// -*- c++ -*-

#ifndef EDMONDS_KARP_H

#define EDMONDS_KARP_H

#include <algorithm>

#include <list>

#include <iterator>

#include <bfs_iterator.h>

#include <invalid.h>

namespace hugo {

  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>

  class ResGraph {

  public:

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

  private:

    typedef typename Graph::SymEdgeIt OldSymEdgeIt;

    const Graph& G;

    FlowMap& flow;

    const CapacityMap& capacity;

  public:

    ResGraph(const Graph& _G, FlowMap& _flow, 

	     const CapacityMap& _capacity) : 

      G(_G), flow(_flow), capacity(_capacity) { }

    class Edge; 

    class OutEdgeIt; 

    friend class Edge; 

    friend class OutEdgeIt; 

    class Edge {

      friend class ResGraph<Graph, Number, FlowMap, CapacityMap>;

    protected:

      const ResGraph<Graph, Number, FlowMap, CapacityMap>* resG;

      OldSymEdgeIt sym;

    public:

      Edge() { } 

      //Edge(const Edge& e) : resG(e.resG), sym(e.sym) { }

      Number free() const { 

	if (resG->G.aNode(sym)==resG->G.tail(sym)) { 

	  return (resG->capacity.get(sym)-resG->flow.get(sym)); 

	} else { 

	  return (resG->flow.get(sym)); 

	}

      }

      bool valid() const { return sym.valid(); }

      void augment(Number a) const {

	if (resG->G.aNode(sym)==resG->G.tail(sym)) { 

	  resG->flow.set(sym, resG->flow.get(sym)+a);

	  //resG->flow[sym]+=a;

	} else { 

	  resG->flow.set(sym, resG->flow.get(sym)-a);

	  //resG->flow[sym]-=a;

	}

      }

    };

    class OutEdgeIt : public Edge {

      friend class ResGraph<Graph, Number, FlowMap, CapacityMap>;

    public:

      OutEdgeIt() { }

      //OutEdgeIt(const OutEdgeIt& e) { resG=e.resG; sym=e.sym; }

    private:

      OutEdgeIt(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _resG, Node v) { 

      	resG=&_resG;

	sym=resG->G.template first<OldSymEdgeIt>(v);

	while( sym.valid() && !(free()>0) ) { ++sym; }

      }

    public:

      OutEdgeIt& operator++() { 

	++sym; 

	while( sym.valid() && !(free()>0) ) { ++sym; }

	return *this; 

      }

    };

    void /*getF*/first(OutEdgeIt& e, Node v) const { 

      e=OutEdgeIt(*this, v); 

    }

    void /*getF*/first(NodeIt& v) const { G./*getF*/first(v); }

    template< typename It >

    It first() const { 

      It e;      

      /*getF*/first(e);

      return e; 

    }

    template< typename It >

    It first(Node v) const { 

      It e;

      /*getF*/first(e, v);

      return e; 

    }

    Node tail(Edge e) const { return G.aNode(e.sym); }

    Node head(Edge e) const { return G.bNode(e.sym); }

    Node aNode(OutEdgeIt e) const { return G.aNode(e.sym); }

    Node bNode(OutEdgeIt e) const { return G.bNode(e.sym); }

    int id(Node v) const { return G.id(v); }

    template <typename S>

    class NodeMap {

      typename Graph::NodeMap<S> node_map; 

    public:

      NodeMap(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }

      NodeMap(const ResGraph<Graph, Number, FlowMap, CapacityMap>& _G, S a) : node_map(_G.G, a) { }

      void set(Node nit, S a) { node_map.set(nit, a); }

      S get(Node nit) const { return node_map.get(nit); }

      S& operator[](Node nit) { return node_map[nit]; } 

      const S& operator[](Node nit) const { return node_map[nit]; } 

    };

  };

  template<typename Graph, typename Number, typename FlowMap, typename CapacityMap>

  class ResGraph2 {

  public:

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

  private:

    //typedef typename Graph::SymEdgeIt OldSymEdgeIt;

    typedef typename Graph::OutEdgeIt OldOutEdgeIt;

    typedef typename Graph::InEdgeIt OldInEdgeIt;

    const Graph& G;

