"""simple docstring"""


UpperCAmelCase__			=    [
    9_9_9,
    8_0_0,
    7_9_9,
    6_0_0,
    5_9_9,
    5_0_0,
    4_0_0,
    3_9_9,
    3_7_7,
    3_5_5,
    3_3_3,
    3_1_1,
    2_8_8,
    2_6_6,
    2_4_4,
    2_2_2,
    2_0_0,
    1_9_9,
    1_7_7,
    1_5_5,
    1_3_3,
    1_1_1,
    8_8,
    6_6,
    4_4,
    2_2,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_7_6,
    9_5_2,
    9_2_8,
    9_0_5,
    8_8_2,
    8_5_8,
    8_5_7,
    8_1_0,
    7_6_2,
    7_1_5,
    7_1_4,
    5_7_2,
    4_2_9,
    4_2_8,
    2_8_6,
    2_8_5,
    2_3_8,
    1_9_0,
    1_4_3,
    1_4_2,
    1_1_8,
    9_5,
    7_1,
    4_7,
    2_4,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_8_8,
    9_7_7,
    9_6_6,
    9_5_5,
    9_4_4,
    9_3_3,
    9_2_2,
    9_1_1,
    9_0_0,
    8_9_9,
    8_7_9,
    8_5_9,
    8_4_0,
    8_2_0,
    8_0_0,
    7_9_9,
    7_6_6,
    7_3_3,
    7_0_0,
    6_9_9,
    6_5_0,
    6_0_0,
    5_9_9,
    5_0_0,
    4_9_9,
    4_0_0,
    3_9_9,
    3_5_0,
    3_0_0,
    2_9_9,
    2_6_6,
    2_3_3,
    2_0_0,
    1_9_9,
    1_7_9,
    1_5_9,
    1_4_0,
    1_2_0,
    1_0_0,
    9_9,
    8_8,
    7_7,
    6_6,
    5_5,
    4_4,
    3_3,
    2_2,
    1_1,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_9_5,
    9_9_2,
    9_8_9,
    9_8_5,
    9_8_1,
    9_7_8,
    9_7_5,
    9_7_1,
    9_6_7,
    9_6_4,
    9_6_1,
    9_5_7,
    9_5_6,
    9_5_1,
    9_4_7,
    9_4_2,
    9_3_7,
    9_3_3,
    9_2_8,
    9_2_3,
    9_1_9,
    9_1_4,
    9_1_3,
    9_0_8,
    9_0_3,
    8_9_7,
    8_9_2,
    8_8_7,
    8_8_1,
    8_7_6,
    8_7_1,
    8_7_0,
    8_6_4,
    8_5_8,
    8_5_2,
    8_4_6,
    8_4_0,
    8_3_4,
    8_2_8,
    8_2_7,
    8_2_0,
    8_1_3,
    8_0_6,
    7_9_9,
    7_9_2,
    7_8_5,
    7_8_4,
    7_7_7,
    7_7_0,
    7_6_3,
    7_5_6,
    7_4_9,
    7_4_2,
    7_4_1,
    7_3_3,
    7_2_4,
    7_1_6,
    7_0_7,
    6_9_9,
    6_9_8,
    6_8_8,
    6_7_7,
    6_6_6,
    6_5_6,
    6_5_5,
    6_4_5,
    6_3_4,
    6_2_3,
    6_1_3,
    6_1_2,
    5_9_8,
    5_8_4,
    5_7_0,
    5_6_9,
    5_5_5,
    5_4_1,
    5_2_7,
    5_2_6,
    5_0_5,
    4_8_4,
    4_8_3,
    4_6_2,
    4_4_0,
    4_3_9,
    3_9_6,
    3_9_5,
    3_5_2,
    3_5_1,
    3_0_8,
    3_0_7,
    2_6_4,
    2_6_3,
    2_2_0,
    2_1_9,
    1_7_6,
    1_3_2,
    8_8,
    4_4,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_9_7,
    9_9_5,
    9_9_2,
    9_9_0,
    9_8_8,
    9_8_6,
    9_8_4,
    9_8_1,
    9_7_9,
    9_7_7,
    9_7_5,
    9_7_2,
    9_7_0,
    9_6_8,
    9_6_6,
    9_6_4,
    9_6_1,
    9_5_9,
    9_5_7,
    9_5_6,
    9_5_4,
    9_5_1,
    9_4_9,
    9_4_6,
    9_4_4,
    9_4_1,
    9_3_9,
    9_3_6,
    9_3_4,
    9_3_1,
    9_2_9,
    9_2_6,
    9_2_4,
    9_2_1,
    9_1_9,
    9_1_6,
    9_1_4,
    9_1_3,
    9_1_0,
    9_0_7,
    9_0_5,
    9_0_2,
    8_9_9,
    8_9_6,
    8_9_3,
    8_9_1,
    8_8_8,
    8_8_5,
    8_8_2,
    8_7_9,
    8_7_7,
    8_7_4,
    8_7_1,
    8_7_0,
    8_6_7,
    8_6_4,
    8_6_1,
    8_5_8,
    8_5_5,
    8_5_2,
    8_4_9,
    8_4_6,
    8_4_3,
    8_4_0,
    8_3_7,
    8_3_4,
    8_3_1,
    8_2_8,
    8_2_7,
    8_2_4,
    8_2_1,
    8_1_7,
    8_1_4,
    8_1_1,
    8_0_8,
    8_0_4,
    8_0_1,
    7_9_8,
    7_9_5,
    7_9_1,
    7_8_8,
    7_8_5,
    7_8_4,
    7_8_0,
    7_7_7,
    7_7_4,
    7_7_0,
    7_6_6,
    7_6_3,
    7_6_0,
    7_5_6,
    7_5_2,
    7_4_9,
    7_4_6,
    7_4_2,
    7_4_1,
    7_3_7,
    7_3_3,
    7_3_0,
    7_2_6,
    7_2_2,
    7_1_8,
    7_1_4,
    7_1_0,
    7_0_7,
    7_0_3,
    6_9_9,
    6_9_8,
    6_9_4,
    6_9_0,
    6_8_5,
    6_8_1,
    6_7_7,
    6_7_3,
    6_6_9,
    6_6_4,
    6_6_0,
    6_5_6,
    6_5_5,
    6_5_0,
    6_4_6,
    6_4_1,
    6_3_6,
    6_3_2,
    6_2_7,
    6_2_2,
    6_1_8,
    6_1_3,
    6_1_2,
    6_0_7,
    6_0_2,
    5_9_6,
    5_9_1,
    5_8_6,
    5_8_0,
    5_7_5,
    5_7_0,
    5_6_9,
    5_6_3,
    5_5_7,
    5_5_1,
    5_4_5,
    5_3_9,
    5_3_3,
    5_2_7,
    5_2_6,
    5_1_9,
    5_1_2,
    5_0_5,
    4_9_8,
    4_9_1,
    4_8_4,
    4_8_3,
    4_7_4,
    4_6_6,
    4_5_7,
    4_4_9,
    4_4_0,
    4_3_9,
    4_2_8,
    4_1_8,
    4_0_7,
    3_9_6,
    3_9_5,
    3_8_1,
    3_6_6,
    3_5_2,
    3_5_1,
    3_3_0,
    3_0_8,
    3_0_7,
    2_8_6,
    2_6_4,
    2_6_3,
    2_4_2,
    2_2_0,
    2_1_9,
    1_7_6,
    1_7_5,
    1_3_2,
    1_3_1,
    8_8,
    4_4,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_9_1,
    9_8_2,
    9_7_4,
    9_6_6,
    9_5_8,
    9_5_0,
    9_4_1,
    9_3_3,
    9_2_5,
    9_1_6,
    9_0_8,
    9_0_0,
    8_9_9,
    8_7_4,
    8_5_0,
    8_2_5,
    8_0_0,
    7_9_9,
    7_0_0,
    6_0_0,
    5_0_0,
    4_0_0,
    3_0_0,
    2_0_0,
    1_0_0,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_9_2,
    9_8_5,
    9_7_8,
    9_7_1,
    9_6_4,
    9_5_7,
    9_4_9,
    9_4_2,
    9_3_5,
    9_2_8,
    9_2_1,
    9_1_4,
    9_0_7,
    9_0_0,
    8_9_9,
    8_7_9,
    8_5_9,
    8_4_0,
    8_2_0,
    8_0_0,
    7_9_9,
    7_6_6,
    7_3_3,
    7_0_0,
    6_9_9,
    6_5_0,
    6_0_0,
    5_9_9,
    5_0_0,
    4_9_9,
    4_0_0,
    3_9_9,
    3_0_0,
    2_9_9,
    2_0_0,
    1_9_9,
    1_0_0,
    9_9,
    0,
]

