#include "bits/stdc++.h" #include #include #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define SZ(x) ((lint)(x).size()) #define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i=i##_begin_;--i) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) #define endk '\n' using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef double ld; typedef pair plint; typedef pair pld; struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(30); }; } fast_ios_; template auto add = [](T a, T b) -> T { return a + b; }; template auto mul = [](T a, T b) -> T { return a * b; }; template auto f_max = [](T a, T b) -> T { return max(a, b); }; template auto f_min = [](T a, T b) -> T { return min(a, b); }; template using V = vector; using Vl = V; using VVl = V; using VVVl = V>; template< typename T > ostream& operator<<(ostream& os, const vector< T >& v) { for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != v.size() ? " " : ""); return os; } template< typename T >istream& operator>>(istream& is, vector< T >& v) { for (T& in : v) is >> in; return is; } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } template T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } template struct rec { F f; rec(F&& f_) : f(std::forward(f_)) {} template auto operator()(Args &&... args) const { return f(*this, std::forward(args)...); } }; lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); } lint digit(lint a) { return (lint)log10(a); } lint e_dist(plint a, plint b) { return abs(a.first - b.first) * abs(a.first - b.first) + abs(a.second - b.second) * abs(a.second - b.second); } lint m_dist(plint a, plint b) { return abs(a.first - b.first) + abs(a.second - b.second); } bool check_overflow(lint a, lint b, lint limit) { if (b == 0) return false; return a > limit / b; } // a * b > c => true void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); } const long long MOD1000000007 = 1000000007, MOD998244353 = 998244353, INF = 1e18; lint dx[8] = { 0, 1, 0, -1, 1, -1, 1, -1 }, dy[8] = { 1, 0, -1, 0, -1, -1, 1, 1 }; bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; } struct Edge { lint from, to; lint cost; Edge() { } Edge(lint u, lint v, lint c) { cost = c; from = u; to = v; } bool operator<(const Edge& e) const { return cost < e.cost; } }; struct WeightedEdge { lint to; lint cost; WeightedEdge(lint v, lint c) { to = v; cost = c; } bool operator<(const WeightedEdge& e) const { return cost < e.cost; } }; using WeightedGraph = V>; typedef pair tlint; typedef pair pld; typedef pair qlint; typedef pair vstr; typedef pair valv; typedef pair, set> pset; template class modint { using u64 = std::int_fast64_t; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(x% Modulus) {} constexpr u64& value() noexcept { return a; } constexpr const u64& value() const noexcept { return a; } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint& operator+=(const modint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint& operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint& operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint& operator/=(modint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } }; typedef modint ModInt; ModInt mod_pow(ModInt x, lint n) { ModInt ret = 1; while (n > 0) { if (n & 1) (ret *= x); (x *= x); n >>= 1; } return ret; } ModInt func[200000]; void funcinit(int N) { func[0] = 1; for (int i = 1; i <= N; i++) { func[i] = func[i - 1] * i; } } ModInt comb(ModInt n, ModInt r) { if (n.a <= 0 || n.a < r.a) { return 1; } return func[n.a] / (func[r.a] * func[(n - r).a]); } struct UnionFind { public: UnionFind() : _n(0) {} UnionFind(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); if (used_count) { if (count_in_set[x].size() < count_in_set[y].size()) { std::swap(count_in_set[x], count_in_set[y]); } for (auto p : count_in_set[y]) { count_in_set[x][p.first] += p.second; } } if (set_operate) { root_values[x] = f(root_values[y], root_values[x]); } parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } //update root calc //set by set operations void set_operate_and_value(std::vector array, function _f) { f = _f; root_values = array; set_operate = true; } lint get_set_value(int a) { return root_values[leader(a)]; } //regist count void regist_count(int a, int label) { if (!used_count) { used_count = true; count_in_set.assign(_n, std::map()); } count_in_set[leader(a)][label]++; } int get_count(int a, int label) { if (!used_count) return -1; return count_in_set[leader(a)][label]; } private: int _n; std::vector parent_or_size; std::vector> count_in_set; bool used_count = false; std::vector root_values; function f; bool set_operate = false; }; int main() { lint N, Q; cin >> N >> Q; WeightedGraph g(N); UnionFind tree(N); REP(i, Q) { lint A, B, C; cin >> A >> B >> C; A--; B--; g[A].push_back({ B, C }); tree.merge(A, B); } ModInt ans = 1; Vl color(N, -1); auto dfs = [&](auto&& dfs, lint curr) -> void { for (auto e : g[curr]) { if (color[e.to] == -1) { color[e.to] = color[curr] ^ e.cost; dfs(dfs, e.to); } else { if (color[e.to] != (color[curr] ^ e.cost)) ans = 0; } } }; set st; REP(i, N) { if (st.count(tree.leader(i))) continue; st.insert(tree.leader(i)); color[i] = 0; dfs(dfs, i); ans *= 2; } REP(i, N) { for (auto e : g[i]) { if (color[e.to] != (color[i] ^ e.cost)) ans = 0; } } cout << ans.a << endk; }