#ifndef hari64 #include // #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #define debug(...) #else #include "util/viewer.hpp" #define debug(...) viewer::_debug(__LINE__, #__VA_ARGS__, __VA_ARGS__) #endif using namespace std; constexpr int INF = 1001001001; constexpr long long INFll = 1001001001001001001; template bool chmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } template bool chmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; } // clang-format off namespace internal{templateusing is_signed_int128=typename conditional::value||is_same::value,true_type,false_type>::type;templateusing is_unsigned_int128=typename conditional::value||is_same::value,true_type,false_type>::type;templateusing is_integral=typename conditional::value||is_signed_int128::value||is_unsigned_int128::value,true_type,false_type>::type; templateusing is_signed_int=typename conditional<(is_integral::value&&is_signed::value)||is_signed_int128::value,true_type,false_type>::type;templateusing is_unsigned_int=typename conditional<(is_integral::value&&is_unsigned::value)||is_unsigned_int128::value,true_type,false_type>::type;templateusing is_signed_int_t=enable_if_t::value>;templateusing is_unsigned_int_t=enable_if_t::value>; constexpr long long safe_mod(long long x,long long m){x%=m;if(x<0)x+=m;return x;}struct barrett{unsigned int _m;unsigned long long im;explicit barrett(unsigned int m):_m(m),im((unsigned long long)(-1)/m+1){}unsigned int umod()const{return _m;}unsigned int mul(unsigned int a,unsigned int b)const{unsigned long long z=a;z*=b;unsigned long long x=(unsigned long long)(((unsigned __int128)(z)*im)>>64);unsigned int v=(unsigned int)(z-x*_m);if(_m<=v)v+=_m;return v;}}; constexpr long long pow_mod_constexpr(long long x,long long n,int m){if(m==1)return 0;unsigned int _m=(unsigned int)(m);unsigned long long r=1;unsigned long long y=safe_mod(x,m);while(n){if(n&1)r=(r*y)%_m;y=(y*y)%_m;n>>=1;}return r;}constexpr pairinv_gcd(long long a,long long b){a=safe_mod(a,b);if(a==0)return{b,0};long long s=b,t=a;long long m0=0,m1=1;while(t){long long u=s/t;s-=t*u;m0-=m1*u;auto tmp=s;s=t;t=tmp;tmp=m0;m0=m1;m1=tmp;}if(m0<0)m0+=b/s;return{s,m0};} constexpr bool is_prime_constexpr(int n){if(n<=1)return false;if(n==2||n==7||n==61)return true;if(n%2==0)return false;long long d=n-1;while(d%2==0)d/=2;constexpr long long bases[3]={2,7,61};for(long long a:bases){long long t=d;long long y=pow_mod_constexpr(a,t,n);while(t!=n-1&&y!=1&&y!=n-1){y=y*y%n;t<<=1;}if(y!=n-1&&t%2==0)return false;}return true;}templateconstexpr bool is_prime=is_prime_constexpr(n);} // namespace internal templatestruct static_modint{using mint=static_modint;static constexpr int mod(){return m;}static mint raw(int v){mint x;x._v=v;return x;}static_modint():_v(0){}template* =nullptr>static_modint(T v){long long x=(long long)(v%(long long)(umod()));if(x<0)x+=umod();_v=(unsigned int)(x);}template* =nullptr>static_modint(T v){_v=(unsigned int)(v%umod());}unsigned int val()const{return _v;} mint&operator++(){_v++;if(_v==umod())_v=0;return*this;}mint&operator--(){if(_v==0)_v=umod();_v--;return*this;}mint operator++(int){mint result=*this;++*this;return result;}mint operator--(int){mint result=*this;--*this;return result;}mint&operator+=(const mint&rhs){_v+=rhs._v;if(_v>=umod())_v-=umod();return*this;}mint&operator-=(const mint&rhs){_v-=rhs._v;if(_v>=umod())_v+=umod();return*this;} mint&operator*=(const mint&rhs){unsigned long long z=_v;z*=rhs._v;_v=(unsigned int)(z%umod());return*this;}mint&operator/=(const mint&rhs){return*this=*this*rhs.inv();}mint operator+()const{return*this;}mint operator-()const{return mint()-*this;}mint pow(long long n)const{assert(0<=n);mint x=*this,r=1;while(n){if(n&1)r*=x;x*=x;n>>=1;}return r;}mint inv()const{if(prime){assert(_v);return pow(umod()-2);}else{auto eg=internal::inv_gcd(_v,m);assert(eg.first==1);return eg.second;}} friend mint operator+(const mint&lhs,const mint&rhs){return mint(lhs)+=rhs;}friend mint operator-(const mint&lhs,const mint&rhs){return mint(lhs)-=rhs;}friend mint operator*(const mint&lhs,const mint&rhs){return mint(lhs)*=rhs;}friend mint operator/(const mint&lhs,const mint&rhs){return mint(lhs)/=rhs;}friend bool operator==(const mint&lhs,const mint&rhs){return lhs._v==rhs._v;}friend bool operator!