    FlowMap& flow;

    const CapacityMap& capacity;

  public:

    ResGraph2(const Graph& _G, FlowMap& _flow, 

	     const CapacityMap& _capacity) : 

      G(_G), flow(_flow), capacity(_capacity) { }

    class Edge; 

    class OutEdgeIt; 

    friend class Edge; 

    friend class OutEdgeIt; 

    class Edge {

      friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;

    protected:

      const ResGraph2<Graph, Number, FlowMap, CapacityMap>* resG;

      //OldSymEdgeIt sym;

      OldOutEdgeIt out;

      OldInEdgeIt in;

      bool out_or_in; //true, iff out

    public:

      Edge() : out_or_in(true) { } 

      Number free() const { 

	if (out_or_in) { 

	  return (resG->capacity.get(out)-resG->flow.get(out)); 

	} else { 

	  return (resG->flow.get(in)); 

	}

      }

      bool valid() const { 

	return out_or_in && out.valid() || in.valid(); }

      void augment(Number a) const {

	if (out_or_in) { 

	  resG->flow.set(out, resG->flow.get(out)+a);

	} else { 

	  resG->flow.set(in, resG->flow.get(in)-a);

	}

      }

    };

    class OutEdgeIt : public Edge {

      friend class ResGraph2<Graph, Number, FlowMap, CapacityMap>;

    public:

      OutEdgeIt() { }

    private:

      OutEdgeIt(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _resG, Node v) { 

      	resG=&_resG;

	out=resG->G.template first<OldOutEdgeIt>(v);

	while( out.valid() && !(free()>0) ) { ++out; }

	if (!out.valid()) {

	  out_or_in=0;

	  in=resG->G.template first<OldInEdgeIt>(v);

	  while( in.valid() && !(free()>0) ) { ++in; }

	}

      }

    public:

      OutEdgeIt& operator++() { 

	if (out_or_in) {

	  Node v=resG->G.aNode(out);

	  ++out;

	  while( out.valid() && !(free()>0) ) { ++out; }

	  if (!out.valid()) {

	    out_or_in=0;

	    in=resG->G.template first<OldInEdgeIt>(v);

	    while( in.valid() && !(free()>0) ) { ++in; }

	  }

	} else {

	  ++in;

	  while( in.valid() && !(free()>0) ) { ++in; } 

	}

	return *this; 

      }

    };

    void /*getF*/first(OutEdgeIt& e, Node v) const { 

      e=OutEdgeIt(*this, v); 

    }

    void /*getF*/first(NodeIt& v) const { G./*getF*/first(v); }

    template< typename It >

    It first() const { 

      It e;

      /*getF*/first(e);

      return e; 

    }

    template< typename It >

    It first(Node v) const { 

      It e;

      /*getF*/first(e, v);

      return e; 

    }

    Node tail(Edge e) const { 

      return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }

    Node head(Edge e) const { 

      return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

    Node aNode(OutEdgeIt e) const { 

      return ((e.out_or_in) ? G.aNode(e.out) : G.aNode(e.in)); }

    Node bNode(OutEdgeIt e) const { 

      return ((e.out_or_in) ? G.bNode(e.out) : G.bNode(e.in)); }

    int id(Node v) const { return G.id(v); }

    template <typename S>

    class NodeMap {

      typename Graph::NodeMap<S> node_map; 

    public:

      NodeMap(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _G) : node_map(_G.G) { }

      NodeMap(const ResGraph2<Graph, Number, FlowMap, CapacityMap>& _G, S a) : node_map(_G.G, a) { }

      void set(Node nit, S a) { node_map.set(nit, a); }

      S get(Node nit) const { return node_map.get(nit); }

    };

  };

  template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>

  class MaxFlow {

  public:

    typedef typename Graph::Node Node;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::EdgeIt EdgeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

  private:

    const Graph* G;

    Node s;

    Node t;

    FlowMap* flow;

    const CapacityMap* capacity;

    typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;

    typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

    typedef typename AugGraph::Edge AugEdge;

  public:

