// clang-format off #ifdef _LOCAL #include #else #include #define cerr if (false) cerr #define debug_bar #define debug(...) #define debug2(vv) #define debug3(vvv) #endif using namespace std; using ll = long long; using ld = long double; using str = string; using P = pair; using VP = vector

; using VVP = vector; using VC = vector; using VS = vector; using VVS = vector; using VI = vector; using VVI = vector; using VVVI = vector; using VLL = vector; using VVLL = vector; using VVVLL = vector; using VB = vector; using VVB = vector; using VVVB = vector; using VD = vector; using VVD = vector; using VVVD = vector; #define FOR(i,l,r) for (ll i = (l); i < (r); ++i) #define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) RFOR(i,0,n) #define FORE(e,c) for (auto&& e : c) #define ALL(c) (c).begin(), (c).end() #define SORT(c) sort(ALL(c)) #define RSORT(c) sort((c).rbegin(), (c).rend()) #define MIN(c) *min_element(ALL(c)) #define MAX(c) *max_element(ALL(c)) #define COUNT(c,v) count(ALL(c),(v)) #define len(c) ((ll)(c).size()) #define BIT(b,i) (((b)>>(i)) & 1) #define PCNT(b) ((ll)__builtin_popcountll(b)) #define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v))) #define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v))) #define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0) #define END(...) do { print(__VA_ARGS__); exit(0); } while (0) constexpr ld EPS = 1e-10; constexpr ld PI = acosl(-1.0); constexpr int inf = (1 << 30) - (1 << 15); // 1,073,709,056 constexpr ll INF = (1LL << 62) - (1LL << 31); // 4,611,686,016,279,904,256 template void input(T&... a) { (cin >> ... >> a); } void print() { cout << '\n'; } template void print(const T& a) { cout << a << '\n'; } template void print(const pair& a) { cout << a.first << " " << a.second << '\n'; } template void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void cout_line(const vector& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; } template void print(const vector& a) { cout_line(a, 0, a.size()); } template bool chmin(S& a, const T b) { if (b < a) { a = b; return 1; } return 0; } template bool chmax(S& a, const T b) { if (a < b) { a = b; return 1; } return 0; } template T SUM(const vector& A) { return accumulate(ALL(A), T(0)); } template vector cumsum(const vector& A, bool offset = false) { int N = A.size(); vector S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; } template string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; } template ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; } template double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; } template using PQ_max = priority_queue; template using PQ_min = priority_queue, greater>; template T pick(stack& s) { assert(not s.empty()); T x = s.top(); s.pop(); return x; } template T pick(queue& q) { assert(not q.empty()); T x = q.front(); q.pop(); return x; } template T pick_front(deque& dq) { assert(not dq.empty()); T x = dq.front(); dq.pop_front(); return x; } template T pick_back(deque& dq) { assert(not dq.empty()); T x = dq.back(); dq.pop_back(); return x; } template T pick(PQ_min& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; } template T pick(PQ_max& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; } template T pick(vector& v) { assert(not v.empty()); T x = v.back(); v.pop_back(); return x; } int to_int(const char c) { if (islower(c)) { return (c - 'a'); } if (isupper(c)) { return (c - 'A'); } if (isdigit(c)) { return (c - '0'); } assert(false); } char to_a(const int i) { assert(0 <= i && i < 26); return ('a' + i); } char to_A(const int i) { assert(0 <= i && i < 26); return ('A' + i); } char to_d(const int i) { assert(0 <= i && i <= 9); return ('0' + i); } ll min(int a, ll b) { return