/// <summary>
/// Used internally
/// </summary>
/// <param name="sender"></param>
/// <param name="args"></param>
public void FinishVertex(Object sender, VertexEventArgs args)
{
IVertex v = args.Vertex;
foreach (IEdge e in VisitedGraph.OutEdges(v))
{
IVertex w = e.Target;
if (Components[w] == int.MaxValue)
{
Roots[v] = MinDiscoverTime(Roots[v], Roots[w]);
}
}
if (Roots[v] == v)
{
IVertex w = null;
do
{
w = (IVertex)m_Stack.Peek();
m_Stack.Pop();
Components[w] = m_Count;
}while (w != v);
++m_Count;
}
}
/// <inheritdoc />
protected override void InternalCompute()
{
while (_heap.Count != 0)
{
ThrowIfCancellationRequested();
TVertex vertex = _heap.Dequeue();
if (InDegrees[vertex] != 0)
{
throw new NonAcyclicGraphException();
}
_sortedVertices.Add(vertex);
OnVertexAdded(vertex);
// Update the count of its adjacent vertices
foreach (TEdge edge in VisitedGraph.OutEdges(vertex))
{
--InDegrees[edge.Target];
Debug.Assert(InDegrees[edge.Target] >= 0);
_heap.Update(edge.Target);
}
}
SortedVertices = _sortedVertices.ToArray();
}
/// <summary>
/// Execute the EDFS starting with the vertex s
/// </summary>
/// <param name="v">Starting vertex</param>
public void Compute(IVertex v)
{
if (v == null)
{
throw new ArgumentNullException("entry point");
}
Initialize();
// start whith him:
OnStartVertex(v);
// process each out edge of v
foreach (IEdge e in VisitedGraph.OutEdges(v))
{
if (EdgeColors[e] == GraphColor.White)
{
OnStartEdge(e);
Visit(e, 0);
}
}
// process the rest of the graph edges
foreach (IEdge e in VisitedGraph.Edges)
{
if (EdgeColors[e] == GraphColor.White)
{
OnStartEdge(e);
Visit(e, 0);
}
}
}
private void ComputeNoInit([NotNull] TVertex root)
{
IEnumerable <TVertex> orderedVertices = VisitedGraph.TopologicalSort();
OnDiscoverVertex(root);
foreach (TVertex vertex in orderedVertices)
{
OnStartVertex(vertex);
OnExamineVertex(vertex);
foreach (TEdge edge in VisitedGraph.OutEdges(vertex))
{
OnExamineEdge(edge);
OnDiscoverVertex(edge.Target);
bool decreased = Relax(edge);
if (decreased)
{
OnTreeEdge(edge);
}
else
{
OnEdgeNotRelaxed(edge);
}
}
OnFinishVertex(vertex);
}
}
private void InitAlgorithm()
{
vertices = new LinLogVertex[VisitedGraph.VertexCount];
var vertexMap = new Dictionary <TVertex, LinLogVertex>();
//vertexek indexelése
int i = 0;
foreach (TVertex v in VisitedGraph.Vertices)
{
vertices[i] = new LinLogVertex
{
Index = i,
OriginalVertex = v,
Attractions = new LinLogEdge[VisitedGraph.Degree(v)],
RepulsionWeight = 0,
Position = VertexPositions[v]
};
vertexMap[v] = vertices[i];
i++;
}
//minden vertex-hez felépíti az attractionWeights, attractionIndexes,
//és a repulsionWeights struktúrát, valamint átmásolja a pozícióját a VertexPositions-ból
foreach (var v in vertices)
{
int attrIndex = 0;
foreach (var e in VisitedGraph.InEdges(v.OriginalVertex))
{
double weight = e is WeightedEdge <TVertex>?((e as WeightedEdge <TVertex>).Weight) : 1;
v.Attractions[attrIndex] = new LinLogEdge
{
Target = vertexMap[e.Source],
AttractionWeight = weight
};
//TODO look at this line below
//v.RepulsionWeight += weight;
v.RepulsionWeight += 1;
attrIndex++;
}
foreach (var e in VisitedGraph.OutEdges(v.OriginalVertex))
{
double weight = e is WeightedEdge <TVertex>?((e as WeightedEdge <TVertex>).Weight) : 1;
v.Attractions[attrIndex] = new LinLogEdge
{
Target = vertexMap[e.Target],
