/* author:ryo3ihara        ”継続は力なり、雨だれ石を穿つ”           ”slow but steady wins the race” */ #pragma GCC optimize("Ofast") #include namespace atcoder { template 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; }; } // namespace atcoder using namespace atcoder; /* // 多倍長テンプレ #include #include namespace mp = boost::multiprecision; // 任意長整数型 using Bint = mp::cpp_int; // 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする) using Real = mp::number>; */ using namespace std; using ll = long long; using ld = long double; using pll = pair; using pli = pair; using pii = pair; using pld = pair; using ppiii = pair; using ppiill = pair; using ppllll = pair; using pplii = pair; using mii = map; using dll = deque; using qll = queue; using pqll = priority_queue; using pqrll = priority_queue, greater>; using vint = vector; using vll = vector; using vpll = vector; using vvll = vector>; using vvint = vector>; using vvpll = vector>; //マクロ //forループ #define REP(i,n) for(ll i=0;i=0;i--) #define FOR(i,a,b) for(ll i=a;i<=ll(b);i++) #define FORD(i,a,b) for(ll i=a;i>=ll(b);i--) #define ALL(x) x.begin(),x.end() #define rALL(x) x.rbegin(),x.rend() #define SIZE(x) ll(x.size()) #define fs first #define sc second //定数 const ll MOD = 1000000007; const int inf = 1e9; const ll INF = 1e18; const ll MAXR = 100000; //10^5:配列の最大のrange inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; } inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; } //最大化問題最小化問題 template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } //高速冪乗化 modの時は一部入れ替える ll power(ll x, ll y) { if(y == 1) { return x; } ll ans; if(y % 2 == 1) { ll r = power(x,(y-1)/2); //ans = r * r % MOD; //ans = ans * x % MOD; ans = x * r * r; } else { ll r = power(x,y/2); //ans = r * r % MOD; ans = r * r; } return ans; } /* Bint powerb(Bint x, Bint y) { if(y == 1) { return x; } Bint ans; if(y % 2 == 1) { Bint r = powerb(x,(y-1)/2); //ans = r * r % MOD; //ans = ans * x % MOD; ans = x * r * r; } else { Bint r = powerb(x,y/2); //ans = r * r % MOD; ans = r * r; } return ans; } */ signed main(){ //入力の高速化用のコード ios::sync_with_stdio(false); cin.tie(nullptr); //入力 int N ,M; cin >> N >> M; mcf_graph g(N); REP(i, M) { int u, v, c, d; cin >> u >> v >> c >> d; --u, --v; g.add_edge(u, v, 1, c); g.add_edge(v, u, 1, c); g.add_edge(u, v, 1, d); g.add_edge(v, u, 1, d); } cout << g.flow(0, N - 1, 2).second << endl; //cout << fixed << setprecision(10) << ans << endl; return 0; }