結果
問題 | No.2733 Just K-times TSP |
ユーザー |
|
提出日時 | 2024-04-19 22:18:34 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,518 ms / 2,000 ms |
コード長 | 47,384 bytes |
コンパイル時間 | 2,967 ms |
コンパイル使用メモリ | 213,896 KB |
最終ジャッジ日時 | 2025-02-21 04:31:40 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 32 |
ソースコード
#line 2 "/home/shogo314/cpp_include/ou-library/graph.hpp"#include <iostream>#include <limits>#include <queue>#include <vector>/*** @brief グラフの汎用クラス** @tparam Cost 辺のコストの型*/template <typename Cost=int>struct Graph {/*** @brief 有向辺の構造体** operator int()を定義しているので、int型にキャストすると勝手にdstになる* 例えば、* for (auto& e : g[v]) をすると、vから出る辺が列挙されるが、* for (int dst : g[v]) とすると、vから出る辺の行き先が列挙される*/struct Edge {int src; //!< 始点int dst; //!< 終点Cost cost; //!< コストint id; //!< 辺の番号(追加された順、無向辺の場合はidが同じで方向が逆のものが2つ存在する)Edge() = default;Edge(int src, int dst, Cost cost=1, int id=-1) : src(src), dst(dst), cost(cost), id(id) {}operator int() const { return dst; }};int n; //!< 頂点数int m; //!< 辺数std::vector<std::vector<Edge>> g; //!< グラフの隣接リスト表現/*** @brief デフォルトコンストラクタ*/Graph() : n(0), m(0), g(0) {}/*** @brief コンストラクタ* @param n 頂点数*/explicit Graph(int n) : n(n), m(0), g(n) {}/*** @brief 無向辺を追加する* @param u 始点* @param v 終点* @param w コスト 省略したら1*/void add_edge(int u, int v, Cost w=1) {g[u].push_back({u, v, w, m});g[v].push_back({v, u, w, m++});}/*** @brief 有向辺を追加する* @param u 始点* @param v 終点* @param w コスト 省略したら1*/void add_directed_edge(int u, int v, Cost w=1) {g[u].push_back({u, v, w, m++});}/*** @brief 辺の情報を標準入力から受け取って追加する* @param m 辺の数* @param padding 頂点番号を入力からいくつずらすか 省略したら-1* @param weighted 辺の重みが入力されるか 省略したらfalseとなり、重み1で辺が追加される* @param directed 有向グラフかどうか 省略したらfalse*/void read(int m, int padding=-1, bool weighted=false, bool directed=false) {for(int i = 0; i < m; i++) {int u, v; std::cin >> u >> v; u += padding, v += padding;Cost c(1);if(weighted) std::cin >> c;if(directed) add_directed_edge(u, v, c);else add_edge(u, v, c);}}/*** @brief ある頂点から出る辺を列挙する* @param v 頂点番号* @return std::vector<Edge>& vから出る辺のリスト*/std::vector<Edge>& operator[](int v) {return g[v];}/*** @brief ある頂点から出る辺を列挙する* @param v 頂点番号* @return const std::vector<Edge>& vから出る辺のリスト*/const std::vector<Edge>& operator[](int v) const {return g[v];}/*** @brief 辺のリスト* @return std::vector<Edge> 辺のリスト(idの昇順)** 無向辺は代表して1つだけ格納される*/std::vector<Edge> edges() const {std::vector<Edge> res(m);for(int i = 0; i < n; i++) {for(auto& e : g[i]) {res[e.id] = e;}}return res;}/*** @brief ある頂点から各頂点への最短路** @param s 始点* @param weighted 1以外のコストの辺が存在するか 省略するとtrue* @param inf コストのminの単位元 未到達の頂点への距離はinfになる 省略すると-1* @return std::pair<std::vector<Cost>, std::vector<Edge>> first:各頂点への最短路長 second:各頂点への最短路上の直前の辺*/std::pair<std::vector<Cost>, std::vector<Edge>> shortest_path(int s, bool weignted = true, Cost inf = -1) const {if(weignted) return shortest_path_dijkstra(s, inf);return shortest_path_bfs(s, inf);}std::vector<int> topological_sort() {std::vector<int> indeg(n), sorted;std::queue<int> q;for (int i = 0; i < n; i++) {for (int dst : g[i]) indeg[dst]++;}for (int i = 0; i < n; i++) {if (!indeg[i]) q.push(i);}while (!q.empty()) {int cur = q.front(); q.pop();for (int dst : g[cur]) {if (!--indeg[dst]) q.push(dst);}sorted.push_back(cur);}return sorted;}private:std::pair<std::vector<Cost>, std::vector<Edge>> shortest_path_bfs(int s, Cost inf) const {std::vector<Cost> dist(n, inf);std::vector<Edge> prev(n);std::queue<int> que;dist[s] = 0;que.push(s);while(!que.empty()) {int u = que.front(); que.pop();for(auto& e : g[u]) {if(dist[e.dst] == inf) {dist[e.dst] = dist[e.src] + 1;prev[e.dst] = e;que.push(e.dst);}}}return {dist, prev};}std::pair<std::vector<Cost>, std::vector<Edge>> shortest_path_dijkstra(int s, Cost inf) const {std::vector<Cost> dist(n, inf);std::vector<Edge> prev(n);using Node = std::pair<Cost, int>;std::priority_queue<Node, std::vector<Node>, std::greater<Node>> que;dist[s] = 0;que.push({0, s});while(!que.empty()) {auto [d, u] = que.top(); que.pop();if(d > dist[u]) continue;for(auto& e : g[u]) {if(dist[e.dst] == inf || dist[e.dst] > dist[e.src] + e.cost) {dist[e.dst] = dist[e.src] + e.cost;prev[e.dst] = e;que.push({dist[e.dst], e.dst});}}}return {dist, prev};}};#line 2 "/home/shogo314/cpp_include/ou-library/modint.hpp"/*** @file modint.hpp* @brief 四則演算において自動で mod を取るクラス*/#line 9 "/home/shogo314/cpp_include/ou-library/modint.hpp"#include <utility>#line 11 "/home/shogo314/cpp_include/ou-library/modint.hpp"#include <type_traits>#include <cstdint>#include <cassert>namespace detail {static constexpr std::uint16_t prime32_bases[] {15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560, 3128, 5212, 2657,2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028, 2213, 6219, 620, 3763, 4852, 5012,3185, 1333, 6227, 5298, 1074, 2391, 5113, 7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239,746, 2951, 556, 2206, 3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344,17, 15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903, 737, 1887,7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41, 19875, 3110, 13221, 8726, 571,7043, 6943, 1199, 352, 6435, 165, 1169, 3315, 978, 233, 3003, 2562, 2994, 10587, 10030, 2377,1902, 5354, 4447, 1555, 263, 27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784,1661, 524, 3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031, 2226,2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336, 579, 165, 1375, 10018,12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788, 434, 8085, 17618, 727, 3639, 1595, 4944,2129, 2029, 8195, 8344, 6232, 9183, 8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566,5674, 411, 522, 1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785,1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42, 4511, 1660, 166,1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816, 5197, 13330, 7054, 2818, 3199, 811,922, 350, 7514, 4452, 3449, 2663, 4708, 418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194,};static constexpr bool is_SPRP(std::uint32_t n, std::uint32_t a) noexcept {std::uint32_t d = n - 1;std::uint32_t s = 0;while ((d & 1) == 0) {++s;d >>= 1;}std::uint64_t cur = 1;std::uint64_t pw = d;while (pw) {if (pw & 1) cur = (cur * a) % n;a = (static_cast<std::uint64_t>(a) * a) % n;pw >>= 1;}if (cur == 1) return true;for (std::uint32_t r = 0; r < s; ++r) {if (cur == n - 1) return true;cur = (cur * cur) % n;}return false;}// 32ビット符号なし整数の素数判定// 参考: M. Forisek and J. Jancina, “Fast Primality Testing for Integers That Fit into a Machine Word,” presented at the Conference on CurrentTrends in Theory and Practice of Informatics, 2015.[[nodiscard]]static constexpr bool is_prime32(std::uint32_t x) noexcept {if (x == 2 || x == 3 || x == 5 || x == 7) return true;if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;if (x < 121) return (x > 1);std::uint64_t h = x;h = ((h >> 16) ^ h) * 0x45d9f3b;h = ((h >> 16) ^ h) * 0x45d9f3b;h = ((h >> 16) ^ h) & 0xff;return is_SPRP(x, prime32_bases[h]);}}/// @brief static_modint と dynamic_modint の実装を CRTP によって行うためのクラステンプレート/// @tparam Modint このクラステンプレートを継承するクラスtemplate <class Modint>class modint_base {public:/// @brief 保持する値の型using value_type = std::uint32_t;/// @brief 0 で初期化します。constexpr modint_base() noexcept: m_value{ 0 } {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral> && std::is_signed_v<SignedIntegral>>* = nullptr>constexpr modint_base(SignedIntegral value) noexcept: m_value{ static_cast<value_type>((static_cast<long long>(value) % Modint::mod() + Modint::mod()) % Modint::mod()) } {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値template <class UnsignedIntegral, std::enable_if_t<std::is_integral_v<UnsignedIntegral> && std::is_unsigned_v<UnsignedIntegral>>* = nullptr>constexpr modint_base(UnsignedIntegral value) noexcept: m_value{ static_cast<value_type>(value % Modint::mod()) } {}/// @brief 保持している値を取得します。/// @return 保持している値[[nodiscard]]constexpr value_type value() const noexcept {return m_value;}/// @brief 保持している値をインクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint& operator++() noexcept {++m_value;if (m_value == Modint::mod()) {m_value = 0;}return static_cast<Modint&>(*this);}/// @brief 保持している値をインクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint operator++(int) noexcept {auto x = static_cast<const Modint&>(*this);++*this;return x;}/// @brief 保持している値をデクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint& operator--() noexcept {if (m_value == 0) {m_value = Modint::mod();}--m_value;return static_cast<Modint&>(*this);}/// @brief 保持している値をデクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint operator--(int) noexcept {auto x = static_cast<const Modint&>(*this);--*this;return x;}/// @brief 保持している値に @c x の持つ値を足して、剰余を取ります。