from heapq import heappush, heappop class mincostflow: class edge: def __init__(self, from_, to, cap, flow, cost): self.from_ = from_ self.to = to self.cap = cap self.flow = flow self.cost = cost class _edge: def __init__(self, to, rev, cap, cost): self.to = to self.rev = rev self.cap = cap self.cost = cost def __init__(self, n): self.n = n self.pos = [] self.g = [[] for i in range(n)] def add_edge(self, from_, to, cap, cost): m = len(self.pos) self.pos.append((from_, len(self.g[from_]))) self.g[from_].append(self.__class__._edge(to, len(self.g[to]), cap, cost)) self.g[to].append(self.__class__._edge(from_, len(self.g[from_])-1, 0, -cost)) return m def get_edge(self, i): _e = self.g[self.pos[i][0]][self.pos[i][1]] _re = self.g[_e.to][_e.rev] return self.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap, _e.cost) def edges(self): result = [] for i in range(len(self.pos)): result.append(self.get_edge(i)) return result def slope(self, s, t, flow_limit=10**20, inf=10**20): dual = [0]*self.n dist = [inf]*self.n pv = [-1]*self.n pe = [-1]*self.n vis = [False]*self.n def _dual_ref(): nonlocal dual, dist, pv, pe, vis dist = [inf]*self.n pv = [-1]*self.n pe = [-1]*self.n vis = [False]*self.n que = [(0,s)] dist[s] = 0 while que: _,v = heappop(que) if vis[v]: continue vis[v] = True if v == t: break for i in range(len(self.g[v])): e = self.g[v][i] if vis[e.to] or e.cap == 0: continue 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 heappush(que, (dist[e.to],e.to)) if not vis[t]: return False for v in range(self.n): if not vis[v]: continue dual[v] -= dist[t] - dist[v] return True flow = 0 cost = 0 prev_cost = -1 result = [(flow, cost)] while flow < flow_limit: if not _dual_ref(): break c = flow_limit - flow v = t while v != s: c = min(c, self.g[pv[v]][pe[v]].cap) v = pv[v] v = t while v != s: e = self.g[pv[v]][pe[v]] e.cap -= c self.g[v][e.rev].cap += c v = pv[v] d = -dual[s] flow += c cost += c * d if prev_cost == d: result.pop() result.append((flow, cost)) prev_cost = cost return result def flow(self, s, t, flow_limit=10**20): return self.slope(s, t, flow_limit)[-1] n,m = map(int,input().split()) g = mincostflow(n+1) for i in range(m): u,v,c,d = map(int,input().split()) g.add_edge(u,v,1,c) g.add_edge(u,v,1,d) print(g.flow(1,n,2)[1])