





def A_	(		A__				)  ->		Dict:
       a__						:	int =				0
       a__						:	Optional[Any] =				len(__snake_case				)

       for i in range(n - 1				):
              for j in range(i + 1		,      __snake_case				):
                     if arr[i] > arr[j]:
                            num_inversions += 1

       return num_inversions



def A_	(		A__				)  ->		Any:
       if len(__snake_case				) <= 1:
              return arr, 0
       a__						:	Optional[Any] =				len(__snake_case				) // 2
       a__						:	List[Any] =				arr[0:mid]
       a__						:	Union[str, Any] =				arr[mid:]

       a__						:	Tuple =				count_inversions_recursive(__snake_case				)
       a__						:	List[Any] =				count_inversions_recursive(__snake_case				)
       a__						:	List[Any] =				_count_cross_inversions(__snake_case		,      __snake_case				)

       a__						:	List[Any] =				inversion_p + inversions_q + cross_inversions
       return c, num_inversions



def A_	(		A__		,      A__				)  ->		str:
       a__						:	Optional[Any] =				[]
       a__						:	Any =				0
       while i < len(__snake_case				) and j < len(__snake_case				):
              if p[i] > q[j]:
                     # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
                     # These are all inversions. The claim emerges from the
                     # property that P is sorted.
                     num_inversion += len(__snake_case				) - i
                     r.append(q[j]				)
                     j += 1
              else:
                     r.append(p[i]				)
                     i += 1

       if i < len(__snake_case				):
              r.extend(p[i:]				)
       else:
              r.extend(q[j:]				)

       return r, num_inversion



def A_	(		)  ->		List[str]:
       a__						:	Union[str, Any] =				[10, 2, 1, 5, 5, 2, 11]

       # this arr has 8 inversions:
       # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

       a__						:	int =				count_inversions_bf(__snake_case				)
       a__						:	Dict =				count_inversions_recursive(__snake_case				)

       assert num_inversions_bf == num_inversions_recursive == 8

       print('number of inversions = '		,      __snake_case				)

       # testing an array with zero inversion (a sorted arr_1)

       arr_a.sort()
       a__						:	Dict =				count_inversions_bf(__snake_case				)
       a__						:	Dict =				count_inversions_recursive(__snake_case				)

       assert num_inversions_bf == num_inversions_recursive == 0
       print('number of inversions = '		,      __snake_case				)

       # an empty list should also have zero inversions
       a__						:	List[Any] =				[]
       a__						:	Any =				count_inversions_bf(__snake_case				)
       a__						:	List[str] =				count_inversions_recursive(__snake_case				)

       assert num_inversions_bf == num_inversions_recursive == 0
       print('number of inversions = '		,      __snake_case				)


if __name__ == "__main__":
    main()










"""simple docstring"""



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


__A		:       Union[str, Any]  				=		{}

try:
						if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__A		:       Dict  				=		['''NllbTokenizer''']

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__A		:       Dict  				=		['''NllbTokenizerFast''']


if TYPE_CHECKING:
						try:
												if not is_sentencepiece_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_nllb import NllbTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_nllb_fast import NllbTokenizerFast

else:
						import sys

						__A		:       List[Any]  				=		_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



