結果
問題 | No.2214 Products on Tree |
ユーザー |
![]() |
提出日時 | 2022-11-29 10:16:37 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 301 ms / 3,000 ms |
コード長 | 44,355 bytes |
コンパイル時間 | 2,493 ms |
コンパイル使用メモリ | 217,464 KB |
最終ジャッジ日時 | 2025-02-09 02:05:37 |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 35 |
コンパイルメッセージ
/home/nok0/documents/programming/library/template/input.hpp: In function ‘void scanner::scan(char*)’: /home/nok0/documents/programming/library/template/input.hpp:29:33: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
ソースコード
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"#include <bits/stdc++.h>#line 3 "/home/nok0/documents/programming/library/graph/graph.hpp"#pragma region graphtemplate <class cost_type = long long>class graph {public:struct edge {public:int from, to;cost_type cost;int id;edge() = default;edge(int from_, int to_, cost_type cost_ = 1, int id_ = -1) : from(from_), to(to_), cost(cost_), id(id_) {}bool operator<(const edge &a) const { return cost < a.cost; }bool operator>(const edge &a) const { return cost > a.cost; }friend std::ostream &operator<<(std::ostream &s, const edge &a) {s << '(' << a.from << " -> " << a.to << "), cost: " << a.cost << ", id: " << a.id;return s;}};private:std::vector<std::vector<edge>> edges;int next_edge_id = 0;public:inline const std::vector<edge> &operator[](int k) const { return edges[k]; }inline std::vector<edge> &operator[](int k) { return edges[k]; }int size() const { return int(edges.size()); }void resize(const int n) { edges.resize(n); }int edge_count() const { return next_edge_id; }friend std::ostream &operator<<(std::ostream &s, const graph<cost_type> &g) {for(const auto &adj : g.edges)for(const auto &ed : adj) s << ed << '\n';return s;}graph() = default;graph(int n) : edges(n) {}graph(int n, int e, bool weight = 0, bool directed = 0, int idx = 1) : edges(n) { input(e, weight, directed, idx); }const cost_type INF = std::numeric_limits<cost_type>::max() / 3;void input(int e = -1, bool weight = false, bool directed = false, int idx = 1) {if(e == -1) e = size() - 1;while(e--) {int u, v;std::cin >> u >> v;cost_type cost = 1;if(weight) std::cin >> cost;add_edge(u, v, cost, directed, idx);}}inline int add_edge(int u, int v, cost_type cost = 1, bool directed = false, int idx = 0) {u -= idx, v -= idx;edges[u].emplace_back(u, v, cost, next_edge_id);if(!directed && u != v) edges[v].emplace_back(v, u, cost, next_edge_id);return next_edge_id++;}// Ο(V+E)std::vector<cost_type> bfs(int s) const {std::vector<cost_type> dist(size(), INF);std::queue<int> que;dist[s] = 0;que.push(s);while(!que.empty()) {int v = que.front();que.pop();for(auto &e : edges[v]) {if(dist[e.to] != INF) continue;dist[e.to] = dist[v] + e.cost;que.push(e.to);}}return dist;}// Ο(V+E)// constraint: cost of each edge is zero or x (>= 0)std::vector<cost_type> zero_one_bfs(int s) const {std::vector<cost_type> dist(size(), INF);std::deque<int> deq;dist[s] = 0;deq.push_back(s);while(!deq.empty()) {int v = deq.front();deq.pop_front();for(auto &e : edges[v]) {if(dist[e.to] > dist[v] + e.cost) {dist[e.to] = dist[v] + e.cost;e.cost ? deq.push_back(e.to) : deq.push_front(e.to);}}}return dist;}// Ο((E+V) lg E)// unreachable: INFstd::vector<cost_type> dijkstra(int s) const {std::vector<cost_type> dist(size(), INF);const auto compare = [](const std::pair<cost_type, int> &a, const std::pair<cost_type, int> &b) {return a.first > b.first;};std::priority_queue<std::pair<cost_type, int>, std::vector<std::pair<cost_type, int>>, decltype(compare)> que{compare};dist[s] = 0;que.emplace(0, s);while(!que.empty()) {std::pair<cost_type, int> p = que.top();que.pop();int v = p.second;if(dist[v] < p.first) continue;for(auto &e : edges[v]) {if(dist[e.to] > dist[v] + e.cost) {dist[e.to] = dist[v] + e.cost;que.emplace(dist[e.to], e.to);}}}return