase		,    wordpieces_prefix=lowercase		,    **lowercase		,    )

					lowerCamelCase_         =     json.loads(self.backend_tokenizer.normalizer.__getstate__()					)
					if (
					    normalizer_state.get("lowercase"		,    lowercase					) != do_lower_case
					    or normalizer_state.get("strip_accents"		,    lowercase					) != strip_accents
					    or normalizer_state.get("handle_chinese_chars"		,    lowercase					) != tokenize_chinese_chars
					):
									lowerCamelCase_         =     getattr(lowercase		,    normalizer_state.pop("type"					)					)
									lowerCamelCase_         =     do_lower_case
									lowerCamelCase_         =     strip_accents
									lowerCamelCase_         =     tokenize_chinese_chars
									lowerCamelCase_         =     normalizer_class(**lowercase					)

					lowerCamelCase_         =     do_lower_case



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase=None					)							->			str:
					lowerCamelCase_         =     [self.cls_token_id] + token_ids_a + [self.sep_token_id]

					if token_ids_a:
									output += token_ids_a + [self.sep_token_id]

					return output



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase = None					)							->			List[int]:
					lowerCamelCase_         =     [self.sep_token_id]
					lowerCamelCase_         =     [self.cls_token_id]
					if token_ids_a is None:
									return len(cls					) * [self.cls_token_type_id] + len(token_ids_a + sep					) * [0]
					return len(cls					) * [self.cls_token_type_id] + len(token_ids_a + sep					) * [0] + len(token_ids_a + sep					) * [1]



	def        SCREAMING_SNAKE_CASE_(       self		,    lowercase		,    lowercase = None					)							->			Tuple[str]:
					lowerCamelCase_         =     self._tokenizer.model.save(lowercase		,    name=lowercase					)
					return tuple(lowercase					)


