def lowerCamelCase						(     SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    __UpperCamelCase  :int    						=	1  # To kept the Calculated Value
    # Since C(n, k) = C(n, n-k)
    if k > (n - k):
        __UpperCamelCase  :Tuple    						=	n - k
    # Calculate C(n,k)
    for i in range(SCREAMING_SNAKE_CASE			):
        result *= n - i
        result //= i + 1
    return result



def lowerCamelCase						(     SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    return binomial_coefficient(2 * node_count						,    SCREAMING_SNAKE_CASE			) // (node_count + 1)



def lowerCamelCase						(     SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    if n < 0:
        raise ValueError('''factorial() not defined for negative values'''			)
    __UpperCamelCase  :Union[str, Any]    						=	1
    for i in range(1						,    n + 1			):
        result *= i
    return result



def lowerCamelCase						(     SCREAMING_SNAKE_CASE			):
    '''simple docstring'''







    return catalan_number(SCREAMING_SNAKE_CASE			) * factorial(SCREAMING_SNAKE_CASE			)


if __name__ == "__main__":
    __lowercase											=      int(input('''Enter the number of nodes: ''').strip() or 0)
    if node_count <= 0:
        raise ValueError('''We need some nodes to work with.''')
    print(
        F'Given {node_count} nodes, there are {binary_tree_count(node_count)} '
        F'binary trees and {catalan_number(node_count)} binary search trees.'
    )






import unittest

from transformers import is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, require_torch, slow


if is_flax_available():
    import optax
    from flax.training.common_utils import onehot

    from transformers import AutoTokenizer, FlaxMTaForConditionalGeneration
    from transformers.models.ta.modeling_flax_ta import shift_tokens_right


@require_torch
@require_sentencepiece
@require_tokenizers
@require_flax
class 			lowerCamelCase_  (     unittest.TestCase				):






    '''simple docstring'''






    @slow
    def     UpperCamelCase__     (			self) ->			List[str]:
        __UpperCamelCase  :List[str]    						=	FlaxMTaForConditionalGeneration.from_pretrained('''google/mt5-small''')
        __UpperCamelCase  :Dict    						=	AutoTokenizer.from_pretrained('''google/mt5-small''')

        __UpperCamelCase  :Optional[Any]    						=	tokenizer('''Hello there'''				,				return_tensors='''np''').input_ids
        __UpperCamelCase  :List[str]    						=	tokenizer('''Hi I am'''				,				return_tensors='''np''').input_ids

        __UpperCamelCase  :Optional[int]    						=	shift_tokens_right(__lowercase				,				model.config.pad_token_id				,				model.config.decoder_start_token_id)

        __UpperCamelCase  :Tuple    						=	model(__lowercase				,				decoder_input_ids=__lowercase).logits
        __UpperCamelCase  :Any    						=	optax.softmax_cross_entropy(__lowercase				,				onehot(__lowercase				,				logits.shape[-1])).mean()

        __UpperCamelCase  :str    						=	-(labels.shape[-1] * loss.item())

        __UpperCamelCase  :Optional[Any]    						=	-84.91_27
        self.assertTrue(abs(mtf_score - EXPECTED_SCORE) < 1E-4)