    MaxFlow(const Graph& _G, Node _s, Node _t, FlowMap& _flow, const CapacityMap& _capacity) : 

      G(&_G), s(_s), t(_t), flow(&_flow), capacity(&_capacity) { }

    bool augmentOnShortestPath() {

      AugGraph res_graph(*G, *flow, *capacity);

      bool _augment=false;

      typedef typename AugGraph::NodeMap<bool> ReachedMap;

      BfsIterator5< AugGraph, /*AugOutEdgeIt,*/ ReachedMap > res_bfs(res_graph);

      res_bfs.pushAndSetReached(s);

      typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

      pred.set(s, AugEdge(INVALID));

      typename AugGraph::NodeMap<Number> free(res_graph);

      //searching for augmenting path

      while ( !res_bfs.finished() ) { 

	AugOutEdgeIt e=res_bfs;

	if (res_graph.valid(e) && res_bfs.isBNodeNewlyReached()) {

	  Node v=res_graph.tail(e);

	  Node w=res_graph.head(e);

	  pred.set(w, e);

	  if (res_graph.valid(pred.get(v))) {

	    free.set(w, std::min(free.get(v), res_graph.free(e)));

	  } else {

	    free.set(w, res_graph.free(e)); 

	  }

	  if (res_graph.head(e)==t) { _augment=true; break; }

	}

	++res_bfs;

      } //end of searching augmenting path

      if (_augment) {

	Node n=t;

	Number augment_value=free.get(t);

	while (res_graph.valid(pred.get(n))) { 

	  AugEdge e=pred.get(n);

	  res_graph.augment(e, augment_value); 

	  n=res_graph.tail(e);

	}

      }

      return _augment;

    }

    template<typename MutableGraph> bool augmentOnBlockingFlow() {      

      bool _augment=false;

      AugGraph res_graph(*G, *flow, *capacity);

      typedef typename AugGraph::NodeMap<bool> ReachedMap;

      BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > bfs(res_graph);

      bfs.pushAndSetReached(s);

      typename AugGraph::NodeMap<int> dist(res_graph); //filled up with 0's

      while ( !bfs.finished() ) { 

	AugOutEdgeIt e=bfs;

	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

	}

	++bfs;

      } //computing distances from s in the residual graph

      MutableGraph F;

      typename AugGraph::NodeMap<typename MutableGraph::Node> 

	res_graph_to_F(res_graph);

      for(typename AugGraph::NodeIt n=res_graph.template first<typename AugGraph::NodeIt>(); res_graph.valid(n); res_graph.next(n)) {

	res_graph_to_F.set(n, F.addNode());

      }

      typename MutableGraph::Node sF=res_graph_to_F.get(s);

      typename MutableGraph::Node tF=res_graph_to_F.get(t);

      typename MutableGraph::EdgeMap<AugEdge> original_edge(F);

      typename MutableGraph::EdgeMap<Number> residual_capacity(F);

      //Making F to the graph containing the edges of the residual graph 

      //which are in some shortest paths

      for(typename AugGraph::EdgeIt e=res_graph.template first<typename AugGraph::EdgeIt>(); res_graph.valid(e); res_graph.next(e)) {

	if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {

	  typename MutableGraph::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

	  original_edge.update();

	  original_edge.set(f, e);

	  residual_capacity.update();

	  residual_capacity.set(f, res_graph.free(e));

	} 

      }

      bool __augment=true;

      while (__augment) {

	__augment=false;

	//computing blocking flow with dfs

	typedef typename MutableGraph::NodeMap<bool> BlockingReachedMap;

	DfsIterator4< MutableGraph, typename MutableGraph::OutEdgeIt, BlockingReachedMap > dfs(F);

	typename MutableGraph::NodeMap<typename MutableGraph::Edge> pred(F);

	pred.set(sF, typename MutableGraph::Edge(INVALID));

	//invalid iterators for sources

	typename MutableGraph::NodeMap<Number> free(F);

	dfs.pushAndSetReached(sF);      

	while (!dfs.finished()) {

	  ++dfs;

	  if (F.valid(typename MutableGraph::OutEdgeIt(dfs))) {

	    if (dfs.isBNodeNewlyReached()) {

	      typename MutableGraph::Node v=F.aNode(dfs);

	      typename MutableGraph::Node w=F.bNode(dfs);

	      pred.set(w, dfs);

	      if (F.valid(pred.get(v))) {

		free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));

