結果
| 問題 | No.1289 RNG and OR |
| ユーザー |
 jell
|
| 提出日時 | 2020-11-26 15:19:49 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 80 ms / 2,000 ms |
| コード長 | 35,439 bytes |
| コンパイル時間 | 3,753 ms |
| コンパイル使用メモリ | 269,580 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-23 20:50:42 |
| 合計ジャッジ時間 | 5,275 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,812 KB |
| testcase_02 | AC | 2 ms
6,812 KB |
| testcase_03 | AC | 2 ms
6,816 KB |
| testcase_04 | AC | 2 ms
6,812 KB |
| testcase_05 | AC | 2 ms
6,812 KB |
| testcase_06 | AC | 2 ms
6,816 KB |
| testcase_07 | AC | 2 ms
6,816 KB |
| testcase_08 | AC | 2 ms
6,944 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
| testcase_11 | AC | 2 ms
6,940 KB |
| testcase_12 | AC | 2 ms
6,944 KB |
| testcase_13 | AC | 2 ms
6,944 KB |
| testcase_14 | AC | 3 ms
6,944 KB |
| testcase_15 | AC | 4 ms
6,940 KB |
| testcase_16 | AC | 6 ms
6,944 KB |
| testcase_17 | AC | 10 ms
6,944 KB |
| testcase_18 | AC | 20 ms
6,940 KB |
| testcase_19 | AC | 38 ms
6,940 KB |
| testcase_20 | AC | 80 ms
6,944 KB |
ソースコード
#line 1 "other/game.cc"
/*
* @file template.cpp
* @brief Template
*/
#include <bits/extc++.h>
#line 2 "Library/lib/alias"
/*
* @file alias
* @brief Alias
*/
#line 13 "Library/lib/alias"
namespace workspace {
constexpr char eol = '\n';
using namespace std;
using i32 = int_least32_t;
using i64 = int_least64_t;
using i128 = __int128_t;
using u32 = uint_least32_t;
using u64 = uint_least64_t;
using u128 = __uint128_t;
template <class T, class Comp = less<T>>
using priority_queue = std::priority_queue<T, vector<T>, Comp>;
template <class T> using stack = std::stack<T, vector<T>>;
} // namespace workspace
#line 2 "Library/lib/cxx20"
/*
* @file cxx20
* @brief C++20 Features
*/
#if __cplusplus <= 201703L
#include <vector>
namespace std {
/*
* @fn erase_if
* @brief Erase the elements of a container that do not satisfy the condition.
* @param __cont Container.
* @param __pred Predicate.
* @return Number of the erased elements.
*/
template <typename _Tp, typename _Alloc, typename _Predicate>
inline typename vector<_Tp, _Alloc>::size_type erase_if(
vector<_Tp, _Alloc>& __cont, _Predicate __pred) {
const auto __osz = __cont.size();
__cont.erase(std::remove_if(__cont.begin(), __cont.end(), __pred),
__cont.end());
return __osz - __cont.size();
}
/*
* @fn erase
* @brief Erase the elements of a container that are equal to the given value.
* @param __cont Container.
* @param __value Value.
* @return Number of the erased elements.
*/
template <typename _Tp, typename _Alloc, typename _Up>
inline typename vector<_Tp, _Alloc>::size_type erase(
vector<_Tp, _Alloc>& __cont, const _Up& __value) {
const auto __osz = __cont.size();
__cont.erase(std::remove(__cont.begin(), __cont.end(), __value),
__cont.end());
return __osz - __cont.size();
}
} // namespace std
#endif
#line 2 "Library/lib/option"
/*
* @file option
* @brief Optimize Options
*/
#ifdef ONLINE_JUDGE
#pragma GCC optimize("O3")
#pragma GCC target("avx,avx2")
#pragma GCC optimize("unroll-loops")
#endif
#line 2 "Library/src/utils/binary_search.hpp"
/*
* @file binary_search.hpp
* @brief Binary Search
*/
#if __cplusplus >= 201703L
#include <cassert>
#include <cmath>
#include <vector>
namespace workspace {
/*
* @fn binary_search
* @brief binary search on a discrete range.
* @param ok pred(ok) is true
* @param ng pred(ng) is false
* @param pred the predicate
* @return the closest point to (ng) where pred is true
*/
template <class iter_type, class pred_type>
std::enable_if_t<
std::is_convertible_v<std::invoke_result_t<pred_type, iter_type>, bool>,
iter_type>
binary_search(iter_type ok, iter_type ng, pred_type pred) {
assert(ok != ng);
std::make_signed_t<decltype(ng - ok)> dist(ng - ok);
while (1 < dist || dist < -1) {
iter_type mid(ok + dist / 2);
if (pred(mid))
ok = mid, dist -= dist / 2;
else
ng = mid, dist /= 2;
}
return ok;
}
/*
* @fn parallel_binary_search
* @brief parallel binary search on discrete ranges.
