#include using namespace std; using ll = long long; #ifdef MY_DEBUG #define dbg(...) debug_out(__VA_ARGS__) #define dbgn(var) debug_out(#var, "=", var) #else #define dbg(...) #define dbgn(...) #endif void debug_out(); template void debug_out(Head, Tail...); template bool chmax(T&, const T&); template bool chmin(T&, const T&); template T pwr(T, ll); template T squ(T x) { return x * x; } ll fact(ll); ll comb(ll, ll); ll ctoll(char); char lltoc(ll); bool flg(ll b, ll i) { return ((b) >> (i)) & 1LL; } // flg(0b010, 1LL) -> true const ll LINF = (ll)1e18 + 7; const double EPS = 1e-9; const int MAX_DUBUG_SIZE = 200; #include #include using namespace atcoder; const int MOD = 998244353; using mint = modint998244353; ostream& operator<<(ostream& os, const mint& N) { return os << N.val(); } struct edge { ll to; ll w; // edge v; // v.to, v.w でメンバ変数を呼び出す edge(ll to, ll w) : to(to), w(w) {} // graph g(n); で n 頂点のグラフを宣言 // graph[from].push_back(edge(to, w)) の形で使う }; using graph = vector>; // // 参考記事: https://qiita.com/Morifolium/items/6c8f0a188af2f9620db2 // // グラフ、頂点の入次数、頂点数を受け取り、そのトポロジカルソート(辞書式順序)を記録した配列を返す関数 // 頂点は 0 index, しがらみがなくなった頂点から queue に入れていく vector topological_sort(vector>& G, vector& indegree, ll V) { // トポロジカルソートを記録する配列 vector sorted_vertices; //*********************************注意******************************** // 埋める順を小さい順にするためpriority_queue を用いているが // 通常のトポロジカルソートはqueueでよい //********************************************************************* // 入次数が0の頂点を発見したら、処理待ち頂点としてキューに追加する priority_queue, greater> que; for (ll i = 0; i < V; i++) { if (indegree[i] == 0) { que.push(i); } } // キューが空になるまで、操作1~3を繰り返す while (que.empty() == false) { // キューの先頭の頂点を取り出す ll v = que.top(); que.pop(); // その頂点と隣接している頂点の入次数を減らし、0になればキューに追加 for (ll i = 0; i < G[v].size(); i++) { ll u = G[v][i]; indegree[u] -= 1; if (indegree[u] == 0) que.push(u); } // 頂点vを配列の末尾に追加する sorted_vertices.push_back(v); } // トポロジカルソートを返す return sorted_vertices; } void solve([[maybe_unused]] int test) { ll n, q; cin >> n >> q; vector a(q), b(q), c(q); graph g(n); // 0-index, 無向グラフに直し忘れない. vector> g2(n); // 0-index, 無向グラフに直し忘れない. vector indegree(n, 0); for (ll i = 0; i < q; i++) { cin >> a[i] >> b[i] >> c[i]; a[i]--, b[i]--, c[i]; g[a[i]].push_back(edge(b[i], c[i])); g[b[i]].push_back(edge(a[i], c[i])); g2[a[i]].push_back(b[i]); indegree[b[i]]++; } // Aren't they one line? auto sorted_vertices = topological_sort(g2, indegree, n); mint ans = 1; vector dist(n, 0); // グラフの頂点数を合わせる. for (ll i = 0; i < n; i++) { queue qu; ll start_node = i; // BFSの開始点を合わせる. if (dist[start_node] != 0) { continue; } qu.push(start_node); dist[start_node] = i + 1; ll cnt = 2; bool same = false; bool ne = false; while (!qu.empty()) { ll now_node = qu.front(); qu.pop(); for (auto&& [next_node, flg] : g[now_node]) { ll next_dist = 0; if ((flg == 0 and dist[now_node] > 0) or (flg == 1 and dist[now_node] < 0)) { next_dist = dist[start_node]; } else { next_dist = -dist[start_node]; } // dbg(next_dist, next_node, dist[next_node]); // dbg(dist); if (dist[next_node] != 0) { if (same) { if (next_dist * dist[next_node] < 0) { ans = 0; dbg(111); } } if (ne) { if (next_dist * dist[next_node] > 0) { ans = 0; dbg(111); } } if (next_dist == -dist[next_node]) { dbg(now_node, next_node, next_dist, dist[next_node]); dbg(dist); ans = 0; continue; } else if (next_dist == dist[next_node]) { continue; } else if (next_dist * dist[next_node] < 0) { ne = true; } else if (next_dist * dist[next_node] > 0) { same = true; } cnt = 1; continue; } dist[next_node] = next_dist; qu.push(next_node); } } ans *= cnt; } dbg(dist); if (ans == 1) { cout << 0 << "\n"; } else { cout << ans << "\n"; } } int main() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(12); int testcase_size = 1; // cin >> testcase_size; for (int _t = 0; _t < testcase_size; _t++) { solve(_t); } } /* -----------------------------------MY_FUNCTIONS------------------------------------ */ template ostream& operator<<(ostream& os, const pair& pp) { return os << "{" << pp.first << "," << pp.second << "}"; } template ostream& operator<<(ostream& os, const vector& V) { if (V.empty()) return os << "[]"; os << "["; for (ll i = 0; i < (ll)V.size(); i++) { os << V[i] << (i == int(V.size() - 1) ? "]" : ","); } return os; } template ostream& operator<<(ostream& os, const vector>& VV) { if (VV.empty()) return os << "[[]]"; os << "[\n"; for (auto&& V : VV) { os << V << "\n"; } os << "]"; return os; } template ostream& operator<<(ostream& os, const vector>>& VVV) { if (VVV.empty()) return os << "[[[]]]"; os << "[" << "\n"; int cnt = 0; for (auto&& VV : VVV) { os << cnt++ << VV << "\n\n"; } os << "]"; return os; } template ostream& operator<<(ostream& os, const set& SS) { if (SS.empty()) return os << "[]"; os << "["; auto ii = SS.begin(); for (; ii != SS.end(); ii++) os << *ii << (ii == prev(SS.end()) ? "]" : ","); return os; } template ostream& operator<<(ostream& os, const map& MM) { if (MM.empty()) return os << "[{:}]"; os << "["; auto ii = MM.begin(); for (; ii != MM.end(); ii++) os << "{" << ii->first << ":" << ii->second << "}" << (ii == prev(MM.end()) ? "]" : ","); return os; } void debug_out() { cerr << endl; } void debug_out_vl(vector V) { const int MAX_SIZE = min((int)V.size(), MAX_DUBUG_SIZE); cerr << "\033[33m"; if (V.empty()) { cerr << "[]" << endl; return; } cerr << "["; for (int i = 0; i < MAX_SIZE; i++) { if (V[i] == LINF) cerr << "INF"; else cerr << V[i]; if (i == (int)V.size() - 1) cerr << "]\n"; else if (i == MAX_DUBUG_SIZE - 1) cerr << ",...\n"; else cerr << ","; } return; } void debug_out_vvl(vector> VV) { cerr << "\033[33m"; if (VV.empty()) { cerr << "[[]]" << endl; return; } cerr << "[\n"; int MAX_ROW = min((int)VV.size(), MAX_DUBUG_SIZE); for (int i = 0; i < MAX_ROW; i++) { const int MAX_COLUMN = min((int)VV[i].size(), MAX_DUBUG_SIZE); if (VV[i].empty()) { cerr << "[]" << endl; continue; } cerr << "["; for (int j = 0; j < MAX_COLUMN; j++) { if (VV[i][j] == LINF) cerr << "INF"; else cerr << VV[i][j]; if (j == (int)VV[i].size() - 1) cerr << "]\n"; else if (j == MAX_DUBUG_SIZE - 1) cerr << ",...\n"; else cerr << ","; } if (i != (int)VV.size() - 1 and i == MAX_DUBUG_SIZE - 1) { cerr << ":\n:\033[m\n"; return; } } cerr << "]\033[m\n"; return; } template void debug_out(Head H, Tail... T) { if constexpr (std::is_same_v>) { debug_out_vl(H); } else if constexpr (std::is_same_v>>) { debug_out_vvl(H); } else { cerr << "\033[33m" << H << "\033[m "; } debug_out(T...); } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } template T pwr(T x, ll n) { T res = 1; for (int i = 0; i < n; i++) { res *= x; } return res; } ll fact(ll n) { ll res = 1; for (ll i = 1; i <= n; i++) res *= i; return res; } ll comb(ll n, ll r) { // comb(60, 30)までオーバーフローなし ll res = 1; for (int i = 1; i <= r; i++) { res *= n--; res /= i; } return res; } ll ctoll(char c) { if (c < '0' or '9' < c) { cerr << "\n\033[33m ctoll に '0'~'9' 以外の文字が入りました.\033[m\n" << endl; } return ll(c - '0'); } char lltoc(ll n) { if (n < 0 or 9 < n) { cerr << "\n\033[33m lltoc に 0 ~ 9 以外の数字が入りました.\033[m\n" << endl; } return char(n + '0'); }