min((ll)a, b); } ll min(ll a, int b) { return min(a, (ll)b); } ll max(int a, ll b) { return max((ll)a, b); } ll max(ll a, int b) { return max(a, (ll)b); } ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; } ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); } ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); } ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; } pair divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); } ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); } ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; } ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); } ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); } // -------------------------------------------------------- #include using namespace atcoder; // constexpr ll MOD = 1000003; // using mint = modint; // mint::set_mod(MOD); // write in main() // using mint = modint1000000007; using mint = modint998244353; using VM = vector; using VVM = vector; using VVVM = vector; using VVVVM = vector; template istream &operator>>(istream &is, static_modint &m) { ll v; is >> v; m = v; return is; } template istream &operator>>(istream &is, dynamic_modint &m) { ll v; is >> v; m = v; return is; } template ostream &operator<<(ostream &os, const static_modint &m) { return os << m.val(); } template ostream &operator<<(ostream &os, const dynamic_modint &m) { return os << m.val(); } // It is assumed that M (= mod) is prime number struct combination { public: combination() : combination(1) {} combination(int n) : N(1), _fact(2,1), _ifact(2,1) { M = mint().mod(); assert(0 < n && n < M); if (N < n) { build(n); } } mint P(int n, int k) { if (N < n) { build(n); } if (n < 0 || k < 0 || n < k) { return 0; } return _fact[n] * _ifact[n-k]; } mint C(int n, int k) { if (N < n) { build(n); } if (n < 0 || k < 0 || n < k) { return 0; } return _fact[n] * _ifact[n-k] * _ifact[k]; } mint H(int n, int k) { if (n == 0 && k == 0) { return 1; } if (n < 0 || k < 0) { return 0; } return C(n + k - 1, k); } mint fact(int n) { if (N < n) { build(n); } if (n < 0) { return 0; } return _fact[n]; } mint ifact(int n) { if (N < n) { build(n); } if (n < 0) { return 0; } return _ifact[n]; } mint P_naive(ll n, int k) const noexcept { if (n < 0 || k < 0 || n < k) { return 0; } mint res = 1; for (int i = 1; i <= k; i++) { res *= (n - i + 1); } return res; } mint C_naive(ll n, int k) const noexcept { if (n < 0 || k < 0 || n < k) { return 0; } if (k > n - k) { k = n - k; } mint nume = 1, deno = 1; for (int i = 1; i <= k; i++) { nume *= (n - i + 1); deno *= i; } return nume / deno; } mint H_naive(ll n, int k) const noexcept { if (n == 0 && k == 0) { return 1; } if (n < 0 || k < 0) { return 0; } return C_naive(n + k - 1, k); } mint catalan(int n) { if (N < 2 * n) { build(2 * n); } return _fact[2 * n] * _ifact[n + 1] * _ifact[n]; } template mint C_multinomial(int n, int k, Ts... ks) { if (N < n) { build(n); } if (n < 0 || k < 0 || n < k) { return 0; } return C_multinomial(n, ks...) * _ifact[k]; } mint C_multinomial(int n, int k) { if (N < n) { build(n); } if (n < 0 || k < 0 || n < k) { return 0; } return _fact[n] * _ifact[k]; } private: int N; int M; // mod vector _fact, _ifact; void build(int N_new) { assert(N < N_new); assert(N_new < M); _fact.resize(N_new + 1); _ifact.resize(N_new + 1); for (int i = N + 1; i <= N_new; i++) { _fact[i] = _fact[i - 1] * i; } _ifact[N_new] = _fact[N_new].inv(); for (int i = N_new - 1; N + 1 <= i; i--) { _ifact[i] = _ifact[i + 1] * (i + 1); } N = N_new; } }; // References: // // // // ポテンシャル付き Union Find // 各連結成分の根のポテンシャルを 0 とした場合の各頂点のポテンシャルを管理する template struct dsu_potential { public: dsu_potential() : N(0) {} explicit dsu_potential(int n) : N(n), parent_or_size(n, -1), p(n, 