diff --git a/src/Event.cc b/src/Event.cc
index e196ef0..45e17e0 100644
--- a/src/Event.cc
+++ b/src/Event.cc
@@ -1,1176 +1,1294 @@
 /**
  *  \authors   The HEJ collaboration (see AUTHORS for details)
  *  \date      2019-2020
  *  \copyright GPLv2 or later
  */
 #include "HEJ/Event.hh"
 
 #include <algorithm>
 #include <cassert>
 #include <cstdlib>
 #include <iomanip>
 #include <iterator>
 #include <memory>
 #include <numeric>
 #include <ostream>
 #include <string>
 #include <utility>
 
 #include "fastjet/ClusterSequence.hh"
 #include "fastjet/JetDefinition.hh"
 #include "fastjet/PseudoJet.hh"
 
 #include "LHEF/LHEF.h"
 
 #include "HEJ/Constants.hh"
 #include "HEJ/exceptions.hh"
 #include "HEJ/optional.hh"
 #include "HEJ/PDG_codes.hh"
 #include "HEJ/RNG.hh"
 
 namespace HEJ{
 
   namespace {
     using std::size_t;
     constexpr int status_in = -1;
     constexpr int status_decayed = 2;
     constexpr int status_out = 1;
 
     //! true if leptonic W decay
     bool valid_W_decay( int const w_type, // sign of W
                         std::vector<Particle> const & decays
     ){
       if(decays.size() != 2) // no 1->2 decay
         return false;
       const int pidsum = decays[0].type + decays[1].type;
       if( std::abs(pidsum) != 1 || pidsum != w_type ) // correct charge
         return false;
       // leptonic decay (only check first, second follows from pidsum)
       if( w_type == 1 ) // W+
         return is_antilepton(decays[0]) || is_neutrino(decays[0]);
       // W-
       return is_lepton(decays[0]) || is_antineutrino(decays[0]);
     }
 
     //! true for Z decay to charged leptons
     bool valid_Z_decay(std::vector<Particle> const & decays){
       if(decays.size() != 2) // no 1->2 decay
         return false;
       const int pidsum = decays[0].type + decays[1].type;
       if( std::abs(pidsum) != 0 ) // correct charge
         return false;
       // leptonic decay (only check first, second follows from pidsum)
       return is_anylepton(decays[0]) && !is_anyneutrino(decays[0]);
     }
 
     //! true if supported decay
     bool valid_decay(std::vector<Particle> const & decays){
       return valid_W_decay(+1, decays) ||       // Wp
              valid_W_decay(-1, decays) ||       // Wm
              valid_Z_decay(    decays)          // Z/gamma
       ;
     }
 
     /// @name helper functions to determine event type
     //@{
 
     /**
      * \brief check if final state valid for HEJ
      *
      * check final state has the expected number of valid decays for bosons
      * and all the rest are quarks or gluons
      */
     bool final_state_ok(Event const & ev){
       size_t invalid_decays = ev.decays().size();
 
       std::vector<Particle> const & outgoing = ev.outgoing();
       for( size_t i=0; i<outgoing.size(); ++i ){
         auto const & out{ outgoing[i] };
         if(is_AWZH_boson(out.type)){
           auto const decay = ev.decays().find(i);
 
           // W decays (required)
           if(std::abs(out.type) == ParticleID::Wp){
             if( decay != ev.decays().cend() &&
                 valid_W_decay(out.type>0?+1:-1, decay->second)
             ){
               --invalid_decays;
             }
             else return false;
           }
 
           // Higgs decays (optional)
           else if(out.type == ParticleID::h){
             if(decay != ev.decays().cend()) --invalid_decays;
           }
 
           // Z decays (required)
           else if(out.type == ParticleID::Z_photon_mix){
             if( decay != ev.decays().cend() &&
                 valid_Z_decay(decay->second)
             ){
               --invalid_decays;
             }
             else return false;
           }
         }
         else if(! is_parton(out.type)) return false;
       }
       // any invalid decays?
       if(invalid_decays != 0) return false;
 
       return true;
     }
 
     /**
      * returns all EventTypes implemented in HEJ
      */
     size_t implemented_types(std::vector<Particle> const & bosons){
       using namespace event_type;
       if(bosons.empty()) return FKL | unob | unof | qqxexb | qqxexf | qqxmid;
       else if(bosons.size() == 1) {
         switch (bosons[0].type) {
           case ParticleID::Wp:
           case ParticleID::Wm:
             return FKL | unob | unof | qqxexb | qqxexf | qqxmid;
           case ParticleID::Z_photon_mix:
             return FKL | unob | unof;
           case ParticleID::h:
             return FKL | unob | unof;
           default:
             return non_resummable;
         }
       }
       else if(bosons.size() == 2) {
         if(bosons[0].type == ParticleID::Wp && bosons[1].type == ParticleID::Wp) {
           return FKL;
         }
         return non_resummable;
       }
       else {
         return non_resummable;
       }
     }
 
     /**
      * \brief function which determines if type change is consistent with Wp emission.
      * @param in                      incoming Particle id
      * @param out                     outgoing Particle id
      * @param qqx                     Current both incoming/both outgoing?
      *
      * \see is_Wm_Change
      */
     bool is_Wp_Change(ParticleID in, ParticleID out, bool qqx){
       if(!qqx && (in==-1 || in== 2 || in==-3 || in== 4)) return out== (in-1);
       if( qqx && (in== 1 || in==-2 || in== 3 || in==-4)) return out==-(in+1);
       return false;
     }
 