/// @param x 足す数/// @return @c *thisconstexpr Modint& operator+=(const Modint& x) noexcept {m_value += x.m_value;if (m_value >= Modint::mod()) {m_value -= Modint::mod();}return static_cast<Modint&>(*this);}/// @brief 保持している値から @c x の持つ値を引いて、剰余を取ります。/// @param x 引く数/// @return @c *thisconstexpr Modint& operator-=(const Modint& x) noexcept {m_value -= x.m_value;if (m_value >= Modint::mod()) {m_value += Modint::mod();}return static_cast<Modint&>(*this);}/// @brief 保持している値に @c x の持つ値を掛けて、剰余を取ります。/// @param x 掛ける数/// @return @c *thisconstexpr Modint& operator*=(const Modint& x) noexcept {m_value = static_cast<value_type>(static_cast<std::uint64_t>(m_value) * x.m_value % Modint::mod());return static_cast<Modint&>(*this);}/// @brief 保持している値を @c x の持つ値で割って、剰余を取ります。/// @remark 時間計算量: @f$O(\log x)@f$/// @param x 割る数/// @return @c *thisconstexpr Modint& operator/=(const Modint& x) noexcept {return *this *= x.inv();}/// @brief 自身のコピーを返します。/// @return @c *this[[nodiscard]]constexpr Modint operator+() const noexcept {return static_cast<const Modint&>(*this);}/// @brief 自身の反数を返します。/// @return 自身の反数[[nodiscard]]constexpr Modint operator-() const noexcept {return 0 - static_cast<const Modint&>(*this);}/// @brief 自身の @c n 乗を返します。/// @remark 時間計算量: @f$O(\log n)@f$/// @param n 指数/// @return 自身の @c n 乗[[nodiscard]]constexpr Modint pow(unsigned long long n) const noexcept {Modint x = 1;Modint y = static_cast<const Modint&>(*this);while (n) {if (n & 1) {x *= y;}y *= y;n >>= 1;}return x;}/// @brief 自身の逆数を返します。/// @remark 時間計算量: @f$O(\log value)@f$/// @return 自身の逆数[[nodiscard]]constexpr Modint inv() const noexcept {long long a = Modint::mod();long long b = m_value;long long x = 0;long long y = 1;while (b) {auto t = a / b;auto u = a - t * b;a = b;b = u;u = x - t * y;x = y;y = u;}assert(a == 1 && "The inverse element does not exist.");x %= Modint::mod();if (x < 0) {x += Modint::mod();}return x;}/// @brief @c x に @c y を足したオブジェクトを返します。/// @param x 足される数/// @param y 足す数/// @return @c x に @c y を足したオブジェクト[[nodiscard]]friend constexpr Modint operator+(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } += y);}/// @brief @c x から @c y を引いたオブジェクトを返します。/// @param x 引かれる数/// @param y 引く数/// @return @c x から @c y を引いたオブジェクト[[nodiscard]]friend constexpr Modint operator-(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } -= y);}/// @brief @c x に @c y を掛けたオブジェクトを返します。/// @param x 掛けられる数/// @param y 掛ける数/// @return @c x に @c y を掛けたオブジェクト[[nodiscard]]friend constexpr Modint operator*(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } *= y);}/// @brief @c x を @c y で割ったオブジェクトを返します。/// @param x 割られる数/// @param y 割る数/// @return @c x を @c y で割ったオブジェクト[[nodiscard]]friend constexpr Modint operator/(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } /= y);}/// @brief @c x と @c y の保持する値が等しいかどうかを調べます。/// @return @c x と @c y の保持する値が等しければ @c true 、そうでなければ @c false[[nodiscard]]friend constexpr bool operator==(const Modint& x, const Modint& y) noexcept {return x.m_value == y.m_value;}/// @brief @c x と @c y の保持する値が等しくないかどうかを調べます。/// @return @c x と @c y の保持する値が等しければ @c false 、そうでなければ @c true[[nodiscard]]friend constexpr bool operator!=(const Modint& x, const Modint& y) noexcept {return not (x == y);}/// @brief 入力ストリームから符号付き整数を読み取り、 @c x に格納します。/// @tparam CharT 入力ストリームの文字型/// @tparam Traits 入力ストリームの文字トレイト/// @param is 入力ストリーム/// @param x 入力を受け取るオブジェクト/// @return @c istemplate <class CharT, class Traits>friend std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, Modint& x) {long long tmp;is >> tmp;x = tmp;return is;}/// @brief 出力ストリームに @c x の保持する値を出力します。/// @tparam CharT 出力ストリームの文字型/// @tparam Traits 出力ストリームの文字トレイト/// @param os 出力ストリーム/// @param x 出力するオブジェクト/// @return @c ostemplate <class CharT, class Traits>friend std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const Modint& x) {os << x.value();return os;}protected:value_type m_value;};/// @brief コンパイル時に法が決まるとき、四則演算において自動で mod を取るクラス/// @tparam Mod 法template <std::uint32_t Mod>class static_modint : public modint_base<static_modint<Mod>> {static_assert(Mod > 0 && Mod <= std::numeric_limits<std::uint32_t>::max() / 2);private:using base_type = modint_base<static_modint<Mod>>;public:using typename base_type::value_type;/// @brief 法を取得します。/// @return 法[[nodiscard]]static constexpr value_type mod() noexcept {return Mod;}/// @brief 0 で初期化します。