





def A_     (		A__    )  ->		Dict:
       assert isinstance(__lowerCamelCase		,				__lowerCamelCase    ), F'The input value of [n={number}] is not an integer'

       if number == 1:
              return 2
       elif number < 1:
              a__						:     str			=    F'The input value of [n={number}] has to be > 0'
              raise ValueError(__lowerCamelCase    )
       else:
              a__						:     List[str]			=    sylvester(number - 1    )
              a__						:     List[str]			=    num - 1
              a__						:     List[str]			=    num
              return lower * upper + 1


if __name__ == "__main__":
    print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")









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 			A__   (							unittest.TestCase     ):




   """simple docstring"""



   def 							__lowercase		( self ,  lowercase ,  lowercase ,  lowercase)      ->						List[str]:







          '''simple docstring'''

          self.assertEqual(len(lowercase) ,  len(lowercase))
          for a, b in zip(lowercase ,  lowercase):
                 self.assertAlmostEqual(lowercase ,  lowercase ,  delta=lowercase)

   def 							__lowercase		( self)      ->						Any:







          '''simple docstring'''

          a__						:     Tuple			=    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 							__lowercase		( self)      ->						List[Any]:







          '''simple docstring'''

          a__						:     Tuple			=    None
          ops.enable_eager_execution_internal()
          a__						:     Optional[int]			=    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()])
          a__						:     int			=    tf.config.list_logical_devices(device_type='CPU')
          a__						:     Union[str, Any]			=    tf.distribute.MirroredStrategy(devices=devices[:2])

          with strategy.scope():
                 a__						:     str			=    GradientAccumulator()
                 a__						:     Tuple			=    tf.Variable([4.0, 3.0])
                 a__			,							a__						:     Tuple			=    create_optimizer(5e-5 ,  10 ,  5)
                 a__						:     Tuple			=    tf.Variable([0.0, 0.0] ,  trainable=lowercase)

          def accumulate_on_replica(lowercase):
                 accumulator([gradient])

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

          @tf.function
          def accumulate(lowercase ,  lowercase):
                 with strategy.scope():
                        a__						:     Union[str, Any]			=    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 ,  lowercase):
                 a__						:     Union[str, Any]			=    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])