dist;}// Ο(VE)// unreachable: INF// reachable via negative cycle: -INFstd::vector<cost_type> bellman_ford(int s) const {int n = size();std::vector<cost_type> res(n, INF);res[s] = 0;for(int loop = 0; loop < n - 1; loop++) {for(int v = 0; v < n; v++) {if(res[v] == INF) continue;for(auto &e : edges[v]) {res[e.to] = std::min(res[e.to], res[v] + e.cost);}}}std::queue<int> que;std::vector<int> chk(n);for(int v = 0; v < n; v++) {if(res[v] == INF) continue;for(auto &e : edges[v]) {if(res[e.to] > res[v] + e.cost and !chk[e.to]) {que.push(e.to);chk[e.to] = 1;}}}while(!que.empty()) {int now = que.front();que.pop();for(auto &e : edges[now]) {if(!chk[e.to]) {chk[e.to] = 1;que.push(e.to);}}}for(int i = 0; i < n; i++)if(chk[i]) res[i] = -INF;return res;}// Ο(V^3)std::vector<std::vector<cost_type>> warshall_floyd() const {const int n = size();std::vector<std::vector<cost_type>> dist(n, std::vector<cost_type>(n, INF));for(int i = 0; i < n; i++) dist[i][i] = 0;for(int i = 0; i < n; i++)for(auto &e : edges[i]) dist[i][e.to] = std::min(dist[i][e.to], e.cost);for(int k = 0; k < n; k++)for(int i = 0; i < n; i++) {if(dist[i][k] == INF) continue;for(int j = 0; j < n; j++) {if(dist[k][j] == INF) continue;dist[i][j] = std::min(dist[i][j], dist[i][k] + dist[k][j]);}}return dist;}// Ο(V) (using DFS)// if a cycle exists, return {}std::vector<int> topological_sort() const {std::vector<int> res;std::vector<int> used(size(), 0);bool not_DAG = false;auto dfs = [&](auto self, int k) -> void {if(not_DAG) return;if(used[k]) {if(used[k] == 1) not_DAG = true;return;}used[k] = 1;for(auto &e : edges[k]) self(self, e.to);used[k] = 2;res.push_back(k);};for(int i = 0; i < size(); i++) dfs(dfs, i);if(not_DAG) return std::vector<int>{};std::reverse(res.begin(), res.end());return res;}bool is_dag() const { return !topological_sort().empty(); }// Ο(V)// array of the distance to the most distant vertex// constraint: the graph is a treestd::vector<cost_type> height() const {auto vec1 = bfs(0);int v1 = -1, v2 = -1;cost_type dia = -1;for(int i = 0; i < int(size()); i++)if(dia < vec1[i]) dia = vec1[i], v1 = i;vec1 = bfs(v1);dia = -1;for(int i = 0; i < int(size()); i++)if(dia < vec1[i]) dia = vec1[i], v2 = i;auto vec2 = bfs(v2);for(int i = 0; i < int(size()); i++) {if(vec1[i] < vec2[i]) vec1[i] = vec2[i];}return vec1;}// O(V+E)// vector<(int)(0 or 1)>// if it is not bipartite, return {}std::vector<int> bipartite_grouping() const {std::vector<int> colors(size(), -1);auto dfs = [&](auto self, int now, int col) -> bool {colors[now] = col;for(auto &e : edges[now]) {if(col == colors[e.to]) return false;if(colors[e.to] == -1 and !self(self, e.to, !col)) return false;}return true;};for(int i = 0; i < int(size()); i++)if(colors[i] == -1 and !dfs(dfs, i, 0)) return std::vector<int>{};return colors;}bool is_bipartite() const { return !bipartite_grouping().empty(); }// Ο(V+E)// (v1, v2, diameter)std::tuple<int, int, cost_type> diameter() {std::vector<cost_type> dist = bfs(0);auto it = std::max_element(dist.begin(), dist.end());const int v = it - dist.begin();dist = bfs(v);it = std::max_element(dist.begin(), dist.end());return std::make_tuple(v, int(it - dist.begin()), *it);}// Ο(V+E)std::vector<int> subtree_size(const int root) {const int n = size();std::vector<int> ret(n, 1);auto dfs = [&](auto self, int now, int p = -1) -> void {for(const auto &e : (*this)[now]) {if(e.to == p) continue;self(self, e.to, now);ret[now] += ret[e.to];}};dfs(dfs, root);return ret;}// Ο(ElgE)cost_type prim() const {cost_type res = 0;std::priority_queue<edge, std::vector<edge>, std::greater<edge>> que;for(auto &e : edges[0]) que.push(e);std::vector<int> chk(size());chk[0] = 1;int cnt = 1;while(cnt < size()) {auto e = que.top();que.pop();if(chk[e.to]) continue;cnt++;res += e.cost;chk[e.to] = 1;for(auto &e2 : edges[e.to]) que.push(e2);}return