AttractionWeight = weight
};
//v.RepulsionWeight += weight;
v.RepulsionWeight += 1;
attrIndex++;
}
v.RepulsionWeight = Math.Max(v.RepulsionWeight, Parameters.gravitationMultiplier);
}
repulsionMultiplier = ComputeRepulsionMultiplier();
}
internal void ComputeNoInit(IVertex s)
{
VertexCollection orderedVertices = new VertexCollection();
TopologicalSortAlgorithm topoSorter = new TopologicalSortAlgorithm(VisitedGraph, orderedVertices);
topoSorter.Compute();
OnDiscoverVertex(s);
foreach (IVertex v in orderedVertices)
{
OnExamineVertex(v);
foreach (IEdge e in VisitedGraph.OutEdges(v))
{
OnDiscoverVertex(e.Target);
bool decreased = Relax(e);
if (decreased)
{
OnEdgeRelaxed(e);
}
else
{
OnEdgeNotRelaxed(e);
}
}
OnFinishVertex(v);
}
}
private void FirstWalk(TVertex v)
{
var data = datas[v];
visitedVertices.Add(v);
data.d = 0;
float s = 0;
foreach (var edge in VisitedGraph.OutEdges(v))
{
var otherVertex = edge.Target;
var otherData = datas[otherVertex];
if (!visitedVertices.Contains(otherVertex))
{
FirstWalk(otherVertex);
data.d = Math.Max(data.d, otherData.r);
otherData.a = (float)Math.Atan(((float)otherData.r) / (data.d + otherData.r));
s += otherData.a;
}
}
AdjustChildren(v, data, s);
SetRadius(v, data);
}
//=======================================================================
// The main purpose of this routine is to set distance[v]
// to the smallest value allowed by the valid labeling constraints,
// which are:
// distance[t] = 0
// distance[u] <= distance[v] + 1 for every residual edge (u,v)
//
private int RelabelDistance(IVertex u)
{
int minEdges = 0;
workSinceLastUpdate += beta;
int minDistance = VisitedGraph.VerticesCount;
distances[u] = minDistance;
// Examine the residual out-edges of vertex i, choosing the
// edge whose target vertex has the minimal distance.
for (int ai = 0; ai < VisitedGraph.OutDegree(u); ai++)
{
++workSinceLastUpdate;
IEdge a = VisitedGraph.OutEdges(u)[ai];
IVertex v = a.Target;
if (IsResidualEdge(a) && distances[v] < minDistance)
{
minDistance = distances[v];
minEdges = ai;
}
}
++minDistance;
if (minDistance < n)
{
distances[u] = minDistance; // this is the main action
current[u] = minEdges;
maxDistance = Math.Max(minDistance, maxDistance);
}
return(minDistance);
}
private void OnVertexFinished([NotNull] TVertex vertex)
{
foreach (TEdge edge in VisitedGraph.OutEdges(vertex))
{
TVertex target = edge.Target;
if (Components[target] == int.MaxValue)
{
Roots[vertex] = MinDiscoverTime(Roots[vertex], Roots[target]);
}
}
if (Roots[vertex].Equals(vertex))
{
TVertex w;
do
{
w = _stack.Pop();
Components[w] = ComponentCount;
ComponentsPerStep.Add(ComponentCount);
VerticesPerStep.Add(w);
++Steps;
}while (!w.Equals(vertex));
++ComponentCount;
}
}
private bool FindAdjacentOddVertex(
TVertex u,
ICollection <TVertex> oddVertices,
EdgeFactory <TVertex, TEdge> edgeFactory,
out bool foundAdjacent)
{
bool found = false;
foundAdjacent = false;
foreach (TEdge edge in VisitedGraph.OutEdges(u))
{
TVertex v = edge.Target;
if (!EqualityComparer <TVertex> .Default.Equals(v, u) && oddVertices.Contains(v))
{
foundAdjacent = true;
// Check that v does not have an out-edge towards u
if (HasEdgeToward(u, v))
{
continue;
}
// Add temporary edge
AddTemporaryEdge(u, v, oddVertices, edgeFactory);
// Set u to null
found = true;
break;
}
}
return(found);
}
private bool FindAdjacentOddVertex(