     /**
      * \brief function which determines if type change is consistent with Wm emission.
      * @param in                      incoming Particle id
      * @param out                     outgoing Particle id
      * @param qqx                     Current both incoming/both outgoing?
      *
      * Ensures that change type of quark line is possible by a flavour changing
      * Wm emission. Allows checking of qqx currents also.
      */
     bool is_Wm_Change(ParticleID in, ParticleID out, bool qqx){
       if(!qqx && (in== 1 || in==-2 || in== 3 || in==-4)) return out== (in+1);
       if( qqx && (in==-1 || in== 2 || in==-3 || in== 4)) return out==-(in-1);
       return false;
     }
 
     /**
      * \brief checks if particle type remains same from incoming to outgoing
      * @param in                      incoming Particle
      * @param out                     outgoing Particle
      * @param qqx                     Current both incoming/outgoing?
      */
     bool no_flavour_change(ParticleID in, ParticleID out, bool qqx){
       const int qqxCurrent = qqx?-1:1;
       if(std::abs(in)<=6 || in==pid::gluon) return (in==out*qqxCurrent);
       else return false;
     }
 
     bool has_2_jets(Event const & event){
       return event.jets().size() >= 2;
     }
 
     /**
      * \brief check if we have a valid Impact factor
      * @param in                      incoming Particle
      * @param out                     outgoing Particle
      * @param qqx                     Current both incoming/outgoing?
      * @param W_change                returns +1 if Wp, -1 if Wm, else 0
      */
     bool is_valid_impact_factor(
       ParticleID in, ParticleID out, bool qqx, int & W_change
     ){
       if( no_flavour_change(in, out, qqx) ){
         return true;
       }
       if( is_Wp_Change(in, out, qqx) ) {
         W_change+=1;
         return true;
       }
       if( is_Wm_Change(in, out, qqx) ) {
         W_change-=1;
         return true;
       }
       return false;
     }
 
     //! Returns all possible classifications from the impact factors
     // the beginning points are changed s.t. after the the classification they
     // point to the beginning of the (potential) FKL chain
     // sets W_change: + if Wp change
     //                0 if no change
     //                - if Wm change
     // This function can be used with forward & backwards iterators
     template<class OutIterator>
     size_t possible_impact_factors(
       ParticleID incoming_id,                                   // incoming
       OutIterator   & begin_out, OutIterator   const & end_out, // outgoing
       int & W_change, std::vector<Particle> const & boson,
       bool const backward                                       // backward?
     ){
       using namespace event_type;
       // keep track of all states that we don't test
       size_t not_tested = qqxmid;
       if(backward)
         not_tested |= unof | qqxexf;
       else
         not_tested |= unob | qqxexb;
 
       // Is this LL current?
       if( is_valid_impact_factor(incoming_id, begin_out->type, false, W_change) ){
         ++begin_out;
         return not_tested | FKL;
       }
 
       // or NLL current?
       // -> needs two partons in two different jets
       if( std::distance(begin_out, end_out)>=2
       ){
         auto next = std::next(begin_out);
         // Is this unordered emisson?
         if( incoming_id!=pid::gluon && begin_out->type==pid::gluon ){
           if( is_valid_impact_factor(
                 incoming_id, next->type, false, W_change )
           ){
             // veto Higgs inside uno
             assert(next!=end_out);
             if( !boson.empty() && boson.front().type == ParticleID::h
             ){
               if(  (backward && boson.front().rapidity() < next->rapidity())
                 ||(!backward && boson.front().rapidity() > next->rapidity()))
               return non_resummable;
             }
             begin_out = std::next(next);
             return not_tested | (backward?unob:unof);
           }
         }
         // Is this QQbar?
         else if( incoming_id==pid::gluon ){
           if( is_valid_impact_factor(
                 begin_out->type, next->type, true, W_change )
           ){
             // veto Higgs inside qqx
             assert(next!=end_out);
             if( !boson.empty() && boson.front().type == ParticleID::h
             ){
               if(  (backward && boson.front().rapidity() < next->rapidity())
                 ||(!backward && boson.front().rapidity() > next->rapidity()))
               return non_resummable;
             }
             begin_out = std::next(next);
             return not_tested | (backward?qqxexb:qqxexf);
           }
         }
       }
       return non_resummable;
     }
 
     //! Returns all possible classifications from central emissions
     // the beginning points are changed s.t. after the the classification they
     // point to the end of the emission chain
     // sets W_change: + if Wp change
     //               0 if no change
     //               - if Wm change
     template<class OutIterator>
     size_t possible_central(
       OutIterator & begin_out, OutIterator const & end_out,
       int & W_change, std::vector<Particle> const & boson
     ){
       using namespace event_type;
       // if we already passed the central chain,
       // then it is not a valid all-order state
       if(std::distance(begin_out, end_out) < 0) return non_resummable;
       // keep track of all states that we don't test
       size_t possible = unob | unof
                           | qqxexb | qqxexf;
 
       // Find the first non-gluon/non-FKL
       while( (begin_out->type==pid::gluon) && (begin_out!=end_out) ){
         ++begin_out;
       }
       // end of chain -> FKL
       if( begin_out==end_out ){
         return possible | FKL;
       }
 
       // is this a qqbar-pair?
       // needs two partons in two separate jets
       auto next = std::next(begin_out);
       if( is_valid_impact_factor(
             begin_out->type, next->type, true, W_change )
       ){
         // veto Higgs inside qqx
         if( !boson.empty() && boson.front().type == ParticleID::h
             && boson.front().rapidity() > begin_out->rapidity()
             && boson.front().rapidity() < next->rapidity()
         ){
           return non_resummable;
         }
         begin_out = std::next(next);
         // remaining chain should be pure gluon/FKL
         for(; begin_out!=end_out; ++begin_out){
           if(begin_out->type != pid::gluon) return non_resummable;
         }
         return possible | qqxmid;
       }
       return non_resummable;
     }
 