	      } else {

		free.set(w, residual_capacity.get(dfs)); 

	      }

	      if (w==tF) { 

		__augment=true; 

		_augment=true;

		break; 

	      }

	    } else {

	      F.erase(typename MutableGraph::OutEdgeIt(dfs));

	    }

	  } 

	}

	if (__augment) {

	  typename MutableGraph::Node n=tF;

	  Number augment_value=free.get(tF);

	  while (F.valid(pred.get(n))) { 

	    typename MutableGraph::Edge e=pred.get(n);

	    res_graph.augment(original_edge.get(e), augment_value); 

	    n=F.tail(e);

	    if (residual_capacity.get(e)==augment_value) 

	      F.erase(e); 

	    else 

	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);

	  }

	}

      }

      return _augment;

    }

    bool augmentOnBlockingFlow2() {

      bool _augment=false;

      //typedef ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> EAugGraph;

      typedef FilterGraphWrapper< ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> > EAugGraph;

      typedef typename EAugGraph::OutEdgeIt EAugOutEdgeIt;

      typedef typename EAugGraph::Edge EAugEdge;

      EAugGraph res_graph(*G, *flow, *capacity);

      //typedef typename EAugGraph::NodeMap<bool> ReachedMap;

      BfsIterator4< 

	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 

	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt, 

	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);

      bfs.pushAndSetReached(s);

      typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::

	NodeMap<int>& dist=res_graph.dist;

      while ( !bfs.finished() ) {

	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt e=bfs;

	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

	}

	++bfs;	

      } //computing distances from s in the residual graph

      bool __augment=true;

      while (__augment) {

	__augment=false;

	//computing blocking flow with dfs

	typedef typename EAugGraph::NodeMap<bool> BlockingReachedMap;

	DfsIterator4< EAugGraph, EAugOutEdgeIt, BlockingReachedMap > 

	  dfs(res_graph);

	typename EAugGraph::NodeMap<EAugEdge> pred(res_graph); 

	pred.set(s, EAugEdge(INVALID));

	//invalid iterators for sources

	typename EAugGraph::NodeMap<Number> free(res_graph);

	dfs.pushAndSetReached(s);

	while (!dfs.finished()) {

	  ++dfs;

	  if (res_graph.valid(EAugOutEdgeIt(dfs))) { 

	    if (dfs.isBNodeNewlyReached()) {

	      typename EAugGraph::Node v=res_graph.aNode(dfs);

	      typename EAugGraph::Node w=res_graph.bNode(dfs);

	      pred.set(w, EAugOutEdgeIt(dfs));

	      if (res_graph.valid(pred.get(v))) {

		free.set(w, std::min(free.get(v), res_graph.free(dfs)));

	      } else {

		free.set(w, res_graph.free(dfs)); 

	      }

	      if (w==t) { 

		__augment=true; 

		_augment=true;

		break; 

	      }

	    } else {

	      res_graph.erase(dfs);

	    }

	  } 

	}

	if (__augment) {

	  typename EAugGraph::Node n=t;

	  Number augment_value=free.get(t);

	  while (res_graph.valid(pred.get(n))) { 

	    EAugEdge e=pred.get(n);

	    res_graph.augment(e, augment_value);

	    n=res_graph.tail(e);

	    if (res_graph.free(e)==0)

	      res_graph.erase(e);

	  }

	}

      }

      return _augment;

    }

    void run() {

      //int num_of_augmentations=0;

      while (augmentOnShortestPath()) { 

	//while (augmentOnBlockingFlow<MutableGraph>()) { 

	//std::cout << ++num_of_augmentations << " ";

	//std::cout<<std::endl;

      } 

    }

    template<typename MutableGraph> void run() {

      //int num_of_augmentations=0;

      //while (augmentOnShortestPath()) { 

	while (augmentOnBlockingFlow<MutableGraph>()) { 

	//std::cout << ++num_of_augmentations << " ";

