// -*- c++ -*-

 // -*- c++ -*-

 #include <iostream>

 #include <iostream>

 #include <fstream>

 #include <fstream>

 #include <lemon/time_measure.h>

 #include <lemon/time_measure.h>

 using std::cout;

 using std::cout;

 using std::endl;

 using std::endl;

 using namespace lemon;

 using namespace lemon;

 int main(int, char **) {

 int main(int, char **) {

   const int n=4;

   const int n=4;

   const double row_sum=(1.0+n*n)*n/2;

   const double row_sum=(1.0+n*n)*n/2;

   Timer ts;

   Timer ts;

   ts.reset();

   ts.reset();

   typedef LPSolver::Col Col;

   typedef LPSolver::Col Col;

   LPSolver lp;

   LPSolver lp;

   typedef std::map<std::pair<int, int>, Col> Coords;

   typedef std::map<std::pair<int, int>, Col> Coords;

   Coords x;

   Coords x;

   // we create a new variable for each entry 

   // we create a new variable for each entry