     /**
      * \brief Checks for all event types
      * @param ev          Event
      * @returns           Event Type
      *
      */
     event_type::EventType classify(Event const & ev){
       using namespace event_type;
       if(! has_2_jets(ev))
         return no_2_jets;
       // currently we can't handle multiple boson states in the ME. So they are
       // considered "bad_final_state" even though the "classify" could work with
       // them.
       if(! final_state_ok(ev))
         return bad_final_state;
 
       // initialise variables
       auto const & in = ev.incoming();
 
       // range for current checks
       auto begin_out{ev.cbegin_partons()};
       auto end_out{ev.crbegin_partons()};
 
       assert(std::distance(begin(in), end(in)) == 2);
       assert(std::distance(begin_out, end_out.base()) >= 2);
       assert(std::is_sorted(begin_out, end_out.base(), rapidity_less{}));
 
       auto const bosons{ filter_AWZH_bosons(ev.outgoing()) };
 
       // keep track of potential W couplings, at the end the sum should be 0
       int remaining_Wp = 0;
       int remaining_Wm = 0;
       for(auto const & boson : bosons){
           if(boson.type == ParticleID::Wp) ++remaining_Wp;
           else if(boson.type == ParticleID::Wm) ++remaining_Wm;
       }
 
       size_t final_type = ~(no_2_jets | bad_final_state);
 
       // check forward impact factor
       int W_change = 0;
       final_type &= possible_impact_factors(
         in.front().type,
         begin_out, end_out.base(),
         W_change, bosons, true );
       if( final_type == non_resummable )
         return non_resummable;
       if(W_change>0) remaining_Wp-=W_change;
       else if(W_change<0) remaining_Wm+=W_change;
 
       // check backward impact factor
       W_change = 0;
       final_type &= possible_impact_factors(
         in.back().type,
         end_out, std::make_reverse_iterator(begin_out),
         W_change, bosons, false );
       if( final_type == non_resummable )
         return non_resummable;
       if(W_change>0) remaining_Wp-=W_change;
       else if(W_change<0) remaining_Wm+=W_change;
 
       // check central emissions
       W_change = 0;
       final_type &= possible_central(
         begin_out, end_out.base(), W_change, bosons );
       if( final_type == non_resummable )
         return non_resummable;
       if(W_change>0) remaining_Wp-=W_change;
       else if(W_change<0) remaining_Wm+=W_change;
 
       // Check whether the right number of Ws are present
       if( remaining_Wp != 0 || remaining_Wm != 0 ) return non_resummable;
 
       // result has to be unique
       if( (final_type & (final_type-1)) != 0) return non_resummable;
 
       // check that each sub processes is implemented
       // (has to be done at the end)
       if( (final_type & ~implemented_types(bosons)) != 0 )
         return non_resummable;
 
       return static_cast<EventType>(final_type);
     }
     //@}
 
     Particle extract_particle(LHEF::HEPEUP const & hepeup, size_t i){
       const ParticleID id = static_cast<ParticleID>(hepeup.IDUP[i]);
       const fastjet::PseudoJet momentum{
         hepeup.PUP[i][0], hepeup.PUP[i][1],
         hepeup.PUP[i][2], hepeup.PUP[i][3]
       };
       if(is_parton(id))
         return Particle{ id, std::move(momentum), hepeup.ICOLUP[i] };
       return Particle{ id, std::move(momentum), {} };
     }
 
     bool is_decay_product(std::pair<int, int> const & mothers){
       if(mothers.first == 0) return false;
       return mothers.second == 0 || mothers.first == mothers.second;
     }
 
   } // namespace anonymous
 
   Event::EventData::EventData(LHEF::HEPEUP const & hepeup){
     parameters.central = EventParameters{
       hepeup.scales.mur, hepeup.scales.muf, hepeup.XWGTUP
     };
     size_t in_idx = 0;
     for (int i = 0; i < hepeup.NUP; ++i) {
       // skip decay products
       // we will add them later on, but we have to ensure that
       // the decayed particle is added before
       if(is_decay_product(hepeup.MOTHUP[i])) continue;
 
       auto particle = extract_particle(hepeup, i);
       // needed to identify mother particles for decay products
       particle.p.set_user_index(i+1);
 
       if(hepeup.ISTUP[i] == status_in){
         if(in_idx > incoming.size()) {
           throw std::invalid_argument{
             "Event has too many incoming particles"
           };
         }
         incoming[in_idx++] = std::move(particle);
       }
       else outgoing.emplace_back(std::move(particle));
     }
 
     // add decay products
     for (int i = 0; i < hepeup.NUP; ++i) {
       if(!is_decay_product(hepeup.MOTHUP[i])) continue;
       const int mother_id = hepeup.MOTHUP[i].first;
       const auto mother = std::find_if(
           begin(outgoing), end(outgoing),
           [mother_id](Particle const & particle){
             return particle.p.user_index() == mother_id;
           }
       );
       if(mother == end(outgoing)){
         throw std::invalid_argument{"invalid decay product parent"};
       }
       const int mother_idx = std::distance(begin(outgoing), mother);
       assert(mother_idx >= 0);
       decays[mother_idx].emplace_back(extract_particle(hepeup, i));
     }
   }
 
   Event::Event(
     UnclusteredEvent const & ev,
     fastjet::JetDefinition const & jet_def, double const min_jet_pt
   ):
     Event( Event::EventData{
       ev.incoming, ev.outgoing, ev.decays,
       Parameters<EventParameters>{ev.central, ev.variations}
     }.cluster(jet_def, min_jet_pt) )
   {}
 