	//std::cout<<std::endl;

      } 

    }

    Number flowValue() { 

      Number a=0;

      OutEdgeIt e;

      for(G->/*getF*/first(e, s); G->valid(e); G->next(e)) {

	a+=flow->get(e);

      }

      return a;

    }

  };

  template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>

  class MaxMatching {

  public:

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::EdgeIt EdgeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

    typedef typename Graph::NodeMap<bool> SMap;

    typedef typename Graph::NodeMap<bool> TMap;

  private:

    const Graph* G;

    SMap* S;

    TMap* T;

    //Node s;

    //Node t;

    FlowMap* flow;

    const CapacityMap* capacity;

    typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;

    typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

    typedef typename AugGraph::Edge AugEdge;

    typename Graph::NodeMap<int> used; //0

  public:

    MaxMatching(const Graph& _G, SMap& _S, TMap& _T, FlowMap& _flow, const CapacityMap& _capacity) : 

      G(&_G), S(&_S), T(&_T), flow(&_flow), capacity(&_capacity), used(_G) { }

    bool augmentOnShortestPath() {

      AugGraph res_graph(*G, *flow, *capacity);

      bool _augment=false;

      typedef typename AugGraph::NodeMap<bool> ReachedMap;

      BfsIterator5< AugGraph, /*AugOutEdgeIt,*/ ReachedMap > res_bfs(res_graph);

      typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

      for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {

	if ((S->get(s)) && (used.get(s)<1) ) {

	  //Number u=0;

	  //for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))

	  //u+=flow->get(e);

	  //if (u<1) {

	    res_bfs.pushAndSetReached(s);

	    pred.set(s, AugEdge(INVALID));

	    //}

	}

      }

      typename AugGraph::NodeMap<Number> free(res_graph);

      Node n;

      //searching for augmenting path

      while ( !res_bfs.finished() ) { 

	AugOutEdgeIt e=res_bfs;

	if (res_graph.valid(e) && res_bfs.isBNodeNewlyReached()) {

	  Node v=res_graph.tail(e);

	  Node w=res_graph.head(e);

	  pred.set(w, e);

	  if (res_graph.valid(pred.get(v))) {

	    free.set(w, std::min(free.get(v), res_graph.free(e)));

	  } else {

	    free.set(w, res_graph.free(e)); 

	  }

	  n=res_graph.head(e);

	  if (T->get(n) && (used.get(n)<1) ) { 

	    //Number u=0;

	    //for(InEdgeIt f=G->template first<InEdgeIt>(n); G->valid(f); G->next(f))

	    //u+=flow->get(f);

	    //if (u<1) {

	      _augment=true; 

	      break; 

	      //}

	  }

	}

	++res_bfs;

      } //end of searching augmenting path

      if (_augment) {

	//Node n=t;

	used.set(n, 1); //mind2 vegen jav

	Number augment_value=free.get(n);

	while (res_graph.valid(pred.get(n))) { 

	  AugEdge e=pred.get(n);

	  res_graph.augment(e, augment_value); 

	  n=res_graph.tail(e);

	}

	used.set(n, 1); //mind2 vegen jav

      }

      return _augment;

    }

//     template<typename MutableGraph> bool augmentOnBlockingFlow() {      

//       bool _augment=false;

//       AugGraph res_graph(*G, *flow, *capacity);

//       typedef typename AugGraph::NodeMap<bool> ReachedMap;

//       BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > bfs(res_graph);

//       //typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

//       for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {

// 	if (S->get(s)) {

// 	  Number u=0;

// 	  for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))

// 	    u+=flow->get(e);

// 	  if (u<1) {

// 	    res_bfs.pushAndSetReached(s);

// 	    //pred.set(s, AugEdge(INVALID));

// 	  }

// 	}

//       }

//       //bfs.pushAndSetReached(s);

//       typename AugGraph::NodeMap<int> dist(res_graph); //filled up with 0's

//       while ( !bfs.finished() ) { 

// 	AugOutEdgeIt e=bfs;

// 	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

// 	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

// 	}

// 	++bfs;

//       } //computing distances from s in the residual graph

//       MutableGraph F;

