
"""simple docstring"""

def 							A						(    snake_case				:List[Any]		)				->     List[Any]:
 __UpperCamelCase      =	0
 __UpperCamelCase      =	len(a__		)

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

 return num_inversions






def 							A						(    snake_case				:Any		)				->     Union[str, Any]:
 if len(a__		) <= 1:
  return arr, 0
 __UpperCamelCase      =	len(a__		) // 2
 __UpperCamelCase      =	arr[0:mid]
 __UpperCamelCase      =	arr[mid:]

 __UpperCamelCase  ,     __UpperCamelCase      =	count_inversions_recursive(a__		)
 __UpperCamelCase  ,     __UpperCamelCase      =	count_inversions_recursive(a__		)
 __UpperCamelCase  ,     __UpperCamelCase      =	_count_cross_inversions(a__    , a__		)

 __UpperCamelCase      =	inversion_p + inversions_q + cross_inversions
 return c, num_inversions






def 							A						(    snake_case				:Dict    , snake_case				:List[str]		)				->     Any:
 __UpperCamelCase      =	[]
 __UpperCamelCase      =	__UpperCamelCase      =	__UpperCamelCase      =	0
 while i < len(a__		) and j < len(a__		):
  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(a__		) - i
   r.append(q[j]		)
   j += 1
  else:
   r.append(p[i]		)
   i += 1

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

 return r, num_inversion






def 							A						(    )				->     Optional[int]:
 __UpperCamelCase      =	[1_0, 2, 1, 5, 5, 2, 1_1]

 # 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(a__		)
 __UpperCamelCase  ,     __UpperCamelCase      =	count_inversions_recursive(a__		)

 assert num_inversions_bf == num_inversions_recursive == 8

 print('number of inversions = '    , a__		)

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

 arr_a.sort()
 __UpperCamelCase      =	count_inversions_bf(a__		)
 __UpperCamelCase  ,     __UpperCamelCase      =	count_inversions_recursive(a__		)

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

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

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


if __name__ == "__main__":
      main()





"""simple docstring"""

UpperCamelCase     :    Union[str, Any]       =			[
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]






def 							A						(    snake_case				:Dict    , snake_case				:Tuple    , snake_case				:str    , snake_case				:Optional[int]		)				->     Union[str, Any]:
 # Return True if there is node that has not iterated.
 __UpperCamelCase      =	[False] * len(snake_case		)
 __UpperCamelCase      =	[s]
 __UpperCamelCase      =	True

 while queue:
  __UpperCamelCase      =	queue.pop(0		)
  for ind in range(len(graph[u]		)		):
   if visited[ind] is False and graph[u][ind] > 0:
    queue.append(snake_case		)
    __UpperCamelCase      =	True
    __UpperCamelCase      =	u

 return visited[t]






def 							A						(    snake_case				:int    , snake_case				:Any    , snake_case				:Union[str, Any]		)				->     Optional[int]:
 __UpperCamelCase      =	[-1] * (len(snake_case		))
 __UpperCamelCase      =	0
 __UpperCamelCase      =	[]
 __UpperCamelCase      =	[i[:] for i in graph]  # Record original cut, copy.
 while bfs(snake_case    , snake_case    , snake_case    , snake_case		):
  __UpperCamelCase      =	float('Inf'		)
  __UpperCamelCase      =	sink

  while s != source:
   # Find the minimum value in select path
   __UpperCamelCase      =	min(snake_case    , graph[parent[s]][s]		)
   __UpperCamelCase      =	parent[s]

  max_flow += path_flow
  __UpperCamelCase      =	sink

  while v != source:
   __UpperCamelCase      =	parent[v]
   graph[u][v] -= path_flow
   graph[v][u] += path_flow
   __UpperCamelCase      =	parent[v]

 for i in range(len(snake_case		)		):
  for j in range(len(graph[0]		)		):
   if graph[i][j] == 0 and temp[i][j] > 0:
    res.append((i, j)		)

 return res


if __name__ == "__main__":
      print(mincut(test_graph, source=0, sink=5))



