#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 #include #include #include #include #define endl codeforces #define ALL(v) std::begin(v), std::end(v) #define ALLR(v) std::rbegin(v), std::rend(v) using ll = std::int64_t; using ull = std::uint64_t; using pii = std::pair; using tii = std::tuple; using pll = std::pair; using tll = std::tuple; using size_type = ssize_t; template using vec = std::vector; template using vvec = vec>; template const T& var_min(const T &t) { return t; } template const T& var_max(const T &t) { return t; } template const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); } template const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); } template void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); } template void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); } template struct multi_dim_array { using type = std::array::type, Head>; }; template struct multi_dim_array { using type = std::array; }; template using mdarray = typename multi_dim_array::type; template void fill_seq(T &t, F f, Args... args) { if constexpr (std::is_invocable::value) { t = f(args...); } else { for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); } } template vec make_v(size_type sz) { return vec(sz); } template auto make_v(size_type hs, Tail&&... ts) { auto v = std::move(make_v(std::forward(ts)...)); return vec(hs, v); } namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; } template T ceil_pow2(T bound) { T ret = 1; while (ret < bound) ret *= 2; return ret; } template T ceil_div(T a, T b) { return a / b + !!(a % b); } namespace graph { using Node = ll; using Weight = ll; using Edge = std::pair; template struct Graph : public vvec { using vvec::vvec; void add_edge(Node f, Node t, Weight w = 1) { (*this)[f].emplace_back(t, w); if (!Directed) (*this)[t].emplace_back(f, w); } Graph build_inv() const { Graph ret(this->size()); for (Node i = 0; i < this->size(); i++) { for (const Edge &e : (*this)[i]) { Node j; Weight w; std::tie(j, w) = e; if (!Directed && j < i) continue; ret.add_edge(j, i, w); } } return ret; } }; template class dst_iterator { Iterator ite; public: dst_iterator(Iterator ite) : ite(ite) { } bool operator ==(const dst_iterator &oth) const { return ite == oth.ite; } bool operator !=(const dst_iterator &oth) const { return !(*this == oth); } bool operator <(const dst_iterator &oth) const { return ite < oth.ite; } bool operator >(const dst_iterator &oth) const { return ite > oth.ite; } bool operator <=(const dst_iterator &oth) const { return ite <= oth.ite; } bool operator >=(const dst_iterator &oth) const { return ite >= oth.ite; } const Node& operator *() { return ite->first; } const Node& operator *() const { return ite->first; } dst_iterator operator ++() { ++ite; return ite; } }; class dst_iteration { using ite_type = vec::const_iterator; const vec &edges; public: dst_iteration(const vec &edges) : edges(edges) { } auto begin() const { return dst_iterator(edges.cbegin()); } auto end() const { return dst_iterator(edges.cend()); } }; class dst_reverse_iteration { using ite_type = vec::const_reverse_iterator; const vec &edges; public: dst_reverse_iteration(const vec &edges) : edges(edges) { } auto begin() const { return dst_iterator(edges.crbegin()); } auto end() const { return dst_iterator(edges.crend()); } }; dst_iteration dst(const vec &edges) { return dst_iteration(edges); } dst_reverse_iteration rdst(const vec &edges) { return dst_reverse_iteration(edges); } } namespace graph { using Capacity = ll; struct FlowEdge : public std::tuple { using std::tuple::tuple; Node& to() { return std::get<0>(*this); } const Node& to() const { return std::get<0>(*this); } Capacity& cap() { return std::get<1>(*this); } const Capacity& cap() const { return std::get<1>(*this); } ll& rev_idx() { return std::get<2>(*this); } const ll& rev_idx() const { return std::get<2>(*this); } Weight& weight() { return std::get<3>(*this); } const Weight& weight() const { return std::get<3>(*this); } }; template struct FlowGraph : public vvec { using vvec::vvec; void add_edge(Node f, Node t, Capacity c = 1, Weight w = 1) { add_edge_with_rev(f, t, c, w); if (!Directed) add_edge_with_rev(t, f, c, w); } private: void add_edge_with_rev(Node f, Node t, Capacity c, Weight w) { FlowEdge fe(t, c, (ll)((*this)[t].size()), w); (*this)[f].push_back(fe); FlowEdge rfe(f, Capacity(), (ll)((*this)[f].size()) - 1, -w); (*this)[t].push_back(rfe); } }; } namespace flow { using graph::Node; using graph::Weight; using graph::Capacity; template class MinCostFlow { using prev_node_t = std::pair; using pq_ele_t = std::pair; FlowGraph fgraph; const Weight dinf = 5e15; vec dists, potential; vec pnode; void dijk(Node start) { std::priority_queue, std::greater> pq; std::fill(ALL(dists), dinf); dists[start] = 0; pq.emplace(0, start); while (pq.size()) { Weight d; Node from; std::tie(d, from) = pq.top(); pq.pop(); if (dists[from] < d) continue; for (ll i = 0; i < fgraph[from].size(); i++) { const auto &edge = fgraph[from][i]; auto to = edge.to(); Weight dnxt = d + edge.weight() + potential[from] - potential[to]; if (edge.cap() <= 0 || dists[to] <= dnxt) continue; dists[to] = dnxt; pnode[to] = prev_node_t(from, i); pq.emplace(dnxt, to); } } } public: MinCostFlow(const FlowGraph &fgraph) : fgraph(fgraph), dists(fgraph.size()), potential(fgraph.size(), 0), pnode(fgraph.size()) { } Weight solve(Node start, Node goal, Capacity flow) { Weight ret = 0; while (0 < flow) { dijk(start); if (dists[goal] == dinf) return -1; for (ll i = 0; i < fgraph.size(); i++) potential[i] += dists[i]; Capacity max_flow = flow; for (Node cur = goal; cur != start; cur = pnode[cur].first) { Node pre; ll pidx; std::tie(pre, pidx) = pnode[cur]; const auto &edge = fgraph[pre][pidx]; chmin(max_flow, edge.cap()); } if (max_flow == 0) return -1; flow -= max_flow; ret += max_flow * potential[goal]; for (Node cur = goal; cur != start; cur = pnode[cur].first) { Node pre; ll pidx; std::tie(pre, pidx) = pnode[cur]; auto &edge = fgraph[pre][pidx]; edge.cap() -= max_flow; auto &redge = fgraph[cur][edge.rev_idx()]; redge.cap() += max_flow; } } return ret; } const FlowGraph& get_graph() const { return fgraph; } }; } int main() { ll n, m; std::cin >> n >> m; using raw_edge = std::tuple; vec edges(m); for (auto &[ u, v, c, d ] : edges) { std::cin >> u >> v >> c >> d; u--; v--; } graph::FlowGraph fg(n + 2 * m); for (ll i = 0; i < m; i++) { auto [ u, v, c , d ] = edges[i]; ll src = n + 2 * i; ll dst = src + 1; fg.add_edge(u, src, 2, 0); fg.add_edge(v, src, 2, 0); fg.add_edge(dst, u, 2, 0); fg.add_edge(dst, v, 2, 0); fg.add_edge(src, dst, 1, c); fg.add_edge(src, dst, 1, d); } flow::MinCostFlow mcf(fg); std::cout << mcf.solve(0, n - 1, 2) << "\n"; return 0; }