* @param ends a vector of pairs; pred(first) is true, pred(second) is false
* @param pred the predicate
* @return the closest points to (second) where pred is true
*/
template <class iter_type, class pred_type>
std::enable_if_t<std::is_convertible_v<
std::invoke_result_t<pred_type, std::vector<iter_type>>,
std::vector<bool>>,
std::vector<iter_type>>
parallel_binary_search(std::vector<std::pair<iter_type, iter_type>> ends,
pred_type pred) {
std::vector<iter_type> mids(ends.size());
for (;;) {
bool all_found = true;
for (size_t i{}; i != ends.size(); ++i) {
auto [ok, ng] = ends[i];
iter_type mid(ok + (ng - ok) / 2);
if (mids[i] != mid) {
all_found = false;
mids[i] = mid;
}
}
if (all_found) break;
auto res = pred(mids);
for (size_t i{}; i != ends.size(); ++i) {
(res[i] ? ends[i].first : ends[i].second) = mids[i];
}
}
return mids;
}
/*
* @fn binary_search
* @brief binary search on the real number line.
* @param ok pred(ok) is true
* @param ng pred(ng) is false
* @param eps the error tolerance
* @param pred the predicate
* @return the boundary point
*/
template <class real_type, class pred_type>
std::enable_if_t<
std::is_convertible_v<std::invoke_result_t<pred_type, real_type>, bool>,
real_type>
binary_search(real_type ok, real_type ng, const real_type eps, pred_type pred) {
assert(ok != ng);
for (auto loops = 0; loops != std::numeric_limits<real_type>::digits &&
(ok + eps < ng || ng + eps < ok);
++loops) {
real_type mid{(ok + ng) / 2};
(pred(mid) ? ok : ng) = mid;
}
return ok;
}
/*
* @fn parallel_binary_search
* @brief parallel binary search on the real number line.
* @param ends a vector of pairs; pred(first) is true, pred(second) is false
* @param eps the error tolerance
* @param pred the predicate
* @return the boundary points
*/
template <class real_type, class pred_type>
std::enable_if_t<std::is_convertible_v<
std::invoke_result_t<pred_type, std::vector<real_type>>,
std::vector<bool>>,
std::vector<real_type>>
parallel_binary_search(std::vector<std::pair<real_type, real_type>> ends,
const real_type eps, pred_type pred) {
std::vector<real_type> mids(ends.size());
for (auto loops = 0; loops != std::numeric_limits<real_type>::digits;
++loops) {
bool all_found = true;
for (size_t i{}; i != ends.size(); ++i) {
auto [ok, ng] = ends[i];
if (ok + eps < ng || ng + eps < ok) {
all_found = false;
mids[i] = (ok + ng) / 2;
}
}
if (all_found) break;
auto res = pred(mids);
for (size_t i{}; i != ends.size(); ++i) {
(res[i] ? ends[i].first : ends[i].second) = mids[i];
}
}
return mids;
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/chval.hpp"
/*
* @file chval.hpp
* @brief Change Less/Greater
*/
#line 9 "Library/src/utils/chval.hpp"
namespace workspace {
/*
* @fn chle
* @brief Substitute y for x if comp(y, x) is true.
* @param x Reference
* @param y Const reference
* @param comp Compare function
* @return Whether or not x is updated
*/
template <class Tp, class Comp = std::less<Tp>>
bool chle(Tp &x, const Tp &y, Comp comp = Comp()) {
return comp(y, x) ? x = y, true : false;
}
/*
* @fn chge
* @brief Substitute y for x if comp(x, y) is true.
* @param x Reference
* @param y Const reference
* @param comp Compare function
* @return Whether or not x is updated
*/
template <class Tp, class Comp = std::less<Tp>>
bool chge(Tp &x, const Tp &y, Comp comp = Comp()) {
return comp(x, y) ? x = y, true : false;
}
} // namespace workspace
#line 2 "Library/src/utils/clock.hpp"
/*
* @fn clock.hpp
* @brief Clock
*/
#line 9 "Library/src/utils/clock.hpp"
namespace workspace {
using namespace std::chrono;
namespace internal {
// The start time of the program.