[NotNull] TVertex u,
[NotNull, ItemNotNull] List <TVertex> oddVertices,
[NotNull, InstantHandle] EdgeFactory <TVertex, TEdge> edgeFactory,
out bool foundAdjacent)
{
bool found = false;
foundAdjacent = false;
foreach (TEdge edge in VisitedGraph.OutEdges(u))
{
TVertex v = edge.Target;
if (!v.Equals(u) && oddVertices.Contains(v))
{
foundAdjacent = true;
// Check that v does not have an out-edge towards u
if (HasEdgeToward(u, v))
{
continue;
}
// Add temporary edge
AddTemporaryEdge(u, v, oddVertices, edgeFactory);
// Set u to null
found = true;
break;
}
}
return(found);
}
private void SecondWalk([NotNull] TVertex vertex, double x, double y, float l, float t)
{
Debug.Assert(vertex != null);
var position = new Point(x, y);
VerticesPositions[vertex] = position;
_visitedVertices.Add(vertex);
BalloonData data = _data[vertex];
float dd = l * data.D;
float p = (float)(t + Math.PI);
int degree = VisitedGraph.OutDegree(vertex);
float fs = degree == 0 ? 0 : data.F / degree;
float pr = 0;
foreach (TEdge edge in VisitedGraph.OutEdges(vertex))
{
TVertex otherVertex = edge.Target;
if (_visitedVertices.Contains(otherVertex))
{
continue;
}
BalloonData otherData = _data[otherVertex];
float aa = data.C * otherData.A;
float rr = (float)(data.D * Math.Tan(aa) / (1 - Math.Tan(aa)));
p += pr + aa + fs;
float xx = (float)((l * rr + dd) * Math.Cos(p));
float yy = (l * rr + dd) * Math.Sign(p);
pr = aa;
SecondWalk(otherVertex, x + xx, y + yy, l * data.C, p);
}
}
private void OnVertexFinished([NotNull] TVertex vertex)
{
foreach (TVertex target in VisitedGraph.OutEdges(vertex).Select(edge => edge.Target))
{
if (Components[target] == int.MaxValue)
{
Roots[vertex] = MinDiscoverTime(Roots[vertex], Roots[target]);
}
}
if (EqualityComparer <TVertex> .Default.Equals(Roots[vertex], vertex))
{
TVertex w;
do
{
w = _stack.Pop();
Components[w] = ComponentCount;
ComponentsPerStep.Add(ComponentCount);
VerticesPerStep.Add(w);
++Steps;
}while (!EqualityComparer <TVertex> .Default.Equals(w, vertex));
++ComponentCount;
}
}
private void SecondWalk(TVertex v, TVertex r, double x, double y, float l, float t)
{
Point pos = new Point(x, y);
VertexPositions[v] = pos;
visitedVertices.Add(v);
BalloonData data = datas[v];
float dd = l * data.d;
float p = (float)(t + Math.PI);
int degree = VisitedGraph.OutDegree(v);
float fs = (degree == 0 ? 0 : data.f / degree);
float pr = 0;
foreach (var edge in VisitedGraph.OutEdges(v))
{
var otherVertex = edge.Target;
if (visitedVertices.Contains(otherVertex))
{
continue;
}
var otherData = datas[otherVertex];
float aa = data.c * otherData.a;
float rr = (float)(data.d * Math.Tan(aa) / (1 - Math.Tan(aa)));
p += pr + aa + fs;
float xx = (float)((l * rr + dd) * Math.Cos(p));
float yy = (float)((l * rr + dd) * Math.Sign(p));
pr = aa;;
SecondWalk(otherVertex, v, x + xx, y + yy, l * data.c, p);
}
}
private void FirstWalk([NotNull] TVertex vertex)
{
Debug.Assert(vertex != null);
BalloonData data = _data[vertex];
_visitedVertices.Add(vertex);
data.D = 0;
float s = 0;
foreach (TEdge edge in VisitedGraph.OutEdges(vertex))
{
TVertex otherVertex = edge.Target;
BalloonData otherData = _data[otherVertex];
if (!_visitedVertices.Contains(otherVertex))
{
FirstWalk(otherVertex);
data.D = Math.Max(data.D, otherData.R);
otherData.A = (float)Math.Atan((float)otherData.R / (data.D + otherData.R));
