import sys input = sys.stdin.readline N, M = map(int, input().split()) from heapq import heappop, heappush, heapify class MinCostFlow(): def __init__(self, n): self.n = n self.graph = [[] for _ in range(n)] self.pos = [] def add_edge(self, fr, to, cap, cost): m = len(self.pos) self.pos.append((fr, len(self.graph[fr]))) self.graph[fr].append([to, len(self.graph[to]), cap, cost]) self.graph[to].append([fr, len(self.graph[fr]) - 1, 0, -cost]) return m def get_edge(self, idx): to, rev, cap, cost = self.graph[self.pos[idx][0]][self.pos[idx][1]] rev_to, rev_rev, rev_cap, rev_cost = self.graph[to][rev] return self.pos[idx][0], to, cap + rev_cap, rev_cap, cost def edges(self): for i in range(len(self.pos)): yield self.get_edge(i) def dual_ref(self, s, t): dist = [2**63 - 1] * self.n dist[s] = 0 vis = [0] * self.n self.pv = [-1] * self.n self.pe = [-1] * self.n queue = [] heappush(queue, (0, s)) while queue: k, v = heappop(queue) if vis[v]: continue vis[v] = True if v == t: break for i in range(len(self.graph[v])): to, rev, cap, cost = self.graph[v][i] if vis[to] or cap == 0: continue cost += self.dual[v] - self.dual[to] if dist[to] - dist[v] > cost: dist[to] = dist[v] + cost self.pv[to] = v self.pe[to] = i heappush(queue, (dist[to], to)) if not vis[t]: return False for v in range(self.n): if not vis[v]: continue self.dual[v] -= dist[t] - dist[v] return True def flow(self, s, t): return self.flow_with_limit(s, t, 2**63 - 1) def flow_with_limit(self, s, t, limit): return self.slope_with_limit(s, t, limit)[-1] def slope(self, s, t): return self.slope_with_limit(s, t, 2**63 - 1) def slope_with_limit(self, s, t, limit): flow = 0 cost = 0 prev_cost = -1 res = [(flow, cost)] self.dual = [0] * self.n while flow < limit: if not self.dual_ref(s, t): break c = limit - flow v = t while v != s: c = min(c, self.graph[self.pv[v]][self.pe[v]][2]) v = self.pv[v] v = t while v != s: to, rev, cap, _ = self.graph[self.pv[v]][self.pe[v]] self.graph[self.pv[v]][self.pe[v]][2] -= c self.graph[v][rev][2] += c v = self.pv[v] d = -self.dual[s] flow += c cost += c * d if prev_cost == d: res.pop() res.append((flow, cost)) prev_cost = cost return res mcf = MinCostFlow(N) edges = [] for _ in range(M): u, v, c, d = map(int, input().split()) edges.append((u, v, c, d)) mcf.add_edge(u - 1, v - 1, 1, c) mcf.add_edge(v - 1, u - 1, 1, c) mcf2 = mcf.flow_with_limit(0, N - 1, 2) mcf = MinCostFlow(N) for u, v, c, d in edges: mcf.add_edge(u - 1, v - 1, 1, c) mcf.add_edge(v - 1, u - 1, 1, c) mcf1 = mcf.flow_with_limit(0, N - 1, 1) mcfedges = list(mcf.edges()) mcf = MinCostFlow(N) for i in range(M): x = i * 2 fr, to, cap, flow, cost = mcfedges[x] flow += mcfedges[x + 1][3] if flow: mcf.add_edge(fr, to, cap, edges[i][-1]) mcf.add_edge(to, fr, cap, edges[i][-1]) else: mcf.add_edge(fr, to, cap, cost) mcf.add_edge(to, fr, cap, cost) res = mcf1[1] + mcf.flow_with_limit(0, N - 1, 1)[1] if mcf2[0] == 2 and mcf2[1] > 0: res = min(res, mcf2[1]) print(res)