   //! @TODO remove in HEJ 2.2.0
   UnclusteredEvent::UnclusteredEvent(LHEF::HEPEUP const & hepeup){
       Event::EventData const evData{hepeup};
       incoming = evData.incoming;
       outgoing = evData.outgoing;
       decays = evData.decays;
       central = evData.parameters.central;
       variations = evData.parameters.variations;
   }
 
   void Event::EventData::sort(){
     // sort particles
     std::sort(
         begin(incoming), end(incoming),
         [](Particle o1, Particle o2){return o1.p.pz()<o2.p.pz();}
     );
 
     auto old_outgoing = std::move(outgoing);
     std::vector<size_t> idx(old_outgoing.size());
     std::iota(idx.begin(), idx.end(), 0);
     std::sort(idx.begin(), idx.end(), [&old_outgoing](size_t i, size_t j){
       return old_outgoing[i].rapidity() < old_outgoing[j].rapidity();
     });
     outgoing.clear();
     outgoing.reserve(old_outgoing.size());
     for(size_t i: idx) {
       outgoing.emplace_back(std::move(old_outgoing[i]));
     }
 
     // find decays again
     if(!decays.empty()){
       auto old_decays = std::move(decays);
       decays.clear();
       for(size_t i=0; i<idx.size(); ++i) {
         auto decay = old_decays.find(idx[i]);
         if(decay != old_decays.end())
           decays.emplace(i, std::move(decay->second));
       }
       assert(old_decays.size() == decays.size());
     }
   }
 
   namespace {
     // use valid_X_decay to determine boson type
     ParticleID reconstruct_type(std::vector<Particle> const & progeny) {
       if(valid_W_decay(+1, progeny)) { return ParticleID::Wp; }
       if(valid_W_decay(-1, progeny)) { return ParticleID::Wm; }
       if(valid_Z_decay(progeny)) { return ParticleID::Z_photon_mix; }
 
       throw not_implemented{
         "final state with decay X -> "
           + name(progeny[0].type)
           + " + "
           + name(progeny[1].type)
       };
     }
 
     // reconstruct particle with explicit ParticleID
     Particle reconstruct_boson(
       std::vector<Particle> const & progeny,
       ParticleID const & type
     ) {
       Particle progenitor;
       progenitor.p = progeny[0].p + progeny[1].p;
       progenitor.type = type;
       return progenitor;
     }
 
     // reconstruct via call to reconstruct_type
     Particle reconstruct_boson(std::vector<Particle> const & progeny) {
       Particle progenitor {reconstruct_boson(progeny, reconstruct_type(progeny))};
       assert(is_AWZH_boson(progenitor));
       return progenitor;
     }
 
+    typedef std::vector< std::vector<Particle> > GroupedParticles;
+    typedef std::pair<Particle, std::vector<Particle> > Decay;
+    typedef std::vector< Decay > Decays;
+
+    // return groups of reconstructable progeny
+    std::vector<GroupedParticles> group_progeny
+    (
+      std::vector<Particle> & leptons
+    ) {
+      /**
+      Warning: The partition in to charged/neutral leptons is valid ONLY for WW.
+      **/
+      assert(leptons.size() == 4);
+      const auto begin_neutrino = std::partition(
+          begin(leptons), end(leptons),
+          [](Particle const & p) {return !is_anyneutrino(p);}
+      );
+
+
+      std::vector<Particle> neutrinos (begin_neutrino, end(leptons));
+      leptons.erase(begin_neutrino, end(leptons));
+
+      std::sort(begin(leptons), end(leptons), type_less{});
+      std::sort(begin(neutrinos), end(neutrinos), type_less{});
+
+      if(leptons.size() != 2 && neutrinos.size() != 2) { return {}; }
+
+      assert(leptons.size() == 2 && neutrinos.size() == 2);
+      std::vector< GroupedParticles > candidate_grouping {
+        {{leptons[0], neutrinos[0]}, {leptons[1], neutrinos[1]}},
+        {{leptons[1], neutrinos[0]}, {leptons[0], neutrinos[1]}}
+      };
+
+      // erase groupings containing invalid decays
+      candidate_grouping.erase(
+        std::remove_if(begin(candidate_grouping), end(candidate_grouping),
+          [] (GroupedParticles & candidate) -> bool {
+            return ! std::accumulate(
+              cbegin(candidate), cend(candidate), true,
+              [] (bool acc_valid, std::vector<Particle> const & decay) -> bool {
+                  return acc_valid && valid_decay(decay);
+              }
+            );
+          }
+        ),
+        candidate_grouping.end()
+      );
+
+      return candidate_grouping;
+    }
+
+    // 'best' decay ordering measure
+    double decay_measure(Particle reconstructed, EWConstants const & params) {
+        ParticleProperties ref = params.prop(reconstructed.type);
+        return std::abs(reconstructed.p.m() - ref.mass);
+    }
+
+    // decay_measure accumulated over decays
+    double decay_measure(Decays const & decays, EWConstants const & params) {
+      return
+      std::accumulate(
+        cbegin(decays), cend(decays), 0.,
+        [&params] (double dm, Decay const & decay) -> double {
+          return dm + decay_measure(decay.first, params);
+        }
+      );
+    }
+
+    // select best combination of decays for the event
+    Decays select_decays
+    (
+      std::vector<Particle> & leptons,
+      EWConstants const & ew_parameters
+    ) {
+      std::vector<GroupedParticles> groupings = group_progeny(leptons);
+
+      std::vector<Decays> valid_decays;
+      valid_decays.reserve(groupings.size());
+
+      // Reconstruct all groupings
+      for(GroupedParticles const & group : groupings) {
+        Decays decays;
+        for(auto const & progeny : group) {
+          decays.emplace_back(make_pair(reconstruct_boson(progeny), progeny));
+        }
+        valid_decays.emplace_back(decays);
+      }
+      if (valid_decays.empty()) {
+        throw not_implemented{"No supported intermediate reconstruction available"};
+      }
+      else if (valid_decays.size() == 1) { return valid_decays[0]; }
+      else {
+        // select decay with smallest decay_measure
+        auto selected = std::min_element(cbegin(valid_decays), cend(valid_decays),
+          [&ew_parameters] (auto const & d1, auto const & d2) -> bool {
+            return decay_measure(d1, ew_parameters) < decay_measure(d2, ew_parameters);
+          }
+        );
+
+        return *selected;
+      }
+    }
+
   }
 