res;}// Ο(ElgE)cost_type kruskal() const {std::vector<std::tuple<int, int, cost_type>> eds;for(const auto &adj : edges)for(const auto &ed : adj) eds.emplace_back(ed.from, ed.to, ed.cost);std::sort(eds.begin(), eds.end(), [](const std::tuple<int, int, cost_type> &a, const std::tuple<int, int, cost_type> &b) {return std::get<2>(a) < std::get<2>(b);});std::vector<int> uf_data(size(), -1);auto root = [&uf_data](auto self, int x) -> int {if(uf_data[x] < 0) return x;return uf_data[x] = self(self, uf_data[x]);};auto unite = [&uf_data, &root](int u, int v) -> bool {u = root(root, u), v = root(root, v);if(u == v) return false;if(uf_data[u] > uf_data[v]) std::swap(u, v);uf_data[u] += uf_data[v];uf_data[v] = u;return true;};cost_type ret = 0;for(auto &e : eds)if(unite(std::get<0>(e), std::get<1>(e))) ret += std::get<2>(e);return ret;}// O(V)std::vector<int> centroid() const {std::vector<int> centroid, sz(size());auto dfs = [&](auto self, int now, int per) -> void {sz[now] = 1;bool is_centroid = true;for(auto &e : edges[now]) {if(e.to != per) {self(self, e.to, now);sz[now] += sz[e.to];if(sz[e.to] > size() / 2) is_centroid = false;}}if(size() - sz[now] > size() / 2) is_centroid = false;if(is_centroid) centroid.push_back(now);};dfs(dfs, 0, -1);return centroid;}// O(V+E)// bridge: (s, t) (s < t);std::pair<std::vector<std::pair<int, int>>, std::vector<int>> bridges_and_articulations() const {std::vector<int> order(size(), -1), low(size()), articulation;int order_next = 0;std::vector<std::pair<int, int>> bridge;auto dfs = [&](auto self, int now, int par = -1) -> void {low[now] = order[now] = order_next++;bool is_articulation = false;int cnt = 0;for(auto &ed : edges[now]) {int &nxt = ed.to;if(nxt == par) continue;if(order[nxt] == -1) {cnt++;self(self, nxt, now);if(order[now] < low[nxt]) bridge.push_back(std::minmax(now, nxt));if(order[now] <= low[nxt]) is_articulation = true;low[now] = std::min(low[now], low[nxt]);} else if(order[now] > order[nxt]) {low[now] = std::min(low[now], order[nxt]);}}if(par == -1 and cnt < 2) is_articulation = false;if(is_articulation) articulation.push_back(now);return;};for(int i = 0; i < (int)size(); i++)if(order[i] == -1) dfs(dfs, i);return std::make_pair(bridge, articulation);}// Ο(V+E)// directed graph from root to leafgraph root_to_leaf(int root = 0) const {graph res(size());std::vector<int> chk(size(), 0);chk[root] = 1;auto dfs = [&](auto self, int now) -> void {for(auto &e : edges[now]) {if(chk[e.to] == 1) continue;chk[e.to] = 1;res.add_edge(now, e.to, e.cost, 1, 0);self(self, e.to);}};dfs(dfs, root);return res;}// Ο(V+E)// directed graph from leaf to rootgraph leaf_to_root(int root = 0) const {graph res(size());std::vector<int> chk(size(), 0);chk[root] = 1;auto dfs = [&](auto self, int now) -> void {for(auto &e : edges[now]) {if(chk[e.to] == 1) continue;chk[e.to] = 1;res.add_edge(e.to, now, e.cost, 1, 0);self(self, e.to);}};dfs(dfs, root);return res;}// cost_type Chu_Liu_Edmonds(int root = 0) {}};#pragma endregion#line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp"#line 6 "/home/nok0/documents/programming/library/atcoder/modint.hpp"#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endif#line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"#line 5 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}// Fast modular multiplication by barrett reduction// Reference: https://en.wikipedia.org/wiki/Barrett_reduction// NOTE: reconsider after Ice Lakestruct barrett {unsigned int _m;unsigned long long im;// @param m `1 <= m < 2^31`explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}// @return munsigned int umod() const { return _m; }// @param a `0 <= a < m`// @param b `0 <= b < m`// @return `a * b % m`unsigned int mul(unsigned int a, unsigned int b) const {// [1] m = 1// a = b = im = 0, so okay// [2] m >= 2// im = ceil(2^64 / m)// -> im * m = 2^64 + r (0 <= r < m)// let z = a*b = c*m + d (0 <= c, d < m)// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2// ((ab * im) >> 64) == c or c + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};// @param n `0 <= n`// @param m `1 <= m`// @return `(x ** n) % m`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;}// Reference:// M. Forisek and J. Jancina,// Fast Primality Testing for Integers That Fit into a Machine Word// @param n `0 <= n`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;}template <int n> constexpr bool is_prime = is_prime_constexpr(n);// @param b `1 <= b`// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/gconstexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};// Contracts:// [1] s - m0 * a = 0 (mod b)// [2] t - m1 * a = 0 (mod b)// [3] s * |m1| + t * |m0| <= blong long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b// [3]:// (s - t * u) * |m1| + t * |m0 - m1 * u|// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)// = s * |m1| + t * |m0| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (m0 < 0) m0 += b / s;return {s, m0};}// Compile time primitive root// @param m must be prime// @return primitive root (and minimum in now)constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root = primitive_root_constexpr(m);// @param n `n < 2^32`// @param m `1 <= m < 2^32`// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcoder#line 1 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"#line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcoder#line 14 "/home/nok0/documents/programming/library/atcoder/modint.hpp"namespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = 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;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}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 += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);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 {auto eg = internal::inv_gcd(_v, mod());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;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcoder#line 4 "/home/nok0/documents/programming/library/math/factorial.hpp"#line 6 "/home/nok0/documents/programming/library/math/factorial.hpp"template<class T>struct factorial {public:static int MAX;static std::vector<T> fac, finv, inv;factorial() {}T binom(int n, int r) {if (n < r or n < 0 or r < 0) return T(0);assert(n < MAX);return fac[n] * finv[r] * finv[n - r];}T large_binom(int n, int r) {if (n < r or n < 0 or r < 0) return T(0);assert(r < MAX);T ret = finv[r];for (int i = 1; i <= r; ++i)ret *= (n + 1 - i);return ret;}static void set_size(int n = 3000000) {MAX = (n > 1 ? n : 1) + 1;if ((int)fac.size() >= MAX) return;fac.resize(MAX);finv.resize(MAX);inv.resize(MAX);const int MOD = T::mod();fac[0] = fac[1] = 1;finv[0] = finv[1] = 1;inv[1] = 1;for (int i = 2; i < MAX; i++) {fac[i] = fac[i - 1] * i;inv[i] = (T)MOD - inv[MOD % i] * (MOD / i);finv[i] = finv[i - 1] * inv[i];}}};template<class T>int factorial<T>::MAX = 0;template<class T>std::vector<T> factorial<T>::fac;template<class T>std::vector<T> factorial<T>::finv;template<class T>std::vector<T> factorial<T>::inv;#line 3 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"#line 5 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"template<int m>std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) {long long v;is >> v;a = v;return is;}template<int m>std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {long long v;is >> v;a = v;return is;}template<int m>std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }template<int m>std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"const int inf = 1000000000;const long long INF = 1000000000000000000ll;#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"namespace viewer {void view(const long long &e) {if(e == INF)std::cerr << "INF";else if(e == -INF)std::cerr << "-INF";elsestd::cerr << e;}void view(const int &e) {if(e == inf)std::cerr << "inf";else if(e == -inf)std::cerr << "-inf";elsestd::cerr << e;}template <typename T>void view(const T &e) {std::cerr << e;}template <typename T, typename U>void view(const std::pair<T, U> &p) {std::cerr << "(";view(p.first);std::cerr << ", ";view(p.second);std::cerr << ")";}template <class T0, class T1, class T2>void view(const std::tuple<T0, T1, T2> &p) {std::cerr << "(";view(std::get<0>(p));std::cerr << ", ";view(std::get<1>(p));std::cerr << ", ";view(std::get<2>(p));std::cerr << ")";}template <class T0, class T1, class T2, class T3>void view(const std::tuple<T0, T1, T2, T3> &p) {std::cerr << "(";view(std::get<0>(p));std::cerr << ", ";view(std::get<1>(p));std::cerr << ", ";view(std::get<2>(p));std::cerr << ", ";view(std::get<3>(p));std::cerr << ")";}template <typename T>void view(const std::set<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::unordered_set<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::multiset<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::unordered_multiset<T> &s) {if(s.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(auto &t : s) {view(t);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::vector<T> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(const auto &e : v) {view(e);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T, std::size_t ary_size>void view(const std::array<T, ary_size> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << "{ ";for(const auto &e : v) {view(e);std::cerr << ", ";}std::cerr << "\b\b }";}template <typename T>void view(const std::vector<std::vector<T>> &vv) {std::cerr << "{\n";for(const auto &v : vv) {std::cerr << "\t";view(v);std::cerr << '\n';}std::cerr << "}";}template <typename T, typename U>void view(const std::vector<std::pair<T, U>> &v) {std::cerr << "{\n";for(const auto &c : v) {std::cerr << "\t(";view(c.first);std::cerr << ", ";view(c.second);std::cerr << ")\n";}std::cerr << "}";}template <class T0, class T1, class T2>void view(const std::vector<std::tuple<T0, T1, T2>> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << '{';for(const auto &t : v) {std::cerr << "\n\t";view(t);std::cerr << ",";}std::cerr << "\n}";}template <class T0, class T1, class T2, class T3>void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {if(v.empty()) {std::cerr << "{ }";return;}std::cerr << '{';for(const auto &t : v) {std::cerr << "\n\t";view(t);std::cerr << ",";}std::cerr << "\n}";}template <typename T, typename U>void view(const std::map<T, U> &m) {std::cerr << "{\n";for(const auto &t : m) {std::cerr << "\t[";view(t.first);std::cerr << "] : ";view(t.second);std::cerr << '\n';}std::cerr << "}";}template <typename T, typename U>void view(const std::unordered_map<T, U> &m) {std::cerr << "{\n";for(const auto &t : m) {std::cerr << "\t[";view(t.first);std::cerr << "] : ";view(t.second);std::cerr << '\n';}std::cerr << "}";}} // namespace viewer// when compiling : g++ foo.cpp -DLOCAL#ifdef LOCALvoid debug_out() {}template <typename Head, typename... Tail>void debug_out(Head H, Tail... T) {viewer::view(H);std::cerr << ", ";debug_out(T...);}#define debug(...) \do { \std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \debug_out(__VA_ARGS__); \std::cerr << "\b\b]\n"; \} while(0)#define dump(x) \do { \std::cerr << __LINE__ << " " << #x << " : "; \viewer::view(x); \std::cerr << '\n'; \} while(0)#else#define debug(...) (void(0))#define dump(x) (void(0))#endif#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"#define pb push_back#define eb emplace_back#define SZ(x) ((int)(x).size())#define all(x) (x).begin(), (x).end()#define rall(x) (x).rbegin(), (x).rend()#define popcnt(x) __builtin_popcountll(x)template<class