






"""simple docstring"""
def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase							):
 lowerCamelCase__	:     Tuple								=		[]
 lowerCamelCase__	:     Any								=		len(UpperCAmelCase_							)
 for i in range(UpperCAmelCase_							):
  lowerCamelCase__	:     Any								=		[]
  for j in range(UpperCAmelCase_							):
   lowerCamelCase__	:     int								=		0
   for k in range(UpperCAmelCase_							):
    lowerCamelCase__	:     str								=		val + matrix_a[i][k] * matrix_b[k][j]
   list_a.append(UpperCAmelCase_							)
  matrix_c.append(UpperCAmelCase_							)
 return matrix_c






def 			lowerCamelCase_    (		_lowerCamelCase							):
 return [[int(row == column							) for column in range(UpperCAmelCase_							)] for row in range(UpperCAmelCase_							)]






def 			lowerCamelCase_    (		_lowerCamelCase							):





 if n <= 1:
  return n
 lowerCamelCase__	:     Union[str, Any]								=		identity(2							)
 lowerCamelCase__	:     Any								=		[[1, 1], [1, 0]]
 lowerCamelCase__	:     int								=		n - 1
 while n > 0:
  if n % 2 == 1:
   lowerCamelCase__	:     Optional[Any]								=		multiply(UpperCAmelCase_     ,  UpperCAmelCase_							)
  lowerCamelCase__	:     Tuple								=		multiply(UpperCAmelCase_     ,  UpperCAmelCase_							)
  lowerCamelCase__	:     Any								=		int(n / 2							)
 return res_matrix[0][0]






def 			lowerCamelCase_    (		_lowerCamelCase							):





 if n <= 1:
  return n
 lowerCamelCase__	:     List[str]								=		0
 lowerCamelCase__	:     Optional[int]								=		1
 for _ in range(2     ,  n + 1							):
  lowerCamelCase__	:     Union[str, Any]								=		fiba, fiba + fiba
 return fiba






def 			lowerCamelCase_    (		):





 for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
  lowerCamelCase__	:     str								=		int(''.join(c for c in ordinal if c in '0123456789'							)							)  # 1000th --> 1000
  print(
      f'''{ordinal} fibonacci number using matrix exponentiation is '''
      f'''{nth_fibonacci_matrix(UpperCAmelCase_							)} and using bruteforce is '''
      f'''{nth_fibonacci_bruteforce(UpperCAmelCase_							)}\n'''							)
 # from timeit import timeit
 # print(timeit("nth_fibonacci_matrix(1000000)",
 #              "from main import nth_fibonacci_matrix", number=5))
 # print(timeit("nth_fibonacci_bruteforce(1000000)",
 #              "from main import nth_fibonacci_bruteforce", number=5))
 # 2.3342058970001744
 # 57.256506615000035


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()


"""simple docstring"""







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


_a	:	Optional[Any]=					{"configuration_gptj": ["GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP", "GPTJConfig", "GPTJOnnxConfig"]}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_a	:	Dict=					[
	    "GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST",
	    "GPTJForCausalLM",
	    "GPTJForQuestionAnswering",
	    "GPTJForSequenceClassification",
	    "GPTJModel",
	    "GPTJPreTrainedModel",
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_a	:	Optional[Any]=					[
	    "TFGPTJForCausalLM",
	    "TFGPTJForQuestionAnswering",
	    "TFGPTJForSequenceClassification",
	    "TFGPTJModel",
	    "TFGPTJPreTrainedModel",
	]

try:
	if not is_flax_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	_a	:	List[str]=					[
	    "FlaxGPTJForCausalLM",
	    "FlaxGPTJModel",
	    "FlaxGPTJPreTrainedModel",
	]


if TYPE_CHECKING:
	from .configuration_gptj import GPTJ_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTJConfig, GPTJOnnxConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_gptj import (
		    GPTJ_PRETRAINED_MODEL_ARCHIVE_LIST,
		    GPTJForCausalLM,
		    GPTJForQuestionAnswering,
		    GPTJForSequenceClassification,
		    GPTJModel,
		    GPTJPreTrainedModel,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_gptj import (
		    TFGPTJForCausalLM,
		    TFGPTJForQuestionAnswering,
		    TFGPTJForSequenceClassification,
		    TFGPTJModel,
		    TFGPTJPreTrainedModel,
		)

	try:
		if not is_flax_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_flax_gptj import FlaxGPTJForCausalLM, FlaxGPTJModel, FlaxGPTJPreTrainedModel

else:
	import sys

	_a	:	Any=					_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