constexpr static_modint() noexcept: base_type{} {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>constexpr static_modint(SignedIntegral value) noexcept: base_type{value} {}/// @brief 自身の逆数を返します。/// @remark 時間計算量: @f$O(\log value)@f$/// @return 自身の逆数[[nodiscard]]constexpr static_modint inv() const noexcept {if constexpr (detail::is_prime32(Mod)) {assert(this->m_value != 0 && "The inverse element of zero does not exist.");return this->pow(Mod - 2);}else {return base_type::inv();}}};/// @brief 実行時に法が決まるとき、四則演算において自動で mod を取るクラス/// @tparam ID このIDごとに法を設定することができますtemplate <int ID>class dynamic_modint : public modint_base<dynamic_modint<ID>> {private:using base_type = modint_base<dynamic_modint<ID>>;public:using typename base_type::value_type;/// @brief 法を取得します。/// @return 法[[nodiscard]]static value_type mod() noexcept {return modulus;}/// @brief 法を設定します。/// @param m 新しい法static void set_mod(value_type m) noexcept {assert(m > 0 && m <= std::numeric_limits<value_type>::max() / 2);modulus = m;}/// @brief 0 で初期化します。constexpr dynamic_modint() noexcept: base_type{} {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>constexpr dynamic_modint(SignedIntegral value) noexcept: base_type{value} {}private:inline static value_type modulus = 998244353;};using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;#line 2 "/home/shogo314/cpp_include/sh-library/base/all"#include <bits/stdc++.h>#line 5 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"#include <initializer_list>#line 4 "/home/shogo314/cpp_include/sh-library/base/traits.hpp"#define HAS_METHOD(func_name) \namespace detail { \template <class T, class = void> \struct has_##func_name##_impl : std::false_type {}; \template <class T> \struct has_##func_name##_impl<T, std::void_t<decltype(std::declval<T>().func_name())>> \: std::true_type {}; \} \template <class T> \struct has_##func_name : detail::has_##func_name##_impl<T>::type {}; \template <class T> \inline constexpr bool has_##func_name##_v = has_##func_name<T>::value;#define HAS_METHOD_ARG(func_name) \namespace detail { \template <class T, typename U, class = void> \struct has_##func_name##_impl : std::false_type {}; \template <class T, typename U> \struct has_##func_name##_impl<T, U, std::void_t<decltype(std::declval<T>().func_name(std::declval<U>()))>> \: std::true_type {}; \} \template <class T, typename U> \struct has_##func_name : detail::has_##func_name##_impl<T, U>::type {}; \template <class T, typename U> \inline constexpr bool has_##func_name##_v = has_##func_name<T, U>::value;HAS_METHOD(repr)HAS_METHOD(type_str)HAS_METHOD(initializer_str)HAS_METHOD(max)HAS_METHOD(min)HAS_METHOD(reversed)HAS_METHOD(sorted)HAS_METHOD(sum)HAS_METHOD(product)HAS_METHOD(product_xor)HAS_METHOD_ARG(count)HAS_METHOD_ARG(find)HAS_METHOD_ARG(lower_bound)HAS_METHOD_ARG(upper_bound)#define ENABLE_IF_T_IMPL(expr) std::enable_if_t<expr, std::nullptr_t> = nullptr#define ENABLE_IF_T(...) ENABLE_IF_T_IMPL((__VA_ARGS__))template <class C>using mem_value_type = typename C::value_type;template <class C>using mem_difference_type = typename C::difference_type;#line 9 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"#define METHOD_EXPAND(func_name) \template <typename T, ENABLE_IF_T(has_##func_name##_v<T>)> \inline constexpr auto func_name(const T &t) -> decltype(t.func_name()) { \return t.func_name(); \}#define METHOD_AND_FUNC_ARG_EXPAND(func_name) \template <typename T, typename U, ENABLE_IF_T(has_##func_name##_v<T, U>)> \inline constexpr auto func_name(const T &t, const U &u) \-> decltype(t.func_name(u)) { \return t.func_name(u); \} \template <typename T, typename U, ENABLE_IF_T(not has_##func_name##_v<T, U>)> \inline constexpr auto func_name(const T &t, const U &u) \-> decltype(std::func_name(t.begin(), t.end(), u)) { \return std::func_name(t.begin(), t.end(), u); \}METHOD_EXPAND(reversed)template <class C, ENABLE_IF_T(not has_reversed_v<C>)>inline constexpr C reversed(C t) {std::reverse(t.begin(), t.end());return t;}METHOD_EXPAND(sorted)template <class C, ENABLE_IF_T(not has_sorted_v<C>)>inline constexpr C sorted(C t) {std::sort(t.begin(), t.end());return t;}template <class C, class F, ENABLE_IF_T(not has_sorted_v<C> and std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>inline constexpr C sorted(C t, F f) {std::sort(t.begin(), t.end(), f);return t;}template <class C>inline constexpr void sort(C &t) {std::sort(t.begin(), t.end());}template <class C, class F, ENABLE_IF_T(std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>inline constexpr void sort(C &t, F f) {std::sort(t.begin(), t.end(), f);}template <class C, class F, ENABLE_IF_T(std::is_invocable_v<F, mem_value_type<C>>)>inline constexpr void sort_by_key(C &t, F f) {std::sort(t.begin(), t.end(), [&](const mem_value_type<C> &left, const mem_value_type<C> &right) {return f(left) < f(right);});}template <class C>inline constexpr void reverse(C &t) {std::reverse(t.begin(), t.end());}METHOD_EXPAND(max)template <class C, ENABLE_IF_T(not has_max_v<C>)>inline constexpr mem_value_type<C> max(const C &v) {assert(v.begin() != v.end());return *std::max_element(v.begin(), v.end());}template <typename T>inline constexpr T max(const std::initializer_list<T> &v) {return std::max(v);}METHOD_EXPAND(min)template <class C, ENABLE_IF_T(not has_max_v<C>)>inline constexpr mem_value_type<C> min(const C &v) {assert(v.begin() != v.end());return *std::min_element(v.begin(), v.end());}template <typename T>inline constexpr T min(const std::initializer_list<T> &v) {return std::min(v);}METHOD_EXPAND(sum)template <class C, ENABLE_IF_T(not has_sum_v<C>)>inline constexpr mem_value_type<C> sum(const C &v) {return std::accumulate(v.begin(), v.end(), mem_value_type<C>{});}template <typename T>inline constexpr T sum(const std::initializer_list<T> &v) {return std::accumulate(v.begin(), v.end(), T{});}METHOD_EXPAND(product)template <class C, ENABLE_IF_T(not has_product_v<C>)>inline constexpr mem_value_type<C> product(const C &v) {return std::accumulate(v.begin(), v.end(), mem_value_type<C>{1}, std::multiplies<mem_value_type<C>>());}template <typename T>inline constexpr T product(const std::initializer_list<T> &v) {return std::accumulate(v.begin(), v.end(), T{1}, std::multiplies<T>());}METHOD_EXPAND(product_xor)template <class C, ENABLE_IF_T(not has_product_xor_v<C>)>inline constexpr mem_value_type<C> product_xor(const C &v) {return std::accumulate(v.begin(), v.end(), mem_value_type<C>{0}, std::bit_xor<mem_value_type<C>>());}template <typename T>inline constexpr T product_xor(const std::initializer_list<T> &v) {return std::accumulate(v.begin(), v.end(), T{0}, std::bit_xor<T>());}template <class C>inline constexpr mem_value_type<C> maximum_subarray(const C &v) {assert(not v.empty());auto itr = v.begin();mem_value_type<C> tmp = *itr++;mem_value_type<C> res = tmp;while (itr != v.end()) {tmp += *itr;if (tmp < *itr) tmp = *itr;if (res < tmp) res = tmp;++itr;}return res;}template <class C>inline constexpr mem_value_type<C> maximum_subarray(const C &v, mem_value_type<C> init) {mem_value_type<C> res = init, tmp = init;for (const auto &a : v) {tmp += a;if (tmp < init) tmp = init;if (res < tmp) res = tmp;}return res;}METHOD_AND_FUNC_ARG_EXPAND(count)METHOD_AND_FUNC_ARG_EXPAND(find)METHOD_AND_FUNC_ARG_EXPAND(lower_bound)METHOD_AND_FUNC_ARG_EXPAND(upper_bound)template <class C, typename T>inline constexpr bool contains(const C &c, const T &t) {return find(c, t) != c.end();}template <class C>inline constexpr mem_value_type<C> gcd(const C &v) {mem_value_type<C> init(0);for (const auto &e : v) init = std::gcd(init, e);return init;}template <class C>inline constexpr mem_value_type<C> average(const C &v) {assert(v.size());return sum(v) / v.size();}template <class C>inline constexpr mem_value_type<C> median(const C &v) {assert(not v.empty());std::vector<size_t> u(v.size());std::iota(u.begin(), u.end(), 0);std::sort(u.begin(), u.end(), [&](size_t a, size_t b) {return v[a] < v[b];});if (v.size() & 1) {return v[u[v.size() / 2]];}// C++20// return std::midpoint(v[u[v.size() / 2]], v[u[v.size() / 2 - 1]]);return (v[u[v.size() / 2]] + v[u[v.size() / 2 - 1]]) / 2;}template <class C, typename U>inline constexpr std::ptrdiff_t index(const C &v, const U &x) {return std::distance(v.begin(), find(v, x));}template <class C, ENABLE_IF_T(std::is_integral_v<mem_value_type<C>>)>inline constexpr mem_value_type<C> mex(const C &v) {std::vector<bool> b(v.size() + 1);for (const auto &a : v) {if (0 <= a and a < b.size()) {b[a] = true;}}mem_value_type<C> ret;for (size_t i = 0; i < b.size(); i++) {if (not b[i]) {ret = i;break;}}return ret;}template <class C>inline constexpr mem_difference_type<C> bisect_left(const C &v, const mem_value_type<C> &x) {return std::distance(v.begin(), lower_bound(v, x));}template <class C>inline constexpr mem_difference_type<C> bisect_right(const C &v, const mem_value_type<C> &x) {return std::distance(v.begin(), upper_bound(v, x));}#line 6 "/home/shogo314/cpp_include/sh-library/base/functions.hpp"template <typename T1, typename T2>inline constexpr bool chmin(T1 &a, T2 b) {if (a > b) {a = b;return true;}return false;}template <typename T1, typename T2>inline constexpr bool chmax(T1 &a, T2 b) {if (a < b) {a = b;return true;}return false;}inline constexpr long long max(const long long &t1, const long long &t2) {return std::max<long long>(t1, t2);}inline constexpr long long min(const long long &t1, const long long &t2) {return std::min<long long>(t1, t2);}using std::abs;using std::gcd;using std::lcm;using std::size;template <typename T>constexpr T extgcd(const T &a, const T &b, T &x, T &y) {T d = a;if (b != 0) {d = extgcd(b, a % b, y, x);y -= (a / b) * x;} else {x = 1;y = 0;}return d;}template <typename M, typename N, class F, ENABLE_IF_T(std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std::common_type_t<M, N>>)>inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {std::common_type_t<M, N> _ok = ok, _ng = ng;assert(f(_ok));while (std::abs(_ok - _ng) > 1) {std::common_type_t<M, N> mid = (_ok + _ng) / 2;if (f(mid)) {_ok = mid;} else {_ng = mid;}}return _ok;}template <typename M, typename N, class F, ENABLE_IF_T(not std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std::common_type_t<M, N>>)>inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {std::common_type_t<M, N> _ok = ok, _ng = ng;assert(f(_ok));for (int i = 0; i < 100; i++) {std::common_type_t<M, N> mid = (_ok + _ng) / 2;if (f(mid)) {_ok = mid;} else {_ng = mid;}}return _ok;}/*** 0 <= x < a*/inline constexpr bool inrange(long long x, long long a) {return 0 <= x and x < a;}/*** a <= x < b*/inline constexpr bool inrange(long long x, long long a, long long b) {return a <= x and x < b;}/*** 0 <= x < a and 0 <= y < b*/inline constexpr bool inrect(long long x, long long y, long long a, long long b) {return 0 <= x and x < a and 0 <= y and y < b;}#line 8 "/home/shogo314/cpp_include/sh-library/base/io.hpp"namespace tuple_io {template <typename Tuple, size_t I, typename CharT, typename Traits>std::basic_istream<CharT, Traits>& read_tuple(std::basic_istream<CharT, Traits>& is, Tuple& t) {is >> std::get<I>(t);if constexpr (I + 1 < std::tuple_size_v<Tuple>) {return read_tuple<Tuple, I + 1>(is, t);}return is;}template <typename Tuple, size_t I, typename CharT, typename Traits>std::basic_ostream<CharT, Traits>& write_tuple(std::basic_ostream<CharT, Traits>& os, const Tuple& t) {os << std::get<I>(t);if constexpr (I + 1 < std::tuple_size_v<Tuple>) {os << CharT(' ');return write_tuple<Tuple, I + 1>(os, t);}return os;}}; // namespace tuple_iotemplate <typename T1, typename T2, typename CharT, typename Traits>std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::pair<T1, T2>& p) {is >> p.first >> p.second;return is;}template <typename... Types, typename CharT, typename Traits>std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::tuple<Types...>& p) {return tuple_io::read_tuple<std::tuple<Types...>, 0>(is, p);}template <typename T, size_t N, typename CharT, typename Traits>std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::array<T, N>& a) {for (auto& e : a) is >> e;return is;}template <typename T, typename CharT, typename Traits>std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::vector<T>& v) {for (auto& e : v) is >> e;return is;}template <typename T1, typename T2, typename CharT, typename Traits>std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::pair<T1, T2>& p) {os << p.first << CharT(' ') << p.second;return os;}template <typename... Types, typename CharT, typename Traits>std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::tuple<Types...>& p) {return tuple_io::write_tuple<std::tuple<Types...