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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def createMultipleL4L2ColumnsWithTopology(network, networkConfig):
 """ Create a network consisting of multiple columns. Each column contains one L4 and one L2, is identical in structure to the network created by createL4L2Column. In addition the L2 columns are connected to each other through their lateral inputs, based on the topological information provided. Region names have a column number appended as in externalInput_0, externalInput_1, etc. networkConfig must be of the following format (see createL4L2Column for further documentation):
 { "networkType": "MultipleL4L2Columns", "numCorticalColumns": 3, "externalInputSize": 1024, "sensorInputSize": 1024, "columnPositions": a list of 2D coordinates, one for each column. Used to calculate the connections between columns. By convention, coordinates are integers. "maxConnectionDistance": should be a value >= 1. Determines how distant of columns will be connected to each other. Useful specific values are 1 and 1.5, which typically create grids without and with diagonal connections, respectively. "longDistanceConnections": Should be a value in [0,1). This is the probability that a column forms a connection with a distant column (i.e. beyond its normal connection distance). If this value is not provided, it defaults to 0, and all connections will be in the local vicinity. "L4Params": { <constructor parameters for ApicalTMPairRegion> }, "L2Params": { <constructor parameters for ColumnPoolerRegion> }, "lateralSPParams": { <constructor parameters for optional SPRegion> }, "feedForwardSPParams": { <constructor parameters for optional SPRegion> } } """

  numCorticalColumns = networkConfig["numCorticalColumns"]
  output_lateral_connections = [[] for i in
      xrange(numCorticalColumns)]
  input_lateral_connections = [[] for i in
      xrange(numCorticalColumns)]


  # If no column positions are provided, create a grid by default.
  # This is typically what the user wants, so it makes sense to have it as
  # a default.
  columnPositions = networkConfig.get("columnPositions", None)
  if columnPositions is None:
    columnPositions = []
    side_length = int(numpy.ceil(numpy.sqrt(numCorticalColumns)))
    for i in range(side_length):
      for j in range(side_length):
        columnPositions.append((i, j))
    columnPositions = columnPositions[:numCorticalColumns]

  # Determine which columns will be mutually connected.
  # This has to be done before the actual creation of the network, as each
  # individual column need to know how many columns it is laterally connected
  # to.  These results are then used to actually connect the columns, once
  # the network is created. It's awkward, but unavoidable.
  longDistanceConnections = networkConfig.get("longDistanceConnections", 0.)
  for i, src_pos in enumerate(columnPositions):
    for j, dest_pos in enumerate(columnPositions):
      if i != j:
        if (numpy.linalg.norm(numpy.asarray(src_pos) -
            numpy.asarray(dest_pos)) <=
            networkConfig["maxConnectionDistance"] or
            numpy.random.rand() < longDistanceConnections):
          output_lateral_connections[i].append(j)
          input_lateral_connections[j].append(i)

  # Create each column
  for i in xrange(numCorticalColumns):
    networkConfigCopy = copy.deepcopy(networkConfig)
    layerConfig = networkConfigCopy["L2Params"]
    layerConfig["seed"] = layerConfig.get("seed", 42) + i

    layerConfig["numOtherCorticalColumns"] = len(input_lateral_connections[i])

    suffix = "_" + str(i)
    network = createL4L2Column(network, networkConfigCopy, suffix)

  # Now connect the L2 columns laterally
  for i, connections in enumerate(output_lateral_connections):
    suffixSrc = "_" + str(i)
    for j in connections:
      suffixDest = "_" + str(j)
      network.link("L2Column" + suffixSrc, "L2Column" + suffixDest,
        "UniformLink", "", srcOutput="feedForwardOutput",
        destInput="lateralInput", propagationDelay=1)

  enableProfiling(network)
  return network