//-------------------------------------------------------------
// MinCost-MaxFlow
//   O(??)
//
// Verified by
//   - SRM 487 Div2 LV3
//   - SRM 491 Div1 LV3
//-------------------------------------------------------------

#include <iostream>
#include <string>
#include <vector>
#include <map>
#include <queue>
using namespace std;

template<typename T>
class IdGen
{
	map<T, int> v2id_;
	vector<T>   id2v_;
public:
	int v2id(const T& v) {
		if( !v2id_.count(v) ) { v2id_[v] = size(); id2v_.push_back(v); }
		return v2id_[v];
	}
	const T& id2v(int i) const { return id2v_[i]; }
	int size() const { return id2v_.size(); }
};

template<typename Vert, typename Cost, typename Flow, int NV=256>
class MinCostFlow
{
	IdGen<Vert> idgen;

	vector<int> G[NV];
	Flow F[NV][NV];
	Cost C[NV][NV];

public:
	void addEdge( Vert s_, Vert t_, Cost c, Flow f )
	{
		int s = idgen.v2id(s_), t = idgen.v2id(t_);
		G[s].push_back(t);
		G[t].push_back(s);
		C[s][t] = c;
		C[t][s] = -c;
		F[s][t] = f;
		F[t][s] = 0;
	}

	pair<Cost, Flow> calc( Vert s_, Vert t_ )
	{
		const int N=idgen.size(), S=idgen.v2id(s_), T=idgen.v2id(t_);
		static const Cost COST_INF = 1e+300; // !!EDIT HERE!!
		static const Flow FLOW_INF = 0x7fffffff;

		Cost total_cost = 0;
		Flow total_flow = 0;
		vector<Cost> h(N, 0); // potential
		for(Flow RF=FLOW_INF; RF>0; ) // residual flow
		{
			// Dijkstra -- find the min-cost path
			vector<Cost> d(N, COST_INF);  d[S] = 0;
			vector<int>  prev(N, -1);

			typedef pair< Cost, pair<int,int> > cedge;
			priority_queue< cedge, vector<cedge>, greater<cedge> > Q;
			Q.push( cedge(0, make_pair(S,S)) );
			while( !Q.empty() ) {
				cedge e = Q.top(); Q.pop();
				if( prev[e.second.second] >= 0 )
					continue;
				prev[e.second.second] = e.second.first;

				int u = e.second.second;
				for(int i=0; i<G[u].size(); ++i) {
					int  v = G[u][i];
					Cost r_cost = C[u][v] + h[u] - h[v];
					if( F[u][v] > 0 && d[v] > d[u]+r_cost )
						Q.push( cedge(d[v]=d[u]+r_cost, make_pair(u,v)) );
				}
			}

			if( prev[T] < 0 )
				break; // Finished

			// Run the flow as much as possible
			Flow f = RF;
			for(int u=T; u!=S; u=prev[u])
				f = min(f, F[prev[u]][u]);
			RF         -= f;
			total_flow += f;

			for(int u=T; u!=S; u=prev[u])
			{
				total_cost    += f * C[prev[u]][u];
				F[prev[u]][u] -= f;
				F[u][prev[u]] += f;
			}

			// Update the potential
			for(int u=0; u<N; ++u)
				h[u] += d[u];
		}
		return make_pair(total_cost, total_flow);
	}
};