0) {} // 頂点 a のポテンシャル P(a) を返す // (※ これを外部で使うケースは恐らくない) // - amortized O(α(N)) T potential(int a) { assert(0 <= a && a < N); leader(a); return p[a]; } // P(b) - P(a) を返す // (a, b) が同じ連結成分であることを想定 // - amortized O(α(N)) T diff(int a, int b) { assert(same(a, b)); return potential(b) - potential(a); } // P(a) + d = P(b) となるように (a, b) に辺を張ってマージ成否を返す // - amortized O(α(N)) bool merge(int a, int b, T d) { assert(0 <= a && a < N); assert(0 <= b && b < N); int x = leader(a), y = leader(b); if (x == y) { return false; } d = (potential(a) + d) - potential(b); if (-parent_or_size[x] < -parent_or_size[y]) { swap(x, y); d = -d; } parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; p[y] = d; return true; } // 頂点 a, b が連結か判定する // - amortized O(α(N)) bool same(int a, int b) { assert(0 <= a && a < N); assert(0 <= b && b < N); return leader(a) == leader(b); } // 頂点 a が属する連結成分のルートを返す // - amortized O(α(N)) int leader(int a) { assert(0 <= a && a < N); if (parent_or_size[a] < 0) { return a; } int r = leader(parent_or_size[a]); p[a] += p[parent_or_size[a]]; return parent_or_size[a] = r; } // 頂点 a が属する連結成分のサイズを返す // - amortized O(α(N)) int size(int a) { assert(0 <= a && a < N); return -parent_or_size[leader(a)]; } // 「一つの連結成分の頂点番号リスト」のリストを返す // - O(N) vector> groups() { vector leader_buf(N), group_size(N); for (int i = 0; i < N; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } 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( remove_if(result.begin(), result.end(), [&](const vector& v) { return v.empty(); }), result.end()); return result; } private: int N; // [x < 0] -x が連結成分のサイズに対応 // [0 <= x] x が parent に対応 vector parent_or_size; vector p; // potential }; // 座標圧縮 template struct compress { public: compress() {} compress(const vector& A) : xs(A) {} compress(const vector& A, const vector& B) { xs.reserve(A.size() + B.size()); for (const auto& a : A) { xs.push_back(a); } for (const auto& b : B) { xs.push_back(b); } } // 値 v を追加する // - amortized O(1) void add(T v) { assert(not is_built); xs.push_back(v); } // 配列 A の値を全て追加する // - O(|A|) void add(const vector& A) { assert(not is_built); xs.reserve(xs.size() + A.size()); for (const auto& a : A) { xs.push_back(a); } } // 座標圧縮して種類数を返す // - O(N log N) int build() { assert(not is_built); sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end()); is_built = true; return xs.size(); } // 座標圧縮前で i 番目に大きい値を返す (0-indexed) // - O(1) T operator[] (int i) const noexcept { assert(is_built); assert(0 <= i && i < (int)xs.size()); return xs[i]; } // 値 v に対応する座標圧縮後の値(番号)を返す // 値 v が元の配列に存在することを想定 // - O(log N) int operator() (T v) const noexcept { assert(is_built); auto it = lower_bound(xs.begin(), xs.end(), v); assert(it != xs.end() && *it == v); return distance(xs.begin(), it); } // 座標圧縮後の値の種類数を返す // - O(1) int size() const noexcept { assert(is_built); return xs.size(); } private: bool is_built = false; vector xs; }; // clang-format on int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); ll N, Q; input(N, Q); mint inv_2 = mint(2).inv(); mint all = mint(2).pow(N); VI T(Q + 1), A(Q + 1), B(Q + 1); REP (i, Q) { input(T[i]); if (T[i] <= 2) { input(A[i], B[i]); } } T[Q] = 3; VM ans; vector> E; REP (i, Q + 1) { int q = T[i]; int u = A[i], v = B[i]; if (q == 1) { E.emplace_back(u, v, 0); } else if (q == 2) { E.emplace_back(u, v, 1); } else { compress z; for (auto [u, v, d] : E) { z.add(u); z.add(v); } int M = z.build(); dsu_potential uf(M); mint res = all; for (auto [u, v, d] : E) { int x = z(u); int y = z(v); if (uf.merge(x, y, d)) { res *= inv_2; } else { auto diff = uf.diff(x, y); if (mod(diff, 2) != d) { res = 0; } } ans.push_back(res); } ans.push_back(all); E.clear(); } } REP (i, Q) { print(ans[i].val()); } return 0; }