UpperCAmelCase__			=    [
    9_9_9,
    9_9_6,
    9_9_2,
    9_8_9,
    9_8_5,
    9_8_2,
    9_7_9,
    9_7_5,
    9_7_2,
    9_6_8,
    9_6_5,
    9_6_1,
    9_5_8,
    9_5_5,
    9_5_1,
    9_4_8,
    9_4_4,
    9_4_1,
    9_3_8,
    9_3_4,
    9_3_1,
    9_2_7,
    9_2_4,
    9_2_0,
    9_1_7,
    9_1_4,
    9_1_0,
    9_0_7,
    9_0_3,
    9_0_0,
    8_9_9,
    8_9_1,
    8_8_4,
    8_7_6,
    8_6_9,
    8_6_1,
    8_5_3,
    8_4_6,
    8_3_8,
    8_3_0,
    8_2_3,
    8_1_5,
    8_0_8,
    8_0_0,
    7_9_9,
    7_8_8,
    7_7_7,
    7_6_6,
    7_5_5,
    7_4_4,
    7_3_3,
    7_2_2,
    7_1_1,
    7_0_0,
    6_9_9,
    6_8_8,
    6_7_7,
    6_6_6,
    6_5_5,
    6_4_4,
    6_3_3,
    6_2_2,
    6_1_1,
    6_0_0,
    5_9_9,
    5_8_5,
    5_7_1,
    5_5_7,
    5_4_2,
    5_2_8,
    5_1_4,
    5_0_0,
    4_9_9,
    4_8_5,
    4_7_1,
    4_5_7,
    4_4_2,
    4_2_8,
    4_1_4,
    4_0_0,
    3_9_9,
    3_7_9,
    3_5_9,
    3_4_0,
    3_2_0,
    3_0_0,
    2_9_9,
    2_7_9,
    2_5_9,
    2_4_0,
    2_2_0,
    2_0_0,
    1_9_9,
    1_6_6,
    1_3_3,
    1_0_0,
    9_9,
    6_6,
    3_3,
    0,
]

"""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()
