#include #include using namespace std; using namespace atcoder; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) a.begin(), a.end() #define Sort(a) sort(a.begin(), a.end()) #define RSort(a) sort(a.rbegin(), a.rend()) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector vi; typedef vector vll; typedef vector vc; typedef vector vst; typedef vector vd; typedef vector vld; typedef pair P; template long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); } template auto min(const T& a){ return *min_element(a.begin(), a.end()); } template auto max(const T& a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 1000000007; const long double EPS = 1e-9; const long double PI = acos(-1); template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p){ os << "(" << p.first << ", " << p.second << ")"; return os; } template istream &operator>>(istream &is, vector &v){ for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const vector &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const map &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void inGraph(vector>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } template struct ModInt{ long long val; constexpr ModInt(const long long &_val = 0) noexcept : val(_val) { normalize(); } void normalize(){ val = (val % Modulus + Modulus) % Modulus; } inline ModInt& operator+=(const ModInt& rhs) noexcept { if(val += rhs.val, val >= Modulus) val -= Modulus; return *this; } inline ModInt& operator-=(const ModInt& rhs) noexcept { if(val -= rhs.val, val < 0) val += Modulus; return *this; } inline ModInt& operator*=(const ModInt& rhs) noexcept { val = val * rhs.val % Modulus; return *this; } inline ModInt& operator/=(const ModInt& rhs) noexcept { val = val * inv(rhs.val).val % Modulus; return *this; } inline ModInt& operator++() noexcept { if(++val >= Modulus) val -= Modulus; return *this; } inline ModInt operator++(int) noexcept { ModInt t = val; if(++val >= Modulus) val -= Modulus; return t; } inline ModInt& operator--() noexcept { if(--val < 0) val += Modulus; return *this; } inline ModInt operator--(int) noexcept { ModInt t = val; if(--val < 0) val += Modulus; return t; } inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; } inline ModInt inv(void) const { return inv(val); } ModInt inv(const long long& n) const { long long a = n, b = Modulus, u = 1, v = 0; while(b){ long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= Modulus; if(u < 0) u += Modulus; return u; } friend inline ModInt operator+(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) += rhs; } friend inline ModInt operator-(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) -= rhs; } friend inline ModInt operator*(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) *= rhs; } friend inline ModInt operator/(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) /= rhs; } friend inline bool operator==(const ModInt& lhs, const ModInt& rhs) noexcept { return lhs.val == rhs.val; } friend inline bool operator!=(const ModInt& lhs, const ModInt& rhs) noexcept { return lhs.val != rhs.val; } friend inline istream& operator>>(istream& is, ModInt& x) noexcept { is >> x.val; x.normalize(); return is; } friend inline ostream& operator<<(ostream& os, const ModInt& x) noexcept { return os << x.val; } }; template struct SCC{ int siz; vector> G_reverse; vector check; vector memo; vector s; vector> result; SCC(const vector> &G) : G_reverse((int) G.size()), check((int) G.size()){ siz = (int) G.size(); for(int i = 0; i < siz; ++i){ for(const auto &x : G[i]){ G_reverse[x].emplace_back(i); } } for(int i = 0; i < siz; ++i){ if(!check[i]){ dfs(G, i); } } reverse(memo.begin(), memo.end()); for(int i = 0; i < siz; ++i) check[i] = false; for(const auto &x : memo){ if(!check[x]){ s = {}; dfs2(G_reverse, x); result.emplace_back(s); } } } void dfs(const vector> &G, int curr){ check[curr] = true; for(const auto &x : G[curr]){ if(check[x]){ continue; } dfs(G, x); } memo.emplace_back(curr); } void dfs2(const vector> &G, int curr){ s.emplace_back(curr); check[curr] = true; for(const auto &x : G[curr]){ if(check[x]){ continue; } dfs2(G, x); } } vector> get() const { return result; } }; struct UnionFind{ vector par; vector siz; vector edg; UnionFind(int N) : par(N), siz(N), edg(N){ for(int i = 0; i < N; ++i){ par[i] = i; siz[i] = 1; edg[i] = 0; } } int root(int x){ if(par[x] == x) return x; return par[x] = root(par[x]); } void unite(int x, int y){ int rx = root(x); int ry = root(y); if(rx == ry){ edg[rx]++; return; } par[rx] = ry; siz[ry] += siz[rx]; edg[ry] += edg[rx] + 1; } bool same(int x, int y){ int rx = root(x); int ry = root(y); return rx == ry; } long long size(int x){ return siz[root(x)]; } long long edge(int x){ return edg[root(x)]; } }; ll n, q; using mint = ModInt<998244353>; void input(){ in(n, q); } void solve(){ vector G(n); map> mp; UnionFind uf(n); rep(i, q){ ll a, b, c; in(a, b, c); a--; b--; G[a].push_back(b); mp[a][b] = c; uf.unite(a, b); } SCC s(G); vector res = s.get(); mint ans = 1; rep(i, n){ if(uf.root(i) == i) ans *= 2; } vll check(n); for(auto v : res){ for(auto x : v){ check[x] = 1; } ll w = 0; for(auto x : v){ for(auto y : G[x]){ if(check[y]){ w += mp[x][y]; } } } if(w % 2){ ans *= 0; } for(auto x : v){ check[x] = 0; } } out(ans); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); input(); solve(); }