s += otherData.A;
}
}
AdjustChildren(data, s);
SetRadius(data);
}
/// <summary>
/// Used internally
/// </summary>
/// <param name="sender"></param>
/// <param name="args"></param>
private void FinishVertex(Object sender, VertexEventArgs args)
{
IVertex v = args.Vertex;
foreach (IEdge e in VisitedGraph.OutEdges(v))
{
IVertex w = e.Target;
if (this.Components[w] == int.MaxValue)
{
this.Roots[v] = MinDiscoverTime(this.Roots[v], this.Roots[w]);
}
}
if (Roots[v] == v)
{
IVertex w = null;
do
{
w = (IVertex)this.stack.Peek();
this.stack.Pop();
this.Components[w] = count;
}while (w != v);
++count;
}
}
protected override void InternalCompute()
{
Initialize();
// start whith him:
if (this.RootVertex != null)
{
OnStartVertex(this.RootVertex);
// process each out edge of v
foreach (Edge e in VisitedGraph.OutEdges(this.RootVertex))
{
if (EdgeColors[e] == GraphColor.White)
{
OnStartEdge(e);
Visit(e, 0);
}
}
}
// process the rest of the graph edges
foreach (Edge e in VisitedGraph.Edges)
{
if (EdgeColors[e] == GraphColor.White)
{
OnStartEdge(e);
Visit(e, 0);
}
}
}
private IEdgeEnumerable SelectOutEdgesNotInCircuit(IVertex v)
{
return(new FilteredEdgeEnumerable(
VisitedGraph.OutEdges(v),
new NotInCircuitEdgePredicate(Circuit, TemporaryCircuit)
));
}
private void FirstWalk(TVertex v)
{
var data = _datas[v];
_visitedVertices.Add(v);
data.D = 0;
float s = 0;
foreach (var edge in VisitedGraph.OutEdges(v))
{
var otherVertex = edge.Target;
var otherData = _datas[otherVertex];
if (_visitedVertices.Contains(otherVertex))
{
continue;
}
FirstWalk(otherVertex);
data.D = Math.Max(data.D, otherData.R);
otherData.A = (float)Math.Atan(((float)otherData.R) / (data.D + otherData.R));
s += otherData.A;
}
AdjustChildren(v, data, s);
SetRadius(v, data);
}
private void ExpandNode(
[NotNull] TVertex n,
[NotNull] IDictionary <TEdge, GraphColor> operators,
double cost,
[NotNull] BinaryHeap <double, TVertex> open)
{
// Skip self-edges
foreach (TEdge edge in VisitedGraph.OutEdges(n).Where(e => !e.IsSelfEdge()))
{
bool hasColor = operators.TryGetValue(edge, out GraphColor edgeColor);
if (!hasColor || edgeColor == GraphColor.White)
{
double weight = _edgeWeights(edge);
double nCost = _distanceRelaxer.Combine(cost, weight);
// (7) For each neighboring node of n' mark the operator from n to n' as used
// (8) For each node n', if there is no copy of n' in Open add it
// else save in open on the copy of n' with lowest cost. Mark as used all operators
// as used in any of the copies
operators[edge] = GraphColor.Gray;
if (open.MinimumUpdate(nCost, edge.Target))
{
OnTreeEdge(edge);
}
}
else
{
Debug.Assert(edgeColor == GraphColor.Gray);
// Edge already seen, remove it
operators.Remove(edge);
}
}
}
private bool TryGetSuccessor([NotNull] IDictionary <TEdge, int> visited, [NotNull] TVertex vertex, out TEdge successor)
{
IEnumerable <TEdge> outEdges = VisitedGraph.OutEdges(vertex);
IEnumerable <TEdge> edges = outEdges.Where(edge => !visited.ContainsKey(edge));
return(EdgeChain.TryGetSuccessor(edges, vertex, out successor));
}
/// <inheritdoc />
protected override void InternalCompute()
{
if (!TryGetRootVertex(out TVertex root))
{
throw new InvalidOperationException("Root vertex not set.");
}
// Start with root vertex
OnStartVertex(root);
ICancelManager cancelManager = Services.CancelManager;