-  void Event::EventData::reconstruct_intermediate(EWConstants const & /* ew_parameters */) {
+  void Event::EventData::reconstruct_intermediate(EWConstants const & ew_parameters) {
     const auto begin_leptons = std::partition(
         begin(outgoing), end(outgoing),
         [](Particle const & p) {return !is_anylepton(p);}
     );
     if(begin_leptons == end(outgoing)) return;
     assert(is_anylepton(*begin_leptons));
     std::vector<Particle> leptons(begin_leptons, end(outgoing));
     outgoing.erase(begin_leptons, end(outgoing));
-    if(leptons.size() != 2) {
-      throw not_implemented{"Final states with one or more than two leptons"};
+    if(leptons.empty()) { return; }  // nothing to do
+    else if(leptons.size() == 2) {
+      outgoing.emplace_back(reconstruct_boson(leptons));
+      std::sort(begin(leptons), end(leptons), type_less{});
+      decays.emplace(outgoing.size()-1, std::move(leptons));
+    }
+    else if(leptons.size() == 4) {
+      // select_decays only supports WpWp
+      Decays valid_decays = select_decays(leptons, ew_parameters);
+      for(auto &decay : valid_decays) {
+        outgoing.emplace_back(decay.first);
+        std::sort(begin(decay.second), end(decay.second), type_less{});
+        decays.emplace(outgoing.size()-1, std::move(decay.second));
+      }
+    }
+    else {
+      throw not_implemented {
+        std::to_string(leptons.size())
+        + " leptons in the final state"
+      };
     }
-    std::sort(begin(leptons), end(leptons), type_less{});
-    outgoing.emplace_back(reconstruct_boson(leptons));
-    decays.emplace(outgoing.size()-1, std::move(leptons));
   }
 
   Event Event::EventData::cluster(
       fastjet::JetDefinition const & jet_def, double const min_jet_pt
   ){
     sort();
     return Event{ std::move(incoming), std::move(outgoing), std::move(decays),
       std::move(parameters),
       jet_def, min_jet_pt
     };
   }
 
   Event::Event(
       std::array<Particle, 2> && incoming,
       std::vector<Particle> && outgoing,
       std::unordered_map<size_t, std::vector<Particle>> && decays,
       Parameters<EventParameters> && parameters,
       fastjet::JetDefinition const & jet_def,
       double const min_jet_pt
     ): incoming_{std::move(incoming)},
        outgoing_{std::move(outgoing)},
        decays_{std::move(decays)},
        parameters_{std::move(parameters)},
        cs_{ to_PseudoJet( filter_partons(outgoing_) ), jet_def },
        min_jet_pt_{min_jet_pt}
     {
       jets_ = sorted_by_rapidity(cs_.inclusive_jets(min_jet_pt_));
       assert(std::is_sorted(begin(outgoing_), end(outgoing_),
         rapidity_less{}));
       type_ = classify(*this);
     }
 
   namespace {
     //! check that Particles have a reasonable colour
     bool correct_colour(Particle const & part){
       ParticleID id{ part.type };
       if(!is_parton(id))
         return !part.colour;
 
       if(!part.colour)
         return false;
 
       Colour const & col{ *part.colour };
       if(is_quark(id))
         return col.first != 0 && col.second == 0;
       if(is_antiquark(id))
         return col.first == 0 && col.second != 0;
       assert(id==ParticleID::gluon);
       return col.first != 0 && col.second != 0 && col.first != col.second;
     }
 
     //! Connect parton to t-channel colour line & update the line
     //! returns false if connection not possible
     template<class OutIterator>
     bool try_connect_t(OutIterator const & it_part, Colour & line_colour){
       if( line_colour.first == it_part->colour->second ){
         line_colour.first = it_part->colour->first;
         return true;
       }
       if( line_colour.second == it_part->colour->first ){
         line_colour.second = it_part->colour->second;
         return true;
       }
       return false;
     }
 
     //! Connect parton to u-channel colour line & update the line
     //! returns false if connection not possible
     template<class OutIterator>
     bool try_connect_u(OutIterator & it_part, Colour & line_colour){
       auto it_next = std::next(it_part);
       if( try_connect_t(it_next, line_colour)
           && try_connect_t(it_part, line_colour)
       ){
         it_part=it_next;
         return true;
       }
       return false;
     }
   } // namespace anonymous
 
   bool Event::is_leading_colour() const {
     if( !correct_colour(incoming()[0]) || !correct_colour(incoming()[1]) )
       return false;
 
     Colour line_colour = *incoming()[0].colour;
     std::swap(line_colour.first, line_colour.second);
 
