import sys import heapq class mcf_graph: def __init__(self, n): self.n = n self.pos = [] self.g = [[] for _ in range(n)] def add_edge(self, from_, to, cap, cost): assert 0 <= from_ < self.n assert 0 <= to < self.n 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 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 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.__class__.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap, _e.cost) def edges(self): ret = [] for i in range(len(self.pos)): _e = self.g[self.pos[i][0]][self.pos[i][1]] _re = self.g[_e.to][_e.rev] ret.append(self.__class__.edge( self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap, _e.cost)) return ret def slope(self, s, t, flow_limit=float('inf')): # assert 0 <= s < self.n # assert 0 <= t < self.n # assert s != t dual = [0] * self.n dist = [float('inf')] * self.n pv = [-1] * self.n pe = [-1] * self.n def _dual_ref(): nonlocal dual, dist, pv, pe dist = [float('inf')] * self.n pv = [-1] * self.n pe = [-1] * self.n que = [(0, s)] dist[s] = 0 while que: dist_v, v = heapq.heappop(que) if dist[v] < dist_v: continue if v == t: break for i in range(len(self.g[v])): e = self.g[v][i] if 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 heapq.heappush(que, (dist[e.to], e.to)) if dist[t] == float('inf'): return False for v in range(self.n): if dist[v] == float('inf'): 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=float('inf')): return self.slope(s, t, flow_limit)[-1] class _edge: def __init__(self, to, rev, cap, cost): self.to = to self.rev = rev self.cap = cap self.cost = cost input = sys.stdin.readline n, m = map(int, input().split()) s, t = 0, n - 1 graph = mcf_graph(n + m) for i in range(m): u, v, c, d = map(int, input().split()) assert 1 <= u <= n and 1 <= v <= n and c <= d u -= 1 v -= 1 mid = n + i graph.add_edge(u, mid, 2, c) graph.add_edge(mid, v, 1, 0) graph.add_edge(mid, v, 1, d - c) graph.add_edge(v, mid, 2, c) graph.add_edge(mid, u, 1, 0) graph.add_edge(mid, u, 1, d - c) flow, cost = graph.flow(s, t, 2) assert flow == 2 print(cost)