// Process each out edge of the root one
foreach (TEdge edge in VisitedGraph.OutEdges(root))
{
if (cancelManager.IsCancelling)
{
return;
}
if (!EdgesColors.ContainsKey(edge))
{
OnStartEdge(edge);
Visit(edge, 0);
}
}
}
/// <summary>
/// Does a depth first search on the vertex u
/// </summary>
/// <param name="u">vertex to explore</param>
/// <param name="depth">current recursion depth</param>
/// <exception cref="ArgumentNullException">u cannot be null</exception>
public void Visit(IVertex u, int depth)
{
if (depth > this.maxDepth)
{
return;
}
if (u == null)
{
throw new ArgumentNullException("u");
}
Colors[u] = GraphColor.Gray;
OnDiscoverVertex(u);
IVertex v = null;
foreach (IEdge e in VisitedGraph.OutEdges(u))
{
OnExamineOutEdge(e);
v = e.Target;
GraphColor c = Colors[v];
if (c == GraphColor.White)
{
OnTreeOutEdge(e);
Visit(v, depth + 1);
}
else if (c == GraphColor.Gray)
{
OnBackOutEdge(e);
}
else
{
OnForwardOrCrossOutEdge(e);
}
}
foreach (IEdge e in VisitedGraph.InEdges(u))
{
OnExamineInEdge(e);
v = e.Source;
GraphColor c = Colors[v];
if (c == GraphColor.White)
{
OnTreeInEdge(e);
Visit(v, depth + 1);
}
else if (c == GraphColor.Gray)
{
OnBackInEdge(e);
}
else
{
OnForwardOrCrossInEdge(e);
}
}
Colors[u] = GraphColor.Black;
OnFinishVertex(u);
}
/// <summary>
/// Compute the condensation graph and store it in the supplied graph 'cg'
/// </summary>
/// <param name="cg">
/// Instance of mutable graph in which the condensation graph
/// transformation is stored
/// </param>
public void Create(IMutableVertexAndEdgeListGraph cg)
{
if (cg == null)
{
throw new ArgumentNullException("cg");
}
if (components == null)
{
ComputeComponents();
}
// components list contains collection of
// input graph Vertex for each SCC Vertex_ID
// (i.e Vector< Vector<Vertex> > )
// Key = SCC Vertex ID
sccVertexMap = BuildSCCVertexMap(components);
// Lsit of SCC vertices
VertexCollection toCgVertices = new VertexCollection();
IDictionaryEnumerator it = sccVertexMap.GetEnumerator();
while (it.MoveNext())
// as scc_vertex_map is a sorted list, order of SCC IDs will match CG vertices
{
IVertex curr = cg.AddVertex();
OnInitCondensationGraphVertex(new CondensationGraphVertexEventArgs(curr, (IVertexCollection)it.Value));
toCgVertices.Add(curr);
}
for (int srcSccId = 0; srcSccId < sccVertexMap.Keys.Count; srcSccId++)
{
VertexCollection adj = new VertexCollection();
foreach (IVertex u in (IVertexCollection)sccVertexMap[srcSccId])
{
foreach (IEdge e in VisitedGraph.OutEdges(u))
{
IVertex v = e.Target;
int targetSccId = components[v];
if (srcSccId != targetSccId)
{
// Avoid loops in the condensation graph
IVertex sccV = toCgVertices[targetSccId];
if (!adj.Contains(sccV)) // Avoid parallel edges
{
adj.Add(sccV);
}
}
}
}
IVertex s = toCgVertices[srcSccId];
foreach (IVertex t in adj)
{
cg.AddEdge(s, t);
}
}
}
private bool HasEdgeToward([NotNull] TVertex u, [NotNull] TVertex v)
{
Debug.Assert(u != null);
Debug.Assert(v != null);
return(VisitedGraph
.OutEdges(v)
.Any(outEdge => EqualityComparer <TVertex> .Default.Equals(outEdge.Target, u)));
}
private IEnumerable <TEdge> SelectOutEdgesNotInCircuit(TVertex v)
{
foreach (var edge in VisitedGraph.OutEdges(v))
{
if (this.NotInCircuit(edge))
{
yield return(edge);
}
}
}
/// <summary>
/// Does a depth first search on the vertex u
/// </summary>
/// <param name="u">vertex to explore</param>