     // reasonable colour
     if(!std::all_of(outgoing().cbegin(), outgoing().cend(), correct_colour))
       return false;
 
     for(auto it_part = cbegin_partons(); it_part!=cend_partons(); ++it_part){
 
       switch (type()) {
       case event_type::FKL:
         if( !try_connect_t(it_part, line_colour) )
           return false;
         break;
       case event_type::unob:
       case event_type::qqxexb: {
         if( !try_connect_t(it_part, line_colour)
             // u-channel only allowed at impact factor
             && (std::distance(cbegin_partons(), it_part)!=0
                 || !try_connect_u(it_part, line_colour)))
           return false;
         break;
       }
       case event_type::unof:
       case event_type::qqxexf: {
         if( !try_connect_t(it_part, line_colour)
             // u-channel only allowed at impact factor
             && (std::distance(it_part, cend_partons())!=2
                 || !try_connect_u(it_part, line_colour)))
           return false;
         break;
       }
       case event_type::qqxmid:{
         auto it_next = std::next(it_part);
         if( !try_connect_t(it_part, line_colour)
             // u-channel only allowed at qqx/qxq pair
             && ( (   !(is_quark(*it_part) && is_antiquark(*it_next))
                   && !(is_antiquark(*it_part) && is_quark(*it_next)))
                 || !try_connect_u(it_part, line_colour))
           )
           return false;
         break;
       }
       default:
         throw std::logic_error{"unreachable"};
       }
 
       // no colour singlet exchange/disconnected diagram
       if(line_colour.first == line_colour.second)
         return false;
     }
 
     return (incoming()[1].colour->first == line_colour.first)
         && (incoming()[1].colour->second == line_colour.second);
   }
 
   namespace {
     //! connect incoming Particle to colour flow
     void connect_incoming(Particle & in, int & colour, int & anti_colour){
       in.colour = std::make_pair(anti_colour, colour);
       // gluon
       if(in.type == pid::gluon)
         return;
       if(in.type > 0){
         // quark
         assert(is_quark(in));
         in.colour->second = 0;
         colour*=-1;
         return;
       }
       // anti-quark
       assert(is_antiquark(in));
       in.colour->first = 0;
       anti_colour*=-1;
       return;
     }
 
     //! connect outgoing Particle to t-channel colour flow
     template<class OutIterator>
     void connect_tchannel(
         OutIterator & it_part, int & colour, int & anti_colour, RNG & ran
     ){
       assert(colour>0 || anti_colour>0);
       if(it_part->type == ParticleID::gluon){
         // gluon
         if(colour>0 && anti_colour>0){
           // on g line => connect to colour OR anti-colour (random)
           if(ran.flat() < 0.5){
             it_part->colour = std::make_pair(colour+2,colour);
             colour+=2;
           } else {
             it_part->colour = std::make_pair(anti_colour, anti_colour+2);
             anti_colour+=2;
           }
         } else if(colour > 0){
           // on q line => connect to available colour
             it_part->colour = std::make_pair(colour+2, colour);
             colour+=2;
         } else {
           assert(colour<0 && anti_colour>0);
           // on qx line => connect to available anti-colour
           it_part->colour = std::make_pair(anti_colour, anti_colour+2);
           anti_colour+=2;
         }
       } else if(is_quark(*it_part)) {
         // quark
         assert(anti_colour>0);
         if(colour>0){
           // on g line => connect and remove anti-colour
           it_part->colour = std::make_pair(anti_colour, 0);
           anti_colour+=2;
           anti_colour*=-1;
         } else {
           // on qx line => new colour
           colour*=-1;
           it_part->colour = std::make_pair(colour, 0);
         }
       } else if(is_antiquark(*it_part)) {
         // anti-quark
         assert(colour>0);
         if(anti_colour>0){
           // on g line => connect and remove colour
           it_part->colour = std::make_pair(0, colour);
           colour+=2;
           colour*=-1;
         } else {
           // on q line => new anti-colour
           anti_colour*=-1;
           it_part->colour = std::make_pair(0, anti_colour);
         }
       } else { // not a parton
         assert(!is_parton(*it_part));
         it_part->colour = {};
       }
     }
 
     //! connect to t- or u-channel colour flow
     template<class OutIterator>
     void connect_utchannel(
         OutIterator & it_part, int & colour, int & anti_colour, RNG & ran
     ){
       OutIterator it_first = it_part++;
       if(ran.flat()<.5) {// t-channel
         connect_tchannel(it_first, colour, anti_colour, ran);
         connect_tchannel(it_part, colour, anti_colour, ran);
       }
       else { // u-channel
         connect_tchannel(it_part, colour, anti_colour, ran);
         connect_tchannel(it_first, colour, anti_colour, ran);
       }
     }
   } // namespace anonymous
 
   bool Event::generate_colours(RNG & ran){
     // generate only for HEJ events
     if(!event_type::is_resummable(type()))
       return false;
     assert(std::is_sorted(
       begin(outgoing()), end(outgoing()), rapidity_less{}));
     assert(incoming()[0].pz() < incoming()[1].pz());
 
     // positive (anti-)colour -> can connect
     // negative (anti-)colour -> not available/used up by (anti-)quark
     int colour = COLOUR_OFFSET;
     int anti_colour = colour+1;
     // initialise first
     connect_incoming(incoming_[0], colour, anti_colour);
 
     // reset outgoing colours
     std::for_each(outgoing_.begin(), outgoing_.end(),
       [](Particle & part){ part.colour = {};});
 
     for(auto it_part = begin_partons(); it_part!=end_partons(); ++it_part){
         switch (type()) {
         // subleading can connect to t- or u-channel
         case event_type::unob:
         case event_type::qqxexb: {
           if( std::distance(begin_partons(), it_part)==0)
             connect_utchannel(it_part, colour, anti_colour, ran);
           else
             connect_tchannel(it_part, colour, anti_colour, ran);
           break;
         }
         case event_type::unof:
         case event_type::qqxexf: {
           if( std::distance(it_part, end_partons())==2)
             connect_utchannel(it_part, colour, anti_colour, ran);
           else
             connect_tchannel(it_part, colour, anti_colour, ran);
           break;
         }
         case event_type::qqxmid:{
           auto it_next = std::next(it_part);
           if( std::distance(begin_partons(), it_part)>0
               && std::distance(it_part, end_partons())>2
               && ( (is_quark(*it_part) && is_antiquark(*it_next))
                 || (is_antiquark(*it_part) && is_quark(*it_next)) )
           )
             connect_utchannel(it_part, colour, anti_colour, ran);
           else
             connect_tchannel(it_part, colour, anti_colour, ran);
           break;
         }
         default: // rest has to be t-channel
           connect_tchannel(it_part, colour, anti_colour, ran);
         }
     }
     // Connect last
     connect_incoming(incoming_[1], anti_colour, colour);
     assert(is_leading_colour());
     return true;
   } // generate_colours
 