=(const mint&lhs,const mint&rhs){return lhs._v!=rhs._v;} friend ostream&operator<<(ostream&os,const mint&rhs){return os<>(istream&is,mint&rhs){long long v;is>>v;v%=(long long)(umod());if(v<0)v+=umod();;rhs._v=(unsigned int)v;return is;}static constexpr bool prime=internal::is_prime;private:unsigned int _v;static constexpr unsigned int umod(){return m;}}; constexpr int MOD = 998244353;using mint=static_modint;vectormint_factorial={mint(1)};/*n>1e8 ⇒ fast_modfact(deprecated)*/mint modfact(int n){assert(n<=100000000);if(int(mint_factorial.size())<=n){for(int i=mint_factorial.size();i<=n;i++){mint next=mint_factorial.back()*i;mint_factorial.push_back(next);}}return mint_factorial[n];} /*x s.t. x^2 ≡ a (mod Prime) or -1*/mint modsqrt(mint a){long long p=mint::mod();if(a.val()==1)return a;if(a.pow((p-1)>>1).val()!=1)return -1;mint b=1,one=1;while(b.pow((p-1)>>1).val()==1)b+=one;long long m=p-1,e=0;while(m%2==0)m>>=1,e++;mint x=a.pow((m-1)>>1);mint y=a*x*x;x*=a;mint z=b.pow(m);while(y!=1){long long j=0;mint t=y;while(t!=one)j++,t*=t;z=z.pow(1ll<<(e-j-1));x*=z;z*=z;y*=z;e=j;}return x;}mint nCk(int n,int k){if(k<0||nap;mint re=a;for(long long r=1;r -sz[a] - 1 = edge[a] O(N) int num_of_tree(){int num_of_tree=0;for(int a=0;a<_n;a++)if(par_or_sz[a]<0&&-par_or_sz[a]>edge[a])num_of_tree++;return num_of_tree;} // the list of the "list of the vertices in a connected component" O(N) vector>groups(bool index1=false){vector>ret(_n);for(int i=0;i<_n;i++)ret[find(i)].push_back(i+int(index1));ret.erase(remove_if(ret.begin(),ret.end(),[&](const vector&v){return v.empty();}),ret.end());return ret;} // UnionFind::groups().size() O(1) int group_count(){return group_cnt;} protected: int _n;int group_cnt;/* root node: -1 * component size , otherwise: parent */vectorpar_or_sz;vectoredge; }; /// @ref https://qiita.com/drken/items/cce6fc5c579051e64fab /// @brief merge(a,b,w): A[a] - A[b] == z /// diff(a,b): A[b]-A[a] (REQUIRE:same(a,b)) template struct weighted_dsu : UnionFind { explicit weighted_dsu(int n,Abel SUM_UNITY=0):diff_weight(n,SUM_UNITY){_n=n;group_cnt=0;par_or_sz.resize(n,-1);} int find(int a)override{assert(0<=a&&a<_n);if(par_or_sz[a]<0)return a;int r=find(par_or_sz[a]);diff_weight[a]+=diff_weight[par_or_sz[a]];return par_or_sz[a]=r;} int merge(int a,int b,Abel w){assert(0<=a&&a<_n&&0<=b&&b<_n);w+=weight(a)-weight(b);int x=find(a),y=find(b);if(x==y)return x;group_cnt--;if(-par_or_sz[x]<-par_or_sz[y])swap(x,y),w=-w;par_or_sz[x]+=par_or_sz[y];diff_weight[y]=w;return par_or_sz[y]=x;} Abel weight(int a){find(a);return diff_weight[a];} Abel diff(int a, int b){assert(same(a,b));return weight(b)-weight(a);} private:vector diff_weight;}; /// @ref https://misteer.hatenablog.com/entry/persistentUF /// @ref https://ei1333.github.io/library/structure/union-find/partially-persistent-union-find.cpp /// @brief UnionFind which can reference all previous versions and update the current (not previous) version. /// @note t = -1 is the initial time.(each node's parent is itself) struct partially_persistent_dsu { partially_persistent_dsu(int n):_n(n),par_or_sz(n,-1),last(n,INF),add(n,{{-1,-1}}){} int merge(int a,int b,int t){assert(0<=a&&a<_n&&0<=b&&b<_n);int x=find(a,t),y=find(b,t);if(x==y)return x;if(-par_or_sz[x]<-par_or_sz[y])swap(x,y);last[y]=t;par_or_sz[x]+=par_or_sz[y];add[x].emplace_back(t,par_or_sz[x]);return par_or_sz[y]=x;} int find(int a,int t){assert(0<=a&&a<_n);if(tsecond;} private:int _n;vectorpar_or_sz;vectorlast;vector>>add;}; // clang-format on int main() { cin.tie(0); ios::sync_with_stdio(false); int N; cin >> N; int Q; cin >> Q; UnionFind uf(2 * N); for (int i = 0; i < Q; i++) { int A, B, C; cin >> A >> B >> C; A--; B--; if (C == 0) { uf.merge(A, B); uf.merge(A + N, B + N); } else { uf.merge(A, B + N); uf.merge(A + N, B); } } for (int i = 0; i < N; i++) { if (uf.same(i, N + i)) { cout << 0 << endl; return 0; } } cout << mint(2).pow(uf.group_count() / 2) << endl; return 0; }