#include<lemon/lp_glpk.h>

#include<lemon/graph_reader.h>

#include<lemon/list_graph.h>

using namespace lemon;

template<class G,class C>

double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)

{

  LpGlpk lp;

  typedef G Graph;

  typedef typename G::Node Node;

  typedef typename G::NodeIt NodeIt;

  typedef typename G::Edge Edge;

  typedef typename G::EdgeIt EdgeIt;

  typedef typename G::OutEdgeIt OutEdgeIt;

  typedef typename G::InEdgeIt InEdgeIt;

  typename G::template EdgeMap<LpGlpk::Col> x(g);

  lp.addColSet(x);

  for(EdgeIt e(g);e!=INVALID;++e) {

    lp.colUpperBound(x[e],cap[e]);

    lp.colLowerBound(x[e],0);

  }

  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {

    LpGlpk::Expr ex;

    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];

    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];

    lp.addRow(ex==0);

  }

  {

    LpGlpk::Expr ex;

    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];

    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];

    lp.setObj(ex);

  }

  lp.max();

  lp.solve();

  return lp.primalValue();

}

int main() 

{

  LpGlpk lp_glpk;

  ListGraph g;

  ListGraph::Node s;

  ListGraph::Node t;

  ListGraph::EdgeMap<double> cap(g);

  GraphReader<ListGraph> reader(std::cin,g);

  reader.addNode("source",s).addNode("target",t)

    .addEdgeMap("capacity",cap).run();

  // std::ifstream file("../test/preflow_");

//   readDimacs(file, g, cap, s, t);

  std::cout << "Max flow value = " << maxFlow(g,cap,s,t) << std::endl;

}