   namespace {
     bool valid_parton(
       std::vector<fastjet::PseudoJet> const & jets,
       Particle const & parton, int const idx,
       double const max_ext_soft_pt_fraction, double const min_extparton_pt
     ){
       // TODO code overlap with PhaseSpacePoint::pass_extremal_cuts
       if(min_extparton_pt > parton.pt()) return false;
       if(idx<0) return false;
       assert(static_cast<int>(jets.size())>=idx);
       auto const & jet{ jets[idx] };
       if( (parton.p - jet).pt()/jet.pt() > max_ext_soft_pt_fraction)
         return false;
       return true;
     }
   }
 
   // this should work with multiple types
   bool Event::valid_hej_state(double const max_frac,
                               double const min_pt
   ) const {
     using namespace event_type;
     if(!is_resummable(type()))
       return false;
 
     auto const & jet_idx{ particle_jet_indices() };
     auto idx_begin{ jet_idx.cbegin() };
     auto idx_end{  jet_idx.crbegin() };
 
     auto part_begin{ cbegin_partons() };
     auto part_end{  crbegin_partons() };
 
     // always seperate extremal jets
     if( !valid_parton(jets(), *part_begin, *idx_begin, max_frac, min_pt) )
       return false;
     ++part_begin;
     ++idx_begin;
     if( !valid_parton(jets(), *part_end,   *idx_end,   max_frac, min_pt) )
       return false;
     ++part_end;
     ++idx_end;
 
     // unob -> second parton in own jet
     if( type() & (unob | qqxexb) ){
       if( !valid_parton(jets(), *part_begin, *idx_begin, max_frac, min_pt) )
         return false;
       ++part_begin;
       ++idx_begin;
     }
 
     if( type() & (unof | qqxexf) ){
       if( !valid_parton(jets(), *part_end,   *idx_end,   max_frac, min_pt) )
         return false;
       ++part_end;
       // ++idx_end; // last check, we don't need idx_end afterwards
     }
 
     if( type() & qqxmid ){
       // find qqx pair
       auto begin_qqx{ std::find_if( part_begin, part_end.base(),
         [](Particle const & part) -> bool {
           return part.type != ParticleID::gluon;
         }
       )};
       assert(begin_qqx != part_end.base());
       long int qqx_pos{ std::distance(part_begin, begin_qqx) };
       assert(qqx_pos >= 0);
       idx_begin+=qqx_pos;
       if( !( valid_parton(jets(),*begin_qqx,    *idx_begin,    max_frac,min_pt)
           && valid_parton(jets(),*(++begin_qqx),*(++idx_begin),max_frac,min_pt)
       ))
         return false;
     }
     return true;
   }
 
   Event::ConstPartonIterator Event::begin_partons() const {
     return cbegin_partons();
   }
   Event::ConstPartonIterator Event::cbegin_partons() const {
     return boost::make_filter_iterator(
         static_cast<bool (*)(Particle const &)>(is_parton),
         cbegin(outgoing()),
         cend(outgoing())
     );
   }
 
   Event::ConstPartonIterator Event::end_partons() const {
     return cend_partons();
   }
   Event::ConstPartonIterator Event::cend_partons() const {
     return boost::make_filter_iterator(
         static_cast<bool (*)(Particle const &)>(is_parton),
         cend(outgoing()),
         cend(outgoing())
     );
   }
 
   Event::ConstReversePartonIterator Event::rbegin_partons() const {
     return crbegin_partons();
   }
   Event::ConstReversePartonIterator Event::crbegin_partons() const {
     return std::reverse_iterator<ConstPartonIterator>( cend_partons() );
   }
 
   Event::ConstReversePartonIterator Event::rend_partons() const {
     return crend_partons();
   }
   Event::ConstReversePartonIterator Event::crend_partons() const {
     return std::reverse_iterator<ConstPartonIterator>( cbegin_partons() );
   }
 
   Event::PartonIterator Event::begin_partons() {
     return boost::make_filter_iterator(
         static_cast<bool (*)(Particle const &)>(is_parton),
         begin(outgoing_),
         end(outgoing_)
     );
   }
 
   Event::PartonIterator Event::end_partons() {
     return boost::make_filter_iterator(
         static_cast<bool (*)(Particle const &)>(is_parton),
         end(outgoing_),
         end(outgoing_)
     );
   }
 
   Event::ReversePartonIterator Event::rbegin_partons() {
     return std::reverse_iterator<PartonIterator>( end_partons() );
   }
 
