"""simple docstring"""


from typing import TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase__			=    {"""configuration_mmbt""": ["""MMBTConfig"""]}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    UpperCAmelCase__			=    ["""MMBTForClassification""", """MMBTModel""", """ModalEmbeddings"""]


if TYPE_CHECKING:
    from .configuration_mmbt import MMBTConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_mmbt import MMBTForClassification, MMBTModel, ModalEmbeddings

else:
    import sys

    UpperCAmelCase__			=    _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

"""simple docstring"""


def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   0
  _UpperCAmelCase    			=   len(lowercase		)

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

  return num_inversions






def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  if len(lowercase		) <= 1:
    return arr, 0
  _UpperCAmelCase    			=   len(lowercase		) // 2
  _UpperCAmelCase    			=   arr[0:mid]
  _UpperCAmelCase    			=   arr[mid:]

  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   _count_cross_inversions(lowercase ,lowercase		)

  _UpperCAmelCase    			=   inversion_p + inversions_q + cross_inversions
  return c, num_inversions






def      __UpperCAmelCase       (      lowercase ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   _UpperCAmelCase    			=   _UpperCAmelCase    			=   0
  while i < len(lowercase		) and j < len(lowercase		):
    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(lowercase		) - i
      r.append(q[j]		)
      j += 1
    else:
      r.append(p[i]		)
      i += 1

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

  return r, num_inversion






def      __UpperCAmelCase       (      ):







  """simple docstring"""
  _UpperCAmelCase    			=   [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)

  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 8

  print("""number of inversions = """ ,lowercase		)

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

  arr_a.sort()
  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """ ,lowercase		)

  # an empty list should also have zero inversions
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """ ,lowercase		)


if __name__ == "__main__":
    main()
