import sys import bisect from collections import defaultdict, deque class Edge: def __init__(self, to, rev, capacity): self.to = to self.rev = rev self.capacity = capacity class MaxFlow: def __init__(self, n): self.size = n self.graph = [[] for _ in range(n)] def add_edge(self, fr, to, capacity): forward = Edge(to, len(self.graph[to]), capacity) backward = Edge(fr, len(self.graph[fr]), 0) self.graph[fr].append(forward) self.graph[to].append(backward) def bfs_level(self, s, t, level): q = deque() level[:] = [-1] * self.size level[s] = 0 q.append(s) while q: v = q.popleft() for edge in self.graph[v]: if edge.capacity > 0 and level[edge.to] == -1: level[edge.to] = level[v] + 1 q.append(edge.to) if edge.to == t: return def dfs_flow(self, v, t, upTo, iter_, level): if v == t: return upTo for i in range(iter_[v], len(self.graph[v])): edge = self.graph[v][i] if edge.capacity > 0 and level[v] < level[edge.to]: d = self.dfs_flow(edge.to, t, min(upTo, edge.capacity), iter_, level) if d > 0: edge.capacity -= d self.graph[edge.to][edge.rev].capacity += d return d iter_[v] += 1 return 0 def max_flow(self, s, t): flow = 0 level = [-1] * self.size while True: self.bfs_level(s, t, level) if level[t] == -1: return flow iter_ = [0] * self.size while True: f = self.dfs_flow(s, t, float('inf'), iter_, level) if f == 0: break flow += f def main(): import sys input = sys.stdin.read().split() idx = 0 N = int(input[idx]); idx +=1 M = int(input[idx]); idx +=1 d = int(input[idx]); idx +=1 flights = [] city_times = defaultdict(list) city_times[1].append(0) # Initial time for city 1 for _ in range(M): u = int(input[idx]); idx +=1 v = int(input[idx]); idx +=1 p = int(input[idx]); idx +=1 q = int(input[idx]); idx +=1 w = int(input[idx]); idx +=1 flights.append( (u, v, p, q, w) ) city_times[v].append(q) # Sort and deduplicate for u in city_times: times = city_times[u] times.sort() # Dedup new_times = [] prev = None for t in times: if t != prev: new_times.append(t) prev = t city_times[u] = new_times # Assign nodes nodes = dict() # (u, t) -> node_id node_counter = 0 for u in city_times: for t in city_times[u]: nodes[ (u, t) ] = node_counter node_counter +=1 # Flight nodes flight_nodes_start = node_counter for i in range(M): nodes[ ('flight', i) ] = flight_nodes_start + i node_counter += M # Super sink sink = node_counter node_counter +=1 # Create MaxFlow instance mf = MaxFlow(node_counter) INF = 10**18 # Add edges for each flight for i in range(M): u, v, p, q, w = flights[i] flight_node = nodes[ ('flight', i) ] # Edge flight_node -> (v, q) dest_node = nodes.get( (v, q), -1 ) if dest_node == -1: continue # Should not happen mf.add_edge( flight_node, dest_node, w ) # Step 2c: if u is 1, add edge from (1,0) to flight_node if u == 1: source_node = nodes.get( (1, 0), -1 ) if source_node != -1: mf.add_edge( source_node, flight_node, INF ) # Step 2d: find latest t <= p -d in u's times times = city_times.get(u, []) if not times: continue latest_arrival = p - d idx_t = bisect.bisect_right(times, latest_arrival) -1 if idx_t >=0: t = times[idx_t] from_node = nodes[ (u, t) ] mf.add_edge( from_node, flight_node, INF ) # Add waiting edges for each city for u in city_times: times = city_times[u] for i in range(len(times)-1): t_prev = times[i] t_next = times[i+1] prev_node = nodes[ (u, t_prev) ] next_node = nodes[ (u, t_next) ] mf.add_edge( prev_node, next_node, INF ) # Add edges from all (N, t) to sink if N in city_times: for t in city_times[N]: node = nodes[ (N, t) ] mf.add_edge( node, sink, INF ) # Source is (1, 0) if (1, 0) not in nodes: print(0) return source = nodes[ (1, 0) ] # Compute max flow result = mf.max_flow(source, sink) print(result) if __name__ == "__main__": main()