   Event::ReversePartonIterator Event::rend_partons() {
     return std::reverse_iterator<PartonIterator>( begin_partons() );
   }
 
   namespace {
     void print_momentum(std::ostream & os, fastjet::PseudoJet const & part){
     const std::streamsize orig_prec = os.precision();
       os <<std::scientific<<std::setprecision(6) << "["
         <<std::setw(13)<<std::right<< part.px() << ", "
         <<std::setw(13)<<std::right<< part.py() << ", "
         <<std::setw(13)<<std::right<< part.pz() << ", "
         <<std::setw(13)<<std::right<< part.E() << "]"<< std::fixed;
       os.precision(orig_prec);
     }
 
     void print_colour(std::ostream & os, optional<Colour> const & col){
       if(!col)
         os << "(no color)"; // American spelling for better alignment
       else
         os << "(" <<std::setw(3)<<std::right<< col->first
            << ", " <<std::setw(3)<<std::right<< col->second << ")";
     }
   }
 
   std::ostream& operator<<(std::ostream & os, Event const & ev){
     const std::streamsize orig_prec = os.precision();
     os <<std::setprecision(4)<<std::fixed;
     os << "########## " << name(ev.type()) << " ##########" << std::endl;
     os << "Incoming particles:\n";
     for(auto const & in: ev.incoming()){
       os <<std::setw(3)<< in.type << ": ";
       print_colour(os, in.colour);
       os << " ";
       print_momentum(os, in.p);
       os << std::endl;
     }
     os << "\nOutgoing particles: " << ev.outgoing().size() << "\n";
     for(auto const & out: ev.outgoing()){
       os <<std::setw(3)<< out.type << ": ";
       print_colour(os, out.colour);
       os << " ";
       print_momentum(os, out.p);
       os << " => rapidity="
         <<std::setw(7)<<std::right<< out.rapidity() << std::endl;
     }
     os << "\nForming Jets: " << ev.jets().size() << "\n";
     for(auto const & jet: ev.jets()){
       print_momentum(os, jet);
       os << " => rapidity="
         <<std::setw(7)<<std::right<< jet.rapidity() << std::endl;
     }
     if(ev.decays().size() > 0 ){
       os << "\nDecays: " << ev.decays().size() << "\n";
       for(auto const & decay: ev.decays()){
         os <<std::setw(3)<< ev.outgoing()[decay.first].type
           << " (" << decay.first << ") to:\n";
         for(auto const & out: decay.second){
           os <<"  "<<std::setw(3)<< out.type << ": ";
           print_momentum(os, out.p);
           os << " => rapidity="
             <<std::setw(7)<<std::right<< out.rapidity() << std::endl;
         }
       }
 
     }
     os << std::defaultfloat;
     os.precision(orig_prec);
     return os;
   }
 
   double shat(Event const & ev){
     return (ev.incoming()[0].p + ev.incoming()[1].p).m2();
   }
 
   LHEF::HEPEUP to_HEPEUP(Event const & event, LHEF::HEPRUP * heprup){
     LHEF::HEPEUP result;
     result.heprup = heprup;
     result.weights = {{event.central().weight, nullptr}};
     for(auto const & var: event.variations()){
       result.weights.emplace_back(var.weight, nullptr);
     }
     size_t num_particles = event.incoming().size() + event.outgoing().size();
     for(auto const & decay: event.decays()) num_particles += decay.second.size();
     result.NUP = num_particles;
     // the following entries are pretty much meaningless
     result.IDPRUP = event.type();  // event type
     result.AQEDUP = 1./128.;  // alpha_EW
     //result.AQCDUP = 0.118 // alpha_QCD
     // end meaningless part
     result.XWGTUP = event.central().weight;
     result.SCALUP = event.central().muf;
     result.scales.muf = event.central().muf;
     result.scales.mur = event.central().mur;
     result.scales.SCALUP = event.central().muf;
     result.pdfinfo.p1 = event.incoming().front().type;
     result.pdfinfo.p2 = event.incoming().back().type;
     result.pdfinfo.scale = event.central().muf;
 
     result.IDUP.reserve(num_particles);   // PID
     result.ISTUP.reserve(num_particles);  // status (in, out, decay)
     result.PUP.reserve(num_particles);    // momentum
     result.MOTHUP.reserve(num_particles); // index mother particle
     result.ICOLUP.reserve(num_particles); // colour
     // incoming
     std::array<Particle, 2> incoming{ event.incoming() };
     // First incoming should be positive pz according to LHE standard
     // (or at least most (everyone?) do it this way, and Pythia assumes it)
     if(incoming[0].pz() < incoming[1].pz())
       std::swap(incoming[0], incoming[1]);
     for(Particle const & in: incoming){
       result.IDUP.emplace_back(in.type);
       result.ISTUP.emplace_back(status_in);
       result.PUP.push_back({in.p[0], in.p[1], in.p[2], in.p[3], in.p.m()});
       result.MOTHUP.emplace_back(0, 0);
       assert(in.colour);
       result.ICOLUP.emplace_back(*in.colour);
     }
     // outgoing
     for(size_t i = 0; i < event.outgoing().size(); ++i){
       Particle const & out = event.outgoing()[i];
       result.IDUP.emplace_back(out.type);
       const int status = event.decays().count(i)?status_decayed:status_out;
       result.ISTUP.emplace_back(status);
       result.PUP.push_back({out.p[0], out.p[1], out.p[2], out.p[3], out.p.m()});
       result.MOTHUP.emplace_back(1, 2);
       if(out.colour)
         result.ICOLUP.emplace_back(*out.colour);
       else{
         result.ICOLUP.emplace_back(std::make_pair(0,0));
       }
     }
     // decays
     for(auto const & decay: event.decays()){
       for(auto const & out: decay.second){
         result.IDUP.emplace_back(out.type);
         result.ISTUP.emplace_back(status_out);
         result.PUP.push_back({out.p[0], out.p[1], out.p[2], out.p[3], out.p.m()});
         const size_t mother_idx = 1 + event.incoming().size() + decay.first;
         result.MOTHUP.emplace_back(mother_idx, mother_idx);
         result.ICOLUP.emplace_back(0,0);
       }
     }
 
     assert(result.ICOLUP.size() == num_particles);
     static constexpr double unknown_spin = 9.;     //per Les Houches accord
     result.VTIMUP = std::vector<double>(num_particles, unknown_spin);
     result.SPINUP = result.VTIMUP;
     return result;
   }
 
 }