
from functools import reduce

_A  =	(
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)






def   lowerCamelCase__							(							__lowerCAmelCase    :    str = N							):




			"""simple docstring"""


			return max(
			    # mypy cannot properly interpret reduce
			    int(reduce(lambda __lowerCAmelCase       ,				__lowerCAmelCase							: str(int(__lowerCAmelCase							) * int(__lowerCAmelCase							)							)       ,				n[i : i + 13]							)							)
			    for i in range(len(__lowerCAmelCase							) - 12							)							)


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





from collections import OrderedDict
from typing import TYPE_CHECKING, Any, Mapping, Optional

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


if TYPE_CHECKING:
			from ... import FeatureExtractionMixin, TensorType

_A  =	logging.get_logger(__name__)

_A  =	{
    "openai/imagegpt-small": "",
    "openai/imagegpt-medium": "",
    "openai/imagegpt-large": "",
}





class       _lowerCAmelCase   (      __a			):
				_lowercase     						='''imagegpt'''
				_lowercase     						=['''past_key_values''']
				_lowercase     						={
				    '''hidden_size''': '''n_embd''',
				    '''max_position_embeddings''': '''n_positions''',
				    '''num_attention_heads''': '''n_head''',
				    '''num_hidden_layers''': '''n_layer''',
				}




				def __init__(   self							,							_UpperCamelCase=512 + 1							,							_UpperCamelCase=32 * 32							,							_UpperCamelCase=512							,							_UpperCamelCase=24							,							_UpperCamelCase=8							,							_UpperCamelCase=None							,							_UpperCamelCase="quick_gelu"							,							_UpperCamelCase=0.1							,							_UpperCamelCase=0.1							,							_UpperCamelCase=0.1							,							_UpperCamelCase=1e-5							,							_UpperCamelCase=0.02							,							_UpperCamelCase=True							,							_UpperCamelCase=True							,							_UpperCamelCase=False							,							_UpperCamelCase=False							,							_UpperCamelCase=False							,							**_UpperCamelCase							,							)							-> Tuple:
							lowerCAmelCase_         =      vocab_size
							lowerCAmelCase_         =      n_positions
							lowerCAmelCase_         =      n_embd
							lowerCAmelCase_         =      n_layer
							lowerCAmelCase_         =      n_head
							lowerCAmelCase_         =      n_inner
							lowerCAmelCase_         =      activation_function
							lowerCAmelCase_         =      resid_pdrop
							lowerCAmelCase_         =      embd_pdrop
							lowerCAmelCase_         =      attn_pdrop
							lowerCAmelCase_         =      layer_norm_epsilon
							lowerCAmelCase_         =      initializer_range
							lowerCAmelCase_         =      scale_attn_weights
							lowerCAmelCase_         =      use_cache
							lowerCAmelCase_         =      scale_attn_by_inverse_layer_idx
							lowerCAmelCase_         =      reorder_and_upcast_attn
							lowerCAmelCase_         =      tie_word_embeddings

							super().__init__(tie_word_embeddings=_UpperCamelCase							,							**_UpperCamelCase	)





class       _lowerCAmelCase   (      __a			):




				@property
				def 	__a		(   self	)							-> Mapping[str, Mapping[int, str]]:
							return OrderedDict(
							    [
							        ("input_ids", {0: "batch", 1: "sequence"}),
							    ]	)




				def 	__a		(   self							,							_UpperCamelCase							,							_UpperCamelCase = 1							,							_UpperCamelCase = -1							,							_UpperCamelCase = False							,							_UpperCamelCase = None							,							_UpperCamelCase = 3							,							_UpperCamelCase = 32							,							_UpperCamelCase = 32							,							)							-> Mapping[str, Any]:
							lowerCAmelCase_         =      self._generate_dummy_images(_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)
							lowerCAmelCase_         =      dict(preprocessor(images=_UpperCamelCase							,							return_tensors=_UpperCamelCase	)	)

							return inputs