const auto start_time{system_clock::now()};
} // namespace internal
/*
* @fn elapsed
* @return elapsed time of the program
*/
int64_t elapsed() {
const auto end_time{system_clock::now()};
return duration_cast<milliseconds>(end_time - internal::start_time).count();
}
} // namespace workspace
#line 5 "Library/src/utils/coordinate_compression.hpp"
template <class T> class coordinate_compression {
std::vector<T> uniquely;
std::vector<size_t> compressed;
public:
coordinate_compression(const std::vector<T> &raw)
: uniquely(raw), compressed(raw.size()) {
std::sort(uniquely.begin(), uniquely.end());
uniquely.erase(std::unique(uniquely.begin(), uniquely.end()),
uniquely.end());
for (size_t i = 0; i != size(); ++i)
compressed[i] =
std::lower_bound(uniquely.begin(), uniquely.end(), raw[i]) -
uniquely.begin();
}
size_t operator[](const size_t idx) const {
assert(idx < size());
return compressed[idx];
}
size_t size() const { return compressed.size(); }
size_t count() const { return uniquely.size(); }
T value(const size_t ord) const {
assert(ord < count());
return uniquely[ord];
}
size_t order(const T &value) const {
return std::lower_bound(uniquely.begin(), uniquely.end(), value) -
uniquely.begin();
}
auto begin() { return compressed.begin(); }
auto end() { return compressed.end(); }
auto rbegin() { return compressed.rbegin(); }
auto rend() { return compressed.rend(); }
};
#line 2 "Library/src/utils/ejection.hpp"
/*
* @file ejection.hpp
* @brief Ejection
*/
#line 9 "Library/src/utils/ejection.hpp"
namespace workspace {
/*
* @brief eject from a try block, throw nullptr
* @param arg output
*/
template <class Tp> void eject(Tp const &arg) {
std::cout << arg << "\n";
throw nullptr;
}
} // namespace workspace
#line 2 "Library/src/utils/exponential_search.hpp"
/*
* @file exponential_search.hpp
* @brief Exponential Search
*/
#line 9 "Library/src/utils/exponential_search.hpp"
#if __cplusplus >= 201703L
namespace workspace {
/*
* @fn exponential_search
* @brief Exponential search on a discrete range.
* @param range Range of search, exclusive
* @param pred Predicate
* @return The minimum non-negative integer where pred is false.
*/
template <class size_type, class pred_type>
std::enable_if_t<
std::is_convertible_v<std::invoke_result_t<pred_type, size_type>, bool>,
size_type>
exponential_search(size_type range, pred_type pred) {
size_type step(1);
while (step < range && pred(step)) step <<= 1;
if (range < step) step = range;
return binary_search(size_type(0), step, pred);
}
/*
* @fn exponential_search
* @brief Exponential search on the real number line.
* @param range Range of search
* @param eps Error tolerance
* @param pred Predicate
* @return The boundary point.
*/
template <class real_type, class pred_type>
std::enable_if_t<
std::is_convertible_v<std::invoke_result_t<pred_type, real_type>, bool>,
real_type>
exponential_search(real_type range, const real_type eps, pred_type pred) {
real_type step(1);
while (step < range && pred(step)) step += step;
if (range < step) step = range;
return binary_search(real_type(0), step, eps, pred);
}
} // namespace workspace
#endif
#line 2 "Library/src/utils/fixed_point.hpp"
/*
* @file fixed_point.hpp
* @brief Fixed Point Combinator
*/
#line 9 "Library/src/utils/fixed_point.hpp"
namespace workspace {
/*
* @class fixed_point
* @brief Recursive calling of lambda expression.
*/
template <class lambda_type> class fixed_point {
lambda_type func;
public:
/*
* @param func 1st arg callable with the rest of args, and the return type
* specified.
*/
fixed_point(lambda_type &&func) : func(std::move(func)) {}
/*
* @brief Recursively apply *this to 1st arg of func.
* @param args Arguments of the recursive method.