T = int>using V = std::vector<T>;template<class T = int>using VV = std::vector<std::vector<T>>;template<class T>using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;using ll = long long;using ld = long double;using int128 = __int128_t;using pii = std::pair<int, int>;using pll = std::pair<long long, long long>;#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"struct fast_io {fast_io() {std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout << std::fixed << std::setprecision(15);}} fast_io_;#line 3 "/home/nok0/documents/programming/library/template/input.hpp"template<class T, class U>std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {is >> p.first >> p.second;return is;}template<class T>std::istream &operator>>(std::istream &is, std::vector<T> &v) {for (T &i : v) is >> i;return is;}std::istream &operator>>(std::istream &is, __int128_t &a) {std::string s;is >> s;__int128_t ret = 0;for (int i = 0; i < (int)s.length(); i++)if ('0' <= s[i] and s[i] <= '9')ret = 10 * ret + s[i] - '0';a = ret * (s[0] == '-' ? -1 : 1);return is;}namespace scanner {void scan(int &a) { std::cin >> a; }void scan(long long &a) { std::cin >> a; }void scan(std::string &a) { std::cin >> a; }void scan(char &a) { std::cin >> a; }void scan(char a[]) { std::scanf("%s", a); }void scan(double &a) { std::cin >> a; }void scan(long double &a) { std::cin >> a; }template<class T, class U>void scan(std::pair<T, U> &p) { std::cin >> p; }template<class T>void scan(std::vector<T> &a) { std::cin >> a; }void INPUT() {}template<class Head, class... Tail>void INPUT(Head &head, Tail &...tail) {scan(head);INPUT(tail...);}} // namespace scanner#define VEC(type, name, size) \std::vector<type> name(size); \scanner::INPUT(name)#define VVEC(type, name, h, w) \std::vector<std::vector<type>> name(h, std::vector<type>(w)); \scanner::INPUT(name)#define INT(...) \int __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define LL(...) \long long __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define STR(...) \std::string __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define DOUBLE(...) \double __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#define LD(...) \long double __VA_ARGS__; \scanner::INPUT(__VA_ARGS__)#line 3 "/home/nok0/documents/programming/library/template/math.hpp"template <class T, class U>inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }template <class T, class U>inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }template <class T>T divup(T x, T y) { return (x + y - 1) / y; }template <class T>T POW(T a, long long n) {T ret = 1;while(n) {if(n & 1) ret *= a;a *= a;n >>= 1;}return ret;}long long POW(long long a, long long n, const int mod) {long long ret = 1;a = (a % mod + mod) % mod;while(n) {if(n & 1) (ret *= a) %= mod;(a *= a) %= mod;n >>= 1;}return ret;}template <class T, class F>T bin_search(T ok, T ng, const F &f) {while(abs(ok - ng) > 1) {T mid = (ok + ng) >> 1;(f(mid) ? ok : ng) = mid;}return ok;}template <class T, class F>T bin_search(T ok, T ng, const F &f, int loop) {for(int i = 0; i < loop; i++) {T mid = (ok + ng) / 2;(f(mid) ? ok : ng) = mid;}return ok;}#line 3 "/home/nok0/documents/programming/library/template/output.hpp"template<class T, class U>std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {os << p.first << " " << p.second;return os;}template<class T>std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {for (int i = 0; i < int(a.size()); ++i) {if (i) os << " ";os << a[i];}return os;}std::ostream &operator<<(std::ostream &dest, __int128_t &value) {std::ostream::sentry s(dest);if (s) {__uint128_t tmp = value < 0 ? -value : value;char buffer[128];char *d = std::end(buffer);do {--d;*d = "0123456789"[tmp % 10];tmp /= 10;} while (tmp != 0);if (value < 0) {--d;*d = '-';}int len = std::end(buffer) - d;if (dest.rdbuf()->sputn(d, len) != len) {dest.setstate(std::ios_base::badbit);}}return dest;}template<class T>void print(const T a) { std::cout << a << '\n'; }template<class Head, class... Tail>void print(Head H, Tail... T) {std::cout << H << ' ';print(T...);}template<class T>void printel(const T a) { std::cout << a << '\n'; }template<class T>void printel(const std::vector<T> &a) {for (const auto &v : a)std::cout << v << '\n';}template<class Head, class... Tail>void printel(Head H, Tail... T) {std::cout << H << '\n';printel(T...);}void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }void No() { std::cout << "No\n"; }void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }void NO() { std::cout << "NO\n"; }#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"#define foa(v, a) for (auto &v : a)#define repname(a, b, c, d, e, ...) e#define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)#define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter)#define rep1(i, x) for (int i = 0; i < (x); ++i)#define rep2(i, l, r) for (int i = (l); i < (r); ++i)#define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c))#define repsname(a, b, c, ...) c#define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)#define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter)#define reps1(i, x) for (int i = 1; i <= (x); ++i)#define rrepname(a, b, c, ...) c#define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)#define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)#define rrep1(i, x) for (int i = (x)-1; i >= 0; --i)#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"template <class T>int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }template <class T>int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }template <class T>void UNIQUE(std::vector<T> &a) {std::sort(a.begin(), a.end());a.erase(std::unique(a.begin(), a.end()), a.end());}template <class T>std::vector<T> press(std::vector<T> &a) {auto res = a;UNIQUE(res);for(auto &v : a)v = lb(res, v);return res;}#define SORTname(a, b, c, ...) c#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)#define SORT0(a) std::sort((a).begin(), (a).end())#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })template <class T>void ADD(std::vector<T> &a, const T x = 1) {for(auto &v : a) v += x;}template <class T>void SUB(std::vector<T> &a, const T x = 1) {for(auto &v : a) v -= x;}template <class T>struct cum_vector {public:cum_vector() = default;template <class U>cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {for(int i = 0; i < (int)vec.size(); i++)cum[i + 1] = cum[i] + vec[i];}T prod(int l, int r) {return cum[r] - cum[l];}private:std::vector<T> cum;};std::vector<std::pair<char, int>> rle(const std::string &s) {const int n = s.size();std::vector<std::pair<char, int>> ret;for(int l = 0; l < n;) {int r = l + 1;for(; r < n and s[l] == s[r]; r++) {}ret.emplace_back(s[l], r - l);l = r;}return ret;}template <class T>std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {int n = v.size();std::vector<std::pair<T, int>> ret;for(int l = 0; l < n;) {int r = l + 1;for(; r < n and v[l] == v[r]; r++) {}ret.emplace_back(v[l], r - l);l = r;}return ret;}std::vector<int> iota(int n) {std::vector<int> p(n);std::iota(p.begin(), p.end(), 0);return p;}#line 11 "/home/nok0/documents/programming/library/template/all"using namespace std;#line 4 "a.cpp"using mint = atcoder::modint998244353;void main_();int main() {int t = 1;while(t--) main_();}void main_() {INT(n);graph tmp(n, -1);auto g = tmp.root_to_leaf(0);vector dp(n, vector(2, mint(1)));auto dfs = [&](auto dfs, int now) -> void {for(auto e : g[now]) {dfs(dfs, e.to);vector ndp(2, mint(0));ndp[0] = dp[now][0] * (dp[e.to][0] + dp[e.to][1]);ndp[1] = dp[now][0] * dp[e.to][1] + dp[now][1] * (dp[e.to][0] + dp[e.to][1]);dp[now] = move(ndp);}};dfs(dfs, 0);print(dp[0][1]);}