>, 0>(os, p);}template <typename T, size_t N, typename CharT, typename Traits>std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::array<T, N>& a) {for (size_t i = 0; i < N; ++i) {if (i) os << CharT(' ');os << a[i];}return os;}template <typename T, typename CharT, typename Traits>std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::vector<T>& v) {for (size_t i = 0; i < v.size(); ++i) {if (i) os << CharT(' ');os << v[i];}return os;}template <typename T, typename CharT, typename Traits>std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::set<T>& s) {for (auto itr = s.begin(); itr != s.end(); ++itr) {if (itr != s.begin()) os << CharT(' ');os << *itr;}return os;}/*** @brief 空行出力*/void print() { std::cout << '\n'; }/*** @brief 出力して改行** @tparam T 型* @param x 出力する値*/template <typename T>void print(const T& x) { std::cout << x << '\n'; }/*** @brief 空白区切りで出力して改行** @tparam T 1つ目の要素の型* @tparam Tail 2つ目以降の要素の型* @param x 1つ目の要素* @param tail 2つ目以降の要素*/template <typename T, typename... Tail>void print(const T& x, const Tail&... tail) {std::cout << x << ' ';print(tail...);}/*** @brief 空行出力*/void err() { std::cerr << std::endl; }/*** @brief 出力して改行** @tparam T 型* @param x 出力する値*/template <typename T>void err(const T& x) { std::cerr << x << std::endl; }/*** @brief 空白区切りで出力して改行** @tparam T 1つ目の要素の型* @tparam Tail 2つ目以降の要素の型* @param x 1つ目の要素* @param tail 2つ目以降の要素*/template <typename T, typename... Tail>void err(const T& x, const Tail&... tail) {std::cerr << x << ' ';err(tail...);}#line 3 "/home/shogo314/cpp_include/sh-library/base/type_alias.hpp"using ll = long long;using ull = unsigned long long;using ld = long double;template <typename T>using vec = std::vector<T>;template <typename T, int N>using ary = std::array<T, N>;using str = std::string;using std::deque;using std::list;using std::map;using std::pair;using std::set;using pl = pair<ll, ll>;using pd = pair<ld, ld>;template <typename T>using vv = vec<vec<T>>;template <typename T>using vvv = vec<vec<vec<T>>>;using vl = vec<ll>;using vvl = vv<ll>;using vvvl = vvv<ll>;using vs = vec<str>;using vc = vec<char>;using vi = vec<int>;using vb = vec<bool>;template <typename T1, typename T2>using vp = vec<pair<T1, T2>>;using vpl = vec<pl>;using vvpl = vv<pl>;using vd = vec<ld>;using vpd = vec<pd>;template <int N>using al = ary<ll, N>;template <int N1, int N2>using aal = ary<ary<ll, N2>, N1>;template <int N>using val = vec<al<N>>;template <int N>using avl = ary<vl,N>;template <typename T>using ml = std::map<ll, T>;using mll = std::map<ll, ll>;using sl = std::set<ll>;using spl = set<pl>;template <int N>using sal = set<al<N>>;template <int N>using asl = ary<sl,N>;template <typename T>using heap_max = std::priority_queue<T, std::vector<T>, std::less<T>>;template <typename T>using heap_min = std::priority_queue<T, std::vector<T>, std::greater<T>>;#line 3 "/home/shogo314/cpp_include/sh-library/base/macro.hpp"#pragma GCC target("avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#define all(obj) (obj).begin(), (obj).end()#define repts(i, a, n, t) for (long long i = (a); i < (n); i+=(t))#define reps(i, a, n) for (long long i = (a); i < (n); i++)#define rep(i, n) reps(i, 0, (n))#define rrep(i, n) reps(i, 1, (n) + 1)#define repds(i, a, n) for (long long i = (n)-1; i >= (a); i--)#define repd(i, n) repds(i, 0, (n))#define rrepd(i, n) repds(i, 1, (n) + 1)#define rep2(i, j, x, y) rep(i, x) rep(j, y)inline void scan(){}template<class Head,class... Tail>inline void scan(Head&head,Tail&... tail){std::cin>>head;scan(tail...);}#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)#define STR(...) str __VA_ARGS__;scan(__VA_ARGS__)#define IN(a, x) a x; std::cin >> x;#define CHAR(x) char x; std::cin >> x;#define VL(a,n) vl a(n); std::cin >> a;#define AL(a,k) al<k> a; std::cin >> a;#define AAL(a,n,m) aal<n,m> a; std::cin >> a;#define VC(a,n) vc a(n); std::cin >> a;#define VS(a,n) vs a(n); std::cin >> a;#define VPL(a,n) vpl a(n); std::cin >> a;#define VAL(a,n,k) val<k> a(n); std::cin >> a;#define VVL(a,n,m) vvl a(n,vl(m)); std::cin >> a;#define SL(a,n) sl a;{VL(b,n);a=sl(all(b));}#define NO std::cout << "NO" << std::endl; return;#define YES std::cout << "YES" << std::endl; return;#define No std::cout << "No" << std::endl; return;#define Yes std::cout << "Yes" << std::endl; return;#line 8 "/home/shogo314/cpp_include/sh-library/base/vector_func.hpp"template <typename T>std::vector<std::ptrdiff_t> sorted_idx(const std::vector<T> &v) {std::vector<std::ptrdiff_t> ret(v.size());std::iota(ret.begin(), ret.end(), 0);std::sort(ret.begin(), ret.end(), [&](std::ptrdiff_t i, std::ptrdiff_t j) {return v[i] < v[j];});return ret;}template <typename T>inline std::vector<T> &operator++(std::vector<T> &v) {for (auto &e : v) e++;return v;}template <typename T>inline std::vector<T> operator++(std::vector<T> &v, int) {auto