//       typename AugGraph::NodeMap<typename MutableGraph::Node> 

// 	res_graph_to_F(res_graph);

//       for(typename AugGraph::NodeIt n=res_graph.template first<typename AugGraph::NodeIt>(); res_graph.valid(n); res_graph.next(n)) {

// 	res_graph_to_F.set(n, F.addNode());

//       }

//       typename MutableGraph::Node sF=res_graph_to_F.get(s);

//       typename MutableGraph::Node tF=res_graph_to_F.get(t);

//       typename MutableGraph::EdgeMap<AugEdge> original_edge(F);

//       typename MutableGraph::EdgeMap<Number> residual_capacity(F);

//       //Making F to the graph containing the edges of the residual graph 

//       //which are in some shortest paths

//       for(typename AugGraph::EdgeIt e=res_graph.template first<typename AugGraph::EdgeIt>(); res_graph.valid(e); res_graph.next(e)) {

// 	if (dist.get(res_graph.head(e))==dist.get(res_graph.tail(e))+1) {

// 	  typename MutableGraph::Edge f=F.addEdge(res_graph_to_F.get(res_graph.tail(e)), res_graph_to_F.get(res_graph.head(e)));

// 	  original_edge.update();

// 	  original_edge.set(f, e);

// 	  residual_capacity.update();

// 	  residual_capacity.set(f, res_graph.free(e));

// 	} 

//       }

//       bool __augment=true;

//       while (__augment) {

// 	__augment=false;

// 	//computing blocking flow with dfs

// 	typedef typename MutableGraph::NodeMap<bool> BlockingReachedMap;

// 	DfsIterator4< MutableGraph, typename MutableGraph::OutEdgeIt, BlockingReachedMap > dfs(F);

// 	typename MutableGraph::NodeMap<typename MutableGraph::Edge> pred(F);

// 	pred.set(sF, typename MutableGraph::Edge(INVALID));

// 	//invalid iterators for sources

// 	typename MutableGraph::NodeMap<Number> free(F);

// 	dfs.pushAndSetReached(sF);      

// 	while (!dfs.finished()) {

// 	  ++dfs;

// 	  if (F.valid(typename MutableGraph::OutEdgeIt(dfs))) {

// 	    if (dfs.isBNodeNewlyReached()) {

// 	      typename MutableGraph::Node v=F.aNode(dfs);

// 	      typename MutableGraph::Node w=F.bNode(dfs);

// 	      pred.set(w, dfs);

// 	      if (F.valid(pred.get(v))) {

// 		free.set(w, std::min(free.get(v), residual_capacity.get(dfs)));

// 	      } else {

// 		free.set(w, residual_capacity.get(dfs)); 

// 	      }

// 	      if (w==tF) { 

// 		__augment=true; 

// 		_augment=true;

// 		break; 

// 	      }

// 	    } else {

// 	      F.erase(typename MutableGraph::OutEdgeIt(dfs));

// 	    }

// 	  } 

// 	}

// 	if (__augment) {

// 	  typename MutableGraph::Node n=tF;

// 	  Number augment_value=free.get(tF);

// 	  while (F.valid(pred.get(n))) { 

// 	    typename MutableGraph::Edge e=pred.get(n);

// 	    res_graph.augment(original_edge.get(e), augment_value); 

// 	    n=F.tail(e);

// 	    if (residual_capacity.get(e)==augment_value) 

// 	      F.erase(e); 

// 	    else 

// 	      residual_capacity.set(e, residual_capacity.get(e)-augment_value);

// 	  }

// 	}

//       }

//       return _augment;

//     }

    bool augmentOnBlockingFlow2() {

      bool _augment=false;

      //typedef ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> EAugGraph;

      typedef FilterGraphWrapper< ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap> > EAugGraph;

      typedef typename EAugGraph::OutEdgeIt EAugOutEdgeIt;

      typedef typename EAugGraph::Edge EAugEdge;

      EAugGraph res_graph(*G, *flow, *capacity);

      //typedef typename EAugGraph::NodeMap<bool> ReachedMap;

