def scc(N,edges): M=len(edges) start=[0]*(N+1) elist=[0]*M for e in edges: start[e[0]+1]+=1 for i in range(1,N+1): start[i]+=start[i-1] counter=start[:] for e in edges: elist[counter[e[0]]]=e[1] counter[e[0]]+=1 visited=[] low=[0]*N Ord=[-1]*N ids=[0]*N NG=[0,0] def dfs(v): stack=[(v,-1,0),(v,-1,1)] while stack: v,bef,t=stack.pop() if t: if bef!=-1 and Ord[v]!=-1: low[bef]=min(low[bef],Ord[v]) stack.pop() continue low[v]=NG[0] Ord[v]=NG[0] NG[0]+=1 visited.append(v) for i in range(start[v],start[v+1]): to=elist[i] if Ord[to]==-1: stack.append((to,v,0)) stack.append((to,v,1)) else: low[v]=min(low[v],Ord[to]) else: if low[v]==Ord[v]: while(True): u=visited.pop() Ord[u]=N ids[u]=NG[1] if u==v: break NG[1]+=1 low[bef]=min(low[bef],low[v]) for i in range(N): if Ord[i]==-1: dfs(i) for i in range(N): ids[i]=NG[1]-1-ids[i] group_num=NG[1] counts=[0]*group_num for x in ids: counts[x]+=1 groups=[[] for i in range(group_num)] for i in range(N): groups[ids[i]].append(i) return groups from collections import defaultdict class UnionFind(): def __init__(self, n): ''' UnionFindクラス。nは要素数を表す。 ''' self.n = n self.parents = [-1] * n def find(self, x): ''' 要素xを含む集合の親を見つける関数。 ''' if self.parents[x] < 0: return x else: self.parents[x] = self.find(self.parents[x]) return self.parents[x] def union(self, x, y): ''' 要素xを含む集合と要素yを含む集合を合体する関数。 基本的には、要素数が多い集合に統合される。 要素数が同じときは要素yを含む集合に統合される。 ''' x = self.find(x) y = self.find(y) if x == y: return if self.parents[x] > self.parents[y]: x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x def size(self, x): ''' 要素xを含む集合の要素数を出す関数。 ''' return -self.parents[self.find(x)] def same(self, x, y): return self.find(x) == self.find(y) def members(self, x): root = self.find(x) return [i for i in range(self.n) if self.find(i) == root] def roots(self): return [i for i, x in enumerate(self.parents) if x < 0] def group_count(self): return len(self.roots()) def all_group_members(self): group_members = defaultdict(list) for member in range(self.n): group_members[self.find(member)].append(member) return group_members def __str__(self): return '\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items()) from collections import deque, defaultdict n, q = map(int, input().split()) OUTs = defaultdict(list) UF = UnionFind(n) E = [] for _ in range(q): a, b, c = map(int, input().split()) a -= 1 b -= 1 OUTs[a].append((b, c)) E.append((a, b)) UF.union(a, b) mod = 998244353 ans = 1 seen = set() G = scc(n, E) g_num = 0 for GG in G: if len(GG) > 1: flag = True for i in GG: if i in seen: flag = False break if not flag: continue g_num += 1 i = GG[0] seen.add(i) P = defaultdict(int) P[i] = 0 Que = deque([i]) flag = True while Que: ci = Que.popleft() pi = P[ci] for j, pj in OUTs[ci]: if j not in seen: P[j] = pj ^ pi seen.add(j) Que.append(j) else: if P[j] != pj ^ pi: flag = False break if flag: ans *= 2 ans %= mod else: print(0) exit() total_g_num = UF.group_count() ans *= pow(2, total_g_num - g_num, mod) ans %= mod print(ans)