//#pragma GCC optimize("Ofast") //#pragma GCC optimize("unroll-loops") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #include using namespace std; using ll = long long; using ull = unsigned long long; using db = double; using ld = long double; template using V = vector; template using VV = vector>; #define fs first #define sc second #define pb push_back #define mp make_pair #define mt make_tuple #define eb emplace_back #define lb lower_bound #define ub upper_bound #define all(v) (v).begin(),(v).end() #define siz(v) (ll)(v).size() #define rep(i,a,n) for(ll i=a;i<(ll)(n);++i) #define repr(i,a,n) for(ll i=n-1;(ll)a<=i;--i) #define ENDL '\n' typedef pair Pi; typedef pair PL; constexpr ll mod = 1000000007; // 998244353; constexpr ll INF = 1000000099; constexpr ll LINF = (ll)(1e18 +99); const ld PI = acos((ld)-1); const vector dx={-1,0,1,0},dy={0,1,0,-1}; template inline bool chmin(T& t, const U& u){if(t>u){t=u;return 1;}return 0;} template inline bool chmax(T& t, const U& u){if(t inline T gcd(T a,T b){return b?gcd(b,a%b):a;} inline void yes() { cout << "Yes" << ENDL; } inline void no() { cout << "No" << ENDL; } template inline T mpow(T a, Y n) { T res = 1; for(;n;n>>=1) { if (n & 1) res = res * a; a = a * a; } return res; } template V prefix_sum(const V& v) { int n = v.size(); V ret(n + 1); rep(i, 0, n) ret[i + 1] = ret[i] + v[i]; return ret; } template istream& operator >> (istream& is, vector& vec){ for(auto&& x: vec) is >> x; return is; } template ostream& operator<<(ostream& os,const pair& p){ return os<<"{"< ostream& operator<<(ostream& os,const V& v){ os<<"{"; for(auto e:v)os< void debug(Args&... args){ for(auto const& x:{args...}){ cerr< struct mcf_graph { public: mcf_graph() {} mcf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap, cost}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{ pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost, }; } std::vector edges() { int m = int(pos.size()); std::vector result(m); for(int i = 0; i < m; i++) { result[i] = get_edge(i); } return result; } std::pair flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } std::pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); // variants (C = maxcost): // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0 // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge std::vector dual(_n, 0), dist(_n); std::vector pv(_n), pe(_n); std::vector vis(_n); auto dual_ref = [&]() { std::fill(dist.begin(), dist.end(), std::numeric_limits::max()); std::fill(pv.begin(), pv.end(), -1); std::fill(pe.begin(), pe.end(), -1); std::fill(vis.begin(), vis.end(), false); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::priority_queue que; dist[s] = 0; que.push(Q{0, s}); while(!que.empty()) { int v = que.top().to; que.pop(); if(vis[v]) continue; vis[v] = true; if(v == t) break; // dist[v] = shortest(s, v) + dual[s] - dual[v] // dist[v] >= 0 (all reduced cost are positive) // dist[v] <= (n-1)C for(int i = 0; i < int(g[v].size()); i++) { auto e = g[v][i]; if(vis[e.to] || !e.cap) continue; // |-dual[e.to] + dual[v]| <= (n-1)C // cost <= C - -(n-1)C + 0 = nC Cost cost = e.cost - dual[e.to] + dual[v]; if(dist[e.to] - dist[v] > cost) { dist[e.to] = dist[v] + cost; pv[e.to] = v; pe[e.to] = i; que.push(Q{dist[e.to], e.to}); } } } if(!vis[t]) { return false; } for(int v = 0; v < _n; v++) { if(!vis[v]) continue; // dual[v] = dual[v] - dist[t] + dist[v] // = dual[v] - (shortest(s, t) + dual[s] - dual[t]) + // (shortest(s, v) + dual[s] - dual[v]) = - shortest(s, t) + // dual[t] + shortest(s, v) = shortest(s, v) - shortest(s, t) >= // 0 - (n-1)C dual[v] -= dist[t] - dist[v]; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost = -1; std::vector> result; result.push_back({flow, cost}); while(flow < flow_limit) { if(!dual_ref()) break; Cap c = flow_limit - flow; for(int v = t; v != s; v = pv[v]) { c = std::min(c, g[pv[v]][pe[v]].cap); } for(int v = t; v != s; v = pv[v]) { auto& e = g[pv[v]][pe[v]]; e.cap -= c; g[v][e.rev].cap += c; } Cost d = -dual[s]; flow += c; cost += c * d; if(prev_cost == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost = cost; } return result; } private: int _n; struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> pos; std::vector> g; }; signed main(){ cin.tie(0);cerr.tie(0);ios::sync_with_stdio(false); cout<>n>>m; mcf_graph mcf(n*2); rep(i,0,m){ int a,b,c,d;cin>>a>>b>>c>>d; --a;--b; mcf.add_edge(n+a,n+b,1,c); mcf.add_edge(n+a,n+b,1,d); mcf.add_edge(a,n+a,2,0); mcf.add_edge(n+b,b,2,0); mcf.add_edge(b,n+a,2,0); mcf.add_edge(n+b,a,2,0); } cout<