



import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf


if is_tf_available():
							import tensorflow as tf
							from tensorflow.python.eager import context
							from tensorflow.python.framework import ops

							from transformers import GradientAccumulator, create_optimizer
@require_tf
class 			_snake_case     (   unittest.TestCase):




				def 							A__ (  self   :  List[Any],   __lowercase   :  Any,   __lowercase   :  Any,   __lowercase   :  Any  ):
							self.assertEqual(len(__lowercase  ),   len(__lowercase  )  )
							for a, b in zip(__lowercase,   __lowercase  ):
										self.assertAlmostEqual(__lowercase,   __lowercase,   delta=__lowercase  )




				def 							A__ (  self   :  List[str]  ):
							lowercase__   					=			GradientAccumulator()
							accumulator([tf.constant([1.0, 2.0]  )]  )
							accumulator([tf.constant([-2.0, 1.0]  )]  )
							accumulator([tf.constant([-1.0, 2.0]  )]  )
							with self.assertRaises(__lowercase  ):
										accumulator([tf.constant([1.0, 1.0]  ), tf.constant([2.0, 2.0]  )]  )
							self.assertEqual(accumulator.step,   3  )
							self.assertEqual(len(accumulator.gradients  ),   1  )
							self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist(),   [-2.0, 5.0],   tol=1e-2  )
							accumulator.reset()
							self.assertEqual(accumulator.step,   0  )
							self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist(),   [0.0, 0.0],   tol=1e-2  )




				def 							A__ (  self   :  Any  ):
							lowercase__   					=			None
							ops.enable_eager_execution_internal()
							lowercase__   					=			tf.config.list_physical_devices("CPU"  )
							if len(__lowercase  ) == 1:
										tf.config.set_logical_device_configuration(
										    physical_devices[0],   [tf.config.LogicalDeviceConfiguration(), tf.config.LogicalDeviceConfiguration()]  )
							lowercase__   					=			tf.config.list_logical_devices(device_type="CPU"  )
							lowercase__   					=			tf.distribute.MirroredStrategy(devices=devices[:2]  )

							with strategy.scope():
										lowercase__   					=			GradientAccumulator()
										lowercase__   					=			tf.Variable([4.0, 3.0]  )
										lowercase__					,    lowercase__   					=			create_optimizer(5e-5,   10,   5  )
										lowercase__   					=			tf.Variable([0.0, 0.0],   trainable=__lowercase  )

							def accumulate_on_replica(__lowercase   :  Optional[Any]  ):
										accumulator([gradient]  )

							def apply_on_replica():
										optimizer.apply_gradients(list(zip(accumulator.gradients,   [variable]  )  )  )

							@tf.function
							def accumulate(__lowercase   :  int,   __lowercase   :  Dict  ):
										with strategy.scope():
													lowercase__   					=			strategy.experimental_local_results(__lowercase  )
													local_variables[0].assign(__lowercase  )
													local_variables[1].assign(__lowercase  )
													strategy.run(__lowercase,   args=(gradient_placeholder,)  )

							@tf.function
							def apply_grad():
										with strategy.scope():
													strategy.run(__lowercase  )

							def _check_local_values(__lowercase   :  int,   __lowercase   :  str  ):
										lowercase__   					=			strategy.experimental_local_results(accumulator._gradients[0]  )
										self.assertListAlmostEqual(values[0].value(),   __lowercase,   tol=1e-2  )
										self.assertListAlmostEqual(values[1].value(),   __lowercase,   tol=1e-2  )

							accumulate([1.0, 2.0],   [-1.0, 1.0]  )
							accumulate([3.0, -1.0],   [-1.0, -1.0]  )
							accumulate([-2.0, 2.0],   [3.0, -2.0]  )
							self.assertEqual(accumulator.step,   3  )
							_check_local_values([2.0, 3.0],   [1.0, -2.0]  )
							apply_grad()
							self.assertListAlmostEqual(variable.value(),   [4.0, 3.0],   tol=1e-2  )
							accumulator.reset()
							self.assertEqual(accumulator.step,   0  )
							_check_local_values([0.0, 0.0],   [0.0, 0.0]  )









def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					):
			lowercase__   					=			1  # To kept the Calculated Value
			# Since C(n, k) = C(n, n-k)
			if k > (n - k):
						lowercase__   					=			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_					):
			return binomial_coefficient(2 * node_count  ,					SCREAMING_SNAKE_CASE_					) // (node_count + 1)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			if n < 0:
						raise ValueError("factorial() not defined for negative values"					)
			lowercase__   					=			1
			for i in range(1  ,					n + 1					):
						result *= i
			return result



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			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.'
							)