/// <exception cref="ArgumentNullException">u cannot be null</exception>
public void Visit(IVertex u)
{
if (u == null)
{
throw new ArgumentNullException("u");
}
IVertex v = null;
Colors[u] = GraphColor.Gray;
VertexEventArgs uArgs = new VertexEventArgs(u);
if (this.DiscoverVertex != null)
{
DiscoverVertex(this, uArgs);
}
foreach (IEdge e in VisitedGraph.OutEdges(u))
{
EdgeEventArgs eArgs = new EdgeEventArgs(e);
if (this.ExamineEdge != null)
{
ExamineEdge(this, eArgs);
}
v = e.Target;
if (Colors[v] == GraphColor.White)
{
if (this.TreeEdge != null)
{
TreeEdge(this, eArgs);
}
Visit(v);
}
else if (Colors[v] == GraphColor.Gray)
{
if (this.BackEdge != null)
{
BackEdge(this, eArgs);
}
}
else
{
if (this.ForwardOrCrossEdge != null)
{
ForwardOrCrossEdge(this, eArgs);
}
}
}
Colors[u] = GraphColor.Black;
if (this.FinishVertex != null)
{
FinishVertex(this, uArgs);
}
}
private bool IsFlow()
{
// check edge flow values
foreach (IVertex u in VisitedGraph.Vertices)
{
foreach (IEdge a in VisitedGraph.OutEdges(u))
{
if (Capacities[a] > 0)
{
if ((ResidualCapacities[a] + ResidualCapacities[ReversedEdges[a]]
!= Capacities[a] + Capacities[ReversedEdges[a]]) ||
(ResidualCapacities[a] < 0) ||
(ResidualCapacities[ReversedEdges[a]] < 0))
{
return(false);
}
}
}
}
// check conservation
double sum;
foreach (IVertex u in VisitedGraph.Vertices)
{
if (u != src && u != sink)
{
if (excessFlow[u] != 0)
{
return(false);
}
sum = 0;
foreach (IEdge a in VisitedGraph.OutEdges(u))
{
if (Capacities[a] > 0)
{
sum -= Capacities[a] - ResidualCapacities[a];
}
else
{
sum += ResidualCapacities[a];
}
}
if (excessFlow[u] != sum)
{
return(false);
}
}
}
return(true);
}
public void Visit(TVertex s)
{
if (this.IsAborting)
{
return;
}
this.VertexColors[s] = GraphColor.Gray;
OnDiscoverVertex(s);
this.vertexQueue.Push(s);
while (this.vertexQueue.Count != 0)
{
if (this.IsAborting)
{
return;
}
TVertex u = this.vertexQueue.Pop();
OnExamineVertex(u);
foreach (TEdge e in VisitedGraph.OutEdges(u))
{
TVertex v = e.Target;
OnExamineEdge(e);
GraphColor vColor = VertexColors[v];
if (vColor == GraphColor.White)
{
OnTreeEdge(e);
VertexColors[v] = GraphColor.Gray;
OnDiscoverVertex(v);
this.vertexQueue.Push(v);
}
else
{
OnNonTreeEdge(e);
if (vColor == GraphColor.Gray)
{
OnGrayTarget(e);
}
else
{
OnBlackTarget(e);
}
}
}
VertexColors[u] = GraphColor.Black;
OnFinishVertex(u);
}
}
//=======================================================================
// This function is called "push" in Goldberg's h_prf implementation,
// but it is called "discharge" in the paper and in hi_pr.c.
private void Discharge(IVertex u)
{
while (true)
{
int ai;
for (ai = current[u]; ai < VisitedGraph.OutDegree(u); ai++)
{
IEdge a = VisitedGraph.OutEdges(u)[ai];
if (IsResidualEdge(a))
{
IVertex v = a.Target;
if (IsAdmissible(u, v))
{
if (v != sink && excessFlow[v] == 0)
{
RemoveFromInactiveList(v);
AddToActiveList(v, layers[distances[v]]);
}
PushFlow(a);
if (excessFlow[u] == 0)
{
break;
}
}
}
}
PreflowLayer layer = layers[distances[u]];
int du = distances[u];
if (ai == VisitedGraph.OutDegree(u)) // i must be relabeled
{
RelabelDistance(u);
if (layer.ActiveVertices.Count == 0 &&
layer.InactiveVertices.Count == 0)
{
Gap(du);
}
if (distances[u] == n)
{
break;
}
}
else
{ // i is no longer active
current[u] = ai;
AddToInactiveList(u, layer);
break;
}
}
}