      BfsIterator4< 

	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>, 

	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt, 

	ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::NodeMap<bool> > bfs(res_graph);

      //typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

      for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {

	if (S->get(s)) {

	  Number u=0;

	  for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))

	    u+=flow->get(e);

	  if (u<1) {

	    bfs.pushAndSetReached(s);

	    //pred.set(s, AugEdge(INVALID));

	  }

	}

      }

      //bfs.pushAndSetReached(s);

      typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::

	NodeMap<int>& dist=res_graph.dist;

      while ( !bfs.finished() ) {

	typename ErasingResGraphWrapper<Graph, Number, FlowMap, CapacityMap>::OutEdgeIt e=bfs;

	if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {

	  dist.set(res_graph.head(e), dist.get(res_graph.tail(e))+1);

	}

	++bfs;	

      } //computing distances from s in the residual graph

      bool __augment=true;

      while (__augment) {

	__augment=false;

	//computing blocking flow with dfs

	typedef typename EAugGraph::NodeMap<bool> BlockingReachedMap;

	DfsIterator4< EAugGraph, EAugOutEdgeIt, BlockingReachedMap > 

	  dfs(res_graph);

	typename EAugGraph::NodeMap<EAugEdge> pred(res_graph, INVALID); 

	//pred.set(s, EAugEdge(INVALID));

	//invalid iterators for sources

	typename EAugGraph::NodeMap<Number> free(res_graph);

	//typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

      for(NodeIt s=G->template first<NodeIt>(); G->valid(s); G->next(s)) {

	if (S->get(s)) {

	  Number u=0;

	  for(OutEdgeIt e=G->template first<OutEdgeIt>(s); G->valid(e); G->next(e))

	    u+=flow->get(e);

	  if (u<1) {

	    dfs.pushAndSetReached(s);

	    //pred.set(s, AugEdge(INVALID));

	  }

	}

      }

      //dfs.pushAndSetReached(s);

      typename EAugGraph::Node n;

	while (!dfs.finished()) {

	  ++dfs;

	  if (res_graph.valid(EAugOutEdgeIt(dfs))) { 

	    if (dfs.isBNodeNewlyReached()) {

	      typename EAugGraph::Node v=res_graph.aNode(dfs);

	      typename EAugGraph::Node w=res_graph.bNode(dfs);

	      pred.set(w, EAugOutEdgeIt(dfs));

	      if (res_graph.valid(pred.get(v))) {

		free.set(w, std::min(free.get(v), res_graph.free(dfs)));

	      } else {

		free.set(w, res_graph.free(dfs)); 

	      }

	      n=w;

	      if (T->get(w)) {

		Number u=0;

		for(InEdgeIt f=G->template first<InEdgeIt>(n); G->valid(f); G->next(f))

		  u+=flow->get(f);

		if (u<1) {

		  __augment=true; 

		  _augment=true;

		  break; 

		}

	      }

	    } else {

	      res_graph.erase(dfs);

	    }

	  } 

	}

	if (__augment) {

	  // typename EAugGraph::Node n=t;

	  Number augment_value=free.get(n);

	  while (res_graph.valid(pred.get(n))) { 

	    EAugEdge e=pred.get(n);

	    res_graph.augment(e, augment_value);

	    n=res_graph.tail(e);

	    if (res_graph.free(e)==0)

	      res_graph.erase(e);

	  }

	}

      }

      return _augment;

    }

    void run() {

      //int num_of_augmentations=0;

      while (augmentOnShortestPath()) { 

	//while (augmentOnBlockingFlow<MutableGraph>()) { 

	//std::cout << ++num_of_augmentations << " ";

	//std::cout<<std::endl;

      } 

    }

//     template<typename MutableGraph> void run() {

//       //int num_of_augmentations=0;

//       //while (augmentOnShortestPath()) { 

// 	while (augmentOnBlockingFlow<MutableGraph>()) { 

// 	//std::cout << ++num_of_augmentations << " ";

// 	//std::cout<<std::endl;

//       } 

//     } 

    Number flowValue() { 

      Number a=0;

      EdgeIt e;

      for(G->/*getF*/first(e); G->valid(e); G->next(e)) {

	a+=flow->get(e);

