# SCC→強連結成分をノードとみなしてDFSで訪問可能判定? from collections import defaultdict #from atcoder.scc import SCCGraph ### # https://github.com/not522/ac-library-python import sys import typing class CSR: def __init__( self, n: int, edges: typing.List[typing.Tuple[int, int]]) -> None: self.start = [0] * (n + 1) self.elist = [0] * len(edges) for e in edges: self.start[e[0] + 1] += 1 for i in range(1, n + 1): self.start[i] += self.start[i - 1] counter = self.start.copy() for e in edges: self.elist[counter[e[0]]] = e[1] counter[e[0]] += 1 class SCCGraph: ''' Reference: R. Tarjan, Depth-First Search and Linear Graph Algorithms ''' def __init__(self, n: int) -> None: self._n = n self._edges: typing.List[typing.Tuple[int, int]] = [] def num_vertices(self) -> int: return self._n def add_edge(self, from_vertex: int, to_vertex: int) -> None: self._edges.append((from_vertex, to_vertex)) def scc_ids(self) -> typing.Tuple[int, typing.List[int]]: g = CSR(self._n, self._edges) now_ord = 0 group_num = 0 visited = [] low = [0] * self._n order = [-1] * self._n ids = [0] * self._n sys.setrecursionlimit(max(self._n + 1000, sys.getrecursionlimit())) def dfs(v: int) -> None: nonlocal now_ord nonlocal group_num nonlocal visited nonlocal low nonlocal order nonlocal ids low[v] = now_ord order[v] = now_ord now_ord += 1 visited.append(v) for i in range(g.start[v], g.start[v + 1]): to = g.elist[i] if order[to] == -1: dfs(to) low[v] = min(low[v], low[to]) else: low[v] = min(low[v], order[to]) if low[v] == order[v]: while True: u = visited[-1] visited.pop() order[u] = self._n ids[u] = group_num if u == v: break group_num += 1 for i in range(self._n): if order[i] == -1: dfs(i) for i in range(self._n): ids[i] = group_num - 1 - ids[i] return group_num, ids def scc(self) -> typing.List[typing.List[int]]: ids = self.scc_ids() group_num = ids[0] counts = [0] * group_num for x in ids[1]: counts[x] += 1 groups: typing.List[typing.List[int]] = [[] for _ in range(group_num)] for i in range(self._n): groups[ids[1][i]].append(i) return groups ### N = int(input()) sccgraph = SCCGraph(N) graph = defaultdict(list) for i in range(1,N+1): A = list(map(int, input().split()))[1:] for a in A: sccgraph.add_edge(i-1, a-1) graph[i-1].append(a-1) groups = sccgraph.scc() if 0 not in groups[0]: print("No") exit() scc_mapping = [-1] * N for i, group in enumerate(groups): for a in group: scc_mapping[a] = i scc_graph = defaultdict(list) for i, group in enumerate(groups): for a in group: a_next = [scc_mapping[n] for n in graph[a]] scc_graph[i] = list(set(scc_graph[i]+a_next)) def dfs(start): todo = [start,] seen = [False] * len(groups) while todo: tgt = todo.pop() if seen[tgt]: continue seen[tgt] = True for next in scc_graph[tgt]: todo.append(next) return seen connected = dfs(0) if(all(connected)): print("Yes") else: print("No")