class Two_SAT: """2-SATを定義する. """ #※ i:変数 i が Trueの頂点, i+N:変数 i がFalseの頂点 #入力定義 def __init__(self,N): """N変数の2-SATを考える. """ self.N=N self.clause_number=0 self.adjacent_out=[set() for k in range(2*N)] #出近傍(vが始点) self.adjacent_in=[set() for k in range(2*N)] #入近傍(vが終点) #節の追加 def add_clause(self,X,F,Y,G): """(X=F) or (Y=G) という節を加える. X,Y:変数の名前 F,G:真偽値(True or False) """ assert 0<=XGroup[i+N]: T[i]=1 elif Group[i]==Group[i+N]: return None return T elif Mode==2: return [i for i in range(N) if Group[i]==Group[i+N]] #================================================ import sys from itertools import product input=sys.stdin.readline N,M=map(int,input().split()) E=[] for _ in range(M): E.append(list(map(int,input().split()))) T=Two_SAT(N+1) K=[["*","*"]] THREE=set() for i in range(1,N+1): t,*L=map(int,input().split()) L.sort() if t==1: K.append(L+[-i]) T.add_clause(i,False,i,False) elif t==2: L.sort() K.append(L) else: K.append(L) THREE.add(i) print("3色の候補がある番号:",*THREE,file=sys.stderr) Cond=[[],[],[]] for a,b,c in E: w=(a in THREE)+(b in THREE) Cond[w].append((a,b,c)) #タイプ0を処理 for a,b,c in Cond[0]: if a==384 and b==834: Y=E.index([a,b,c]) assert 1 if c==0: for s in [0,1]: for t in [0,1]: if K[a][s]==K[b][t]: T.add_clause(a,1-s,b,1-t) else: H=[v for v in K[a] if v in K[b]] if len(H)==0: #矛盾する論理式 T.add_clause(0,0,0,0) T.add_clause(0,1,0,1) elif len(H)==1: h=H[0] s=K[a].index(h) t=K[b].index(h) T.add_clause(a,s,a,s) T.add_clause(b,t,b,t) else: #節 x_a←→x_b を加える T.add_clause(a,1,b,0) T.add_clause(a,0,b,1) #THREEの頂点の彩色を全探索 Index={v:i for i,v in enumerate(THREE)} for G in product([0,1,2],repeat=len(THREE)): Flag=True #タイプ2をチェック for a,b,c in Cond[2]: assert (a in THREE) and (b in THREE) alpha=Index[a] beta =Index[b] if c==0: if K[a][G[alpha]]==K[b][G[beta]]: Flag=False else: if K[a][G[alpha]]!=K[b][G[beta]]: Flag=False if not Flag: continue #タイプ1の条件を追加 Added=[] for a,b,c in Cond[1]: assert (a in THREE)^(b in THREE) if a not in THREE: a,b=b,a if c==0: for d in [0,1]: if K[a][G[Index[a]]]==K[b][d]: T.add_clause(b,1-d,b,1-d) Added.append((b,1-d,b,1-d)) else: for d in [0,1]: if K[a][G[Index[a]]]!=K[b][d]: T.add_clause(b,1-d,b,1-d) Added.append((b,1-d,b,1-d)) X=T.Is_Satisfy(1) if X: print("Possible") for v in THREE: X[v]=K[v][G[Index[v]]] for i in range(1,N+1): print(K[i][X[i]]) exit(0) for V in Added: T.remove_clause(*V) print("Fault")