#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using P = pair; constexpr int INF = 1001001001; // constexpr int mod = 1000000007; constexpr int mod = 998244353; template inline bool chmax(T& x, T y){ if(x < y){ x = y; return true; } return false; } template inline bool chmin(T& x, T y){ if(x > y){ x = y; return true; } return false; } template struct PrimalDual{ const cost_t INF; struct edge{ int to; flow_t cap; cost_t cost; int rev; bool isrev; edge(int to, flow_t cap, cost_t cost, int rev, bool isrev) : to(to), cap(cap), cost(cost), rev(rev), isrev(isrev) {} }; vector> graph; vector potential; // ポテンシャルテーブル vector min_cost; // 最小コストテーブル vector prevv, preve; // 経路復元用 PrimalDual(int V, cost_t INF = numeric_limits::max() / 2) : graph(V), INF(INF) {} void add_edge(int from, int to, flow_t cap, cost_t cost){ graph[from].emplace_back(edge(to, cap, cost, graph[to].size(), false)); graph[to].emplace_back(edge(from, 0, -cost, graph[from].size() - 1, true)); } cost_t min_cost_flow(int s, int t, flow_t f){ int V = (int)graph.size(); cost_t ret = 0; using Pi = pair; priority_queue, greater> que; potential.assign(V, 0); preve.assign(V, -1); prevv.assign(V, -1); while(f > 0){ min_cost.assign(V, INF); // 残余グラフ上の最小コストを毎回調べる que.emplace(0, s); min_cost[s] = 0; while(!que.empty()){ Pi p = que.top(); que.pop(); if(min_cost[p.second] < p.first) continue; for(int i = 0; i < (int)graph[p.second].size(); ++i){ edge &e = graph[p.second][i]; // ポテンシャルを用いたコスト比較 cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to]; if(e.cap > 0 && min_cost[e.to] > nextCost){ min_cost[e.to] = nextCost; prevv[e.to] = p.second, preve[e.to] = i; que.emplace(min_cost[e.to], e.to); } } } if(min_cost[t] == INF) return -1; for(int v = 0; v < V; ++v) potential[v] += min_cost[v]; // ポテンシャルの更新 flow_t addflow = f; // s-t間最短路の沿って目一杯流す for(int v = t; v != s; v = prevv[v]){ addflow = min(addflow, graph[prevv[v]][preve[v]].cap); } f -= addflow; ret += addflow * potential[t]; for(int v = t; v != s; v = prevv[v]){ edge &e = graph[prevv[v]][preve[v]]; e.cap -= addflow; graph[v][e.rev].cap += addflow; } } return ret; } }; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int N, M; cin >> N >> M; PrimalDual pd(N); int s = 0, t = N - 1; for(int i = 0; i < M; ++i){ int u, v, c, d; cin >> u >> v >> c >> d; --u, --v; pd.add_edge(u, v, 1, c); pd.add_edge(v, u, 1, c); pd.add_edge(u, v, 1, d); pd.add_edge(v, u, 1, d); } cout << pd.min_cost_flow(s, t, 2) << endl; }