      }

      return a;

    }

  };

//   template <typename Graph, typename Number, typename FlowMap, typename CapacityMap>

//   class MaxFlow2 {

//   public:

//     typedef typename Graph::Node Node;

//     typedef typename Graph::Edge Edge;

//     typedef typename Graph::EdgeIt EdgeIt;

//     typedef typename Graph::OutEdgeIt OutEdgeIt;

//     typedef typename Graph::InEdgeIt InEdgeIt;

//   private:

//     const Graph& G;

//     std::list<Node>& S;

//     std::list<Node>& T;

//     FlowMap& flow;

//     const CapacityMap& capacity;

//     typedef ResGraphWrapper<Graph, Number, FlowMap, CapacityMap > AugGraph;

//     typedef typename AugGraph::OutEdgeIt AugOutEdgeIt;

//     typedef typename AugGraph::Edge AugEdge;

//     typename Graph::NodeMap<bool> SMap;

//     typename Graph::NodeMap<bool> TMap;

//   public:

//     MaxFlow2(const Graph& _G, std::list<Node>& _S, std::list<Node>& _T, FlowMap& _flow, const CapacityMap& _capacity) : G(_G), S(_S), T(_T), flow(_flow), capacity(_capacity), SMap(_G), TMap(_G) { 

//       for(typename std::list<Node>::const_iterator i=S.begin(); 

// 	  i!=S.end(); ++i) { 

// 	SMap.set(*i, true); 

//       }

//       for (typename std::list<Node>::const_iterator i=T.begin(); 

// 	   i!=T.end(); ++i) { 

// 	TMap.set(*i, true); 

//       }

//     }

//     bool augment() {

//       AugGraph res_graph(G, flow, capacity);

//       bool _augment=false;

//       Node reached_t_node;

//       typedef typename AugGraph::NodeMap<bool> ReachedMap;

//       BfsIterator4< AugGraph, AugOutEdgeIt, ReachedMap > res_bfs(res_graph);

//       for(typename std::list<Node>::const_iterator i=S.begin(); 

// 	  i!=S.end(); ++i) {

// 	res_bfs.pushAndSetReached(*i);

//       }

//       //res_bfs.pushAndSetReached(s);

//       typename AugGraph::NodeMap<AugEdge> pred(res_graph); 

//       //filled up with invalid iterators

//       typename AugGraph::NodeMap<Number> free(res_graph);

//       //searching for augmenting path

//       while ( !res_bfs.finished() ) { 

// 	AugOutEdgeIt e=/*AugOutEdgeIt*/(res_bfs);

// 	if (e.valid() && res_bfs.isBNodeNewlyReached()) {

// 	  Node v=res_graph.tail(e);

// 	  Node w=res_graph.head(e);

// 	  pred.set(w, e);

// 	  if (pred.get(v).valid()) {

// 	    free.set(w, std::min(free.get(v), e.free()));

// 	  } else {

// 	    free.set(w, e.free()); 

// 	  }

// 	  if (TMap.get(res_graph.head(e))) { 

// 	    _augment=true; 

// 	    reached_t_node=res_graph.head(e);

// 	    break; 

// 	  }

// 	}

// 	++res_bfs;

//       } //end of searching augmenting path

//       if (_augment) {

// 	Node n=reached_t_node;

// 	Number augment_value=free.get(reached_t_node);

// 	while (pred.get(n).valid()) { 

// 	  AugEdge e=pred.get(n);

// 	  e.augment(augment_value); 

// 	  n=res_graph.tail(e);

// 	}

//       }

//       return _augment;

//     }

//     void run() {

//       while (augment()) { } 

//     }

//     Number flowValue() { 

//       Number a=0;

//       for(typename std::list<Node>::const_iterator i=S.begin(); 

// 	  i!=S.end(); ++i) { 

// 	for(OutEdgeIt e=G.template first<OutEdgeIt>(*i); e.valid(); ++e) {

// 	  a+=flow.get(e);

// 	}

// 	for(InEdgeIt e=G.template first<InEdgeIt>(*i); e.valid(); ++e) {

// 	  a-=flow.get(e);