




def lowerCamelCase__  (     _lowercase					,		_lowercase ):

     '''simple docstring'''


     UpperCAmelCase_     :				Dict  =     [0 for i in range(r + 1 )]
     # nc0 = 1
     UpperCAmelCase_     :				int  =     1
     for i in range(1					,		n + 1 ):
          # to compute current row from previous row.
          UpperCAmelCase_     :				Union[str, Any]  =     min(_lowercase					,		_lowercase )
          while j > 0:
               c[j] += c[j - 1]
               j -= 1
     return c[r]



print(binomial_coefficient(n=10, r=5))





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     __a(	_a  ):






    """simple docstring"""





    lowerCAmelCase         = '''imagegpt'''
    lowerCAmelCase         = ['''past_key_values''']
    lowerCAmelCase         = {
        '''hidden_size''': '''n_embd''',
        '''max_position_embeddings''': '''n_positions''',
        '''num_attention_heads''': '''n_head''',
        '''num_hidden_layers''': '''n_layer''',
    }





    def __init__( self  ,_SCREAMING_SNAKE_CASE=512 + 1  ,_SCREAMING_SNAKE_CASE=32 * 32  ,_SCREAMING_SNAKE_CASE=512  ,_SCREAMING_SNAKE_CASE=24  ,_SCREAMING_SNAKE_CASE=8  ,_SCREAMING_SNAKE_CASE=None  ,_SCREAMING_SNAKE_CASE="quick_gelu"  ,_SCREAMING_SNAKE_CASE=0.1  ,_SCREAMING_SNAKE_CASE=0.1  ,_SCREAMING_SNAKE_CASE=0.1  ,_SCREAMING_SNAKE_CASE=1e-5  ,_SCREAMING_SNAKE_CASE=0.02  ,_SCREAMING_SNAKE_CASE=True  ,_SCREAMING_SNAKE_CASE=True  ,_SCREAMING_SNAKE_CASE=False  ,_SCREAMING_SNAKE_CASE=False  ,_SCREAMING_SNAKE_CASE=False  ,**_SCREAMING_SNAKE_CASE  ,)					->						Optional[int]:
         UpperCAmelCase_     :				Optional[int]  =     vocab_size
         UpperCAmelCase_     :				Union[str, Any]  =     n_positions
         UpperCAmelCase_     :				Union[str, Any]  =     n_embd
         UpperCAmelCase_     :				Any  =     n_layer
         UpperCAmelCase_     :				Optional[Any]  =     n_head
         UpperCAmelCase_     :				Union[str, Any]  =     n_inner
         UpperCAmelCase_     :				List[Any]  =     activation_function
         UpperCAmelCase_     :				List[str]  =     resid_pdrop
         UpperCAmelCase_     :				str  =     embd_pdrop
         UpperCAmelCase_     :				Optional[Any]  =     attn_pdrop
         UpperCAmelCase_     :				Dict  =     layer_norm_epsilon
         UpperCAmelCase_     :				Union[str, Any]  =     initializer_range
         UpperCAmelCase_     :				Dict  =     scale_attn_weights
         UpperCAmelCase_     :				Any  =     use_cache
         UpperCAmelCase_     :				List[str]  =     scale_attn_by_inverse_layer_idx
         UpperCAmelCase_     :				Tuple  =     reorder_and_upcast_attn
         UpperCAmelCase_     :				int  =     tie_word_embeddings

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


class     __a(	_a  ):






    """simple docstring"""





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





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE = 1  ,_SCREAMING_SNAKE_CASE = -1  ,_SCREAMING_SNAKE_CASE = False  ,_SCREAMING_SNAKE_CASE = None  ,_SCREAMING_SNAKE_CASE = 3  ,_SCREAMING_SNAKE_CASE = 32  ,_SCREAMING_SNAKE_CASE = 32  ,)					->						Mapping[str, Any]:
         UpperCAmelCase_     :				Any  =     self._generate_dummy_images(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Optional[int]  =     dict(preprocessor(images=_SCREAMING_SNAKE_CASE  ,return_tensors=_SCREAMING_SNAKE_CASE    )    )

         return inputs