res = v;for (auto &e : v) e++;return res;}template <typename T>inline std::vector<T> &operator--(std::vector<T> &v) {for (auto &e : v) e--;return v;}template <typename T>inline std::vector<T> operator--(std::vector<T> &v, int) {auto res = v;for (auto &e : v) e--;return res;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> &operator+=(std::vector<T> &v1, const std::vector<U> &v2) {if (v2.size() > v1.size()) {v1.resize(v2.size());}for (size_t i = 0; i < v2.size(); i++) {v1[i] += v2[i];}return v1;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> operator+(const std::vector<T> &v1, const std::vector<U> &v2) {std::vector<T> res(v1);return res += v2;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> &operator+=(std::vector<T> &v, const U &u) {for (T &e : v) {e += u;}return v;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> operator+(const std::vector<T> &v, const U &u) {std::vector<T> res(v);return res += u;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> operator+(const U &u, const std::vector<T> &v) {std::vector<T> res(v);return res += u;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> &operator*=(std::vector<T> &v1, const std::vector<U> &v2) {if (v2.size() > v1.size()) {v1.resize(v2.size());}for (size_t i = 0; i < v2.size(); i++) {v1[i] *= v2[i];}for (size_t i = v2.size(); i < v1.size(); i++) {v1[i] *= U(0);}return v1;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> operator*(const std::vector<T> &v1, const std::vector<U> &v2) {std::vector<T> res(v1);return res *= v2;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> &operator*=(std::vector<T> &v, const U &u) {for (T &e : v) {e *= u;}return v;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> operator*(const std::vector<T> &v, const U &u) {std::vector<T> res(v);return res *= u;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> operator*(const U &u, const std::vector<T> &v) {std::vector<T> res(v);return res *= u;}template <typename T, typename U>inline std::vector<T> &assign(std::vector<T> &v1, const std::vector<U> &v2) {v1.assign(v2.begin(), v2.end());return v1;}template <typename T, typename U>inline std::vector<T> &extend(std::vector<T> &v1, const std::vector<U> &v2) {v1.insert(v1.end(), v2.begin(), v2.end());return v1;}template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>inline std::vector<T> &operator|=(std::vector<T> &v1, const std::vector<U> &v2) {return extend(v1, v2);}template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>inline std::vector<T> &operator|=(std::vector<T> &v, const U &u) {std::vector<T> w(v);v.clear();for (int i = 0; i < u; i++) {extend(v, w);}return v;}template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>inline std::vector<T> operator|(const std::vector<T> &v, const U &u) {std::vector<T> res(v);return res |= u;}template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>inline std::vector<T> operator|(const U &u, const std::vector<T> &v) {std::vector<T> res(v);return res |= u;}template <typename T>inline std::vector<T> abs(const std::vector<T> &v) {std::vector<T> ret;ret.reserve(v.size());for (const T &e : v) ret.push_back(std::abs(e));return ret;}template <typename T>std::vector<T> partial_sum(const std::vector<T> &v) {std::vector<T> ret(v.size());std::partial_sum(v.begin(), v.end(), ret.begin());return ret;}template <typename T, ENABLE_IF_T(std::is_integral_v<T>)>std::vector<T> iota(T n) {assert(n >= 0);std::vector<T> ret(n);std::iota(ret.begin(), ret.end(), 0);return ret;}#line 4 "main.cpp"using mint = modint998244353;void solve() {LL(N, M, K);Graph<> graph(N);graph.read(M);vl powk = {1};rep(_, N) {powk.push_back(powk.back() * (K + 1));}ll MAX = N * powk[N];vec<mint> dp(MAX);auto xx = [&](ll a) -> pair<int, vl> {vl ret(N);int u = a / powk[N];a %= powk[N];rep(i, N) {ret[i] = a % (K + 1);a /= K + 1;}return {u, ret};};auto yy = [&](int u, vl cc) -> ll {ll s = 0;repd(i, N) {s *= K + 1;s += cc[i];}s += powk[N] * u;return s;};rep(i, N) {vl cc(N);cc[i]++;dp[yy(i, cc)] = 1;}rep(cc_, powk[N]) {rep(u, N) {ll l = cc_ + u * powk[N];auto [_, cc] = xx(l);for (int v : graph[u]) {if (cc[v] == K) continue;vl dd(cc);dd[v]++;dp[yy(v, dd)] += dp[l];}}}mint ans = 0;rep(i, N) {ans += dp[(powk[N] - 1) + i * powk[N]];}print(ans);}int main() {std::cin.tie(nullptr);std::ios_base::sync_with_stdio(false);solve();}