*/
template <class... Args> auto operator()(Args &&... args) const {
return func(*this, std::forward<Args>(args)...);
}
};
} // namespace workspace
#line 6 "Library/src/utils/hash.hpp"
#line 2 "Library/src/utils/sfinae.hpp"
/*
* @file sfinae.hpp
* @brief SFINAE
*/
#line 10 "Library/src/utils/sfinae.hpp"
#include <type_traits>
namespace workspace {
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
template <class Container>
using element_type = typename std::decay<decltype(
*std::begin(std::declval<Container&>()))>::type;
template <class T, class = std::nullptr_t>
struct has_begin : std::false_type {};
template <class T>
struct has_begin<T, decltype(std::begin(std::declval<T>()), nullptr)>
: std::true_type {};
template <class T, class = int> struct mapped_of {
using type = element_type<T>;
};
template <class T>
struct mapped_of<T,
typename std::pair<int, typename T::mapped_type>::first_type> {
using type = typename T::mapped_type;
};
template <class T> using mapped_type = typename mapped_of<T>::type;
template <class T, class = void> struct is_integral_ext : std::false_type {};
template <class T>
struct is_integral_ext<
T, typename std::enable_if<std::is_integral<T>::value>::type>
: std::true_type {};
template <> struct is_integral_ext<__int128_t> : std::true_type {};
template <> struct is_integral_ext<__uint128_t> : std::true_type {};
#if __cplusplus >= 201402
template <class T>
constexpr static bool is_integral_ext_v = is_integral_ext<T>::value;
#endif
template <typename T, typename = void> struct multiplicable_uint {
using type = uint_least32_t;
};
template <typename T>
struct multiplicable_uint<T, typename std::enable_if<(2 < sizeof(T))>::type> {
using type = uint_least64_t;
};
template <typename T>
struct multiplicable_uint<T, typename std::enable_if<(4 < sizeof(T))>::type> {
using type = __uint128_t;
};
} // namespace workspace
#line 8 "Library/src/utils/hash.hpp"
namespace workspace {
template <class T, class = void> struct hash : std::hash<T> {};
#if __cplusplus >= 201703L
template <class Unique_bits_type>
struct hash<Unique_bits_type,
enable_if_trait_type<Unique_bits_type,
std::has_unique_object_representations>> {
size_t operator()(uint64_t x) const {
static const uint64_t m = std::random_device{}();
x ^= x >> 23;
x ^= m;
x ^= x >> 47;
return x - (x >> 32);
}
};
#endif
template <class Key> size_t hash_combine(const size_t &seed, const Key &key) {
return seed ^
(hash<Key>()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */);
}
template <class T1, class T2> struct hash<std::pair<T1, T2>> {
size_t operator()(const std::pair<T1, T2> &pair) const {
return hash_combine(hash<T1>()(pair.first), pair.second);
}
};
template <class... T> class hash<std::tuple<T...>> {
template <class Tuple, size_t index = std::tuple_size<Tuple>::value - 1>
struct tuple_hash {
static uint64_t apply(const Tuple &t) {
return hash_combine(tuple_hash<Tuple, index - 1>::apply(t),
std::get<index>(t));
}
};
template <class Tuple> struct tuple_hash<Tuple, size_t(-1)> {
static uint64_t apply(const Tuple &t) { return 0; }
};
public:
uint64_t operator()(const std::tuple<T...> &t) const {
return tuple_hash<std::tuple<T...>>::apply(t);
}
};
template <class hash_table> struct hash_table_wrapper : hash_table {
using key_type = typename hash_table::key_type;
size_t count(const key_type &key) const {
return hash_table::find(key) != hash_table::end();
}
template <class... Args> auto emplace(Args &&... args) {
return hash_table::insert(typename hash_table::value_type(args...));
}
};
template <class Key, class Mapped = __gnu_pbds::null_type>
using cc_hash_table =
hash_table_wrapper<__gnu_pbds::cc_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped = __gnu_pbds::null_type>
using gp_hash_table =
hash_table_wrapper<__gnu_pbds::gp_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped>
using unordered_map = std::unordered_map<Key, Mapped, hash<Key>>;
template <class Key> using unordered_set = std::unordered_set<Key, hash<Key>>;
} // namespace workspace
#line 2 "Library/src/utils/io/casefmt.hpp"
/*
* @file castfmt
* @brief Case Output Format
*/
#line 2 "Library/src/utils/iterate_case.hpp"
/*
* @file iterate_case.hpp
* @brief Iterate Testcases
*/
namespace workspace {
namespace internal {
// The 1-based index of the current testcase.
unsigned caseid;
} // namespace internal
void main();
unsigned case_number();
/*
* @fn iterate_main
* @brief Iterate main function.
*/
void iterate_main() {
for (unsigned total = case_number(), &counter = (internal::caseid = 1);
counter <= total; ++counter) {
try {
main();
} catch (std::nullptr_t) {
}
}
}
} // namespace workspace
#line 9 "Library/src/utils/io/casefmt.hpp"
namespace workspace {
/*
* @fn casefmt
* @brief printf("Case #%u: ", internal::caseid)
* @param os Reference to ostream
* @return os
*/
std::ostream& casefmt(std::ostream& os) {
return os << "Case #" << internal::caseid << ": ";
}
} // namespace workspace
#line 2 "Library/src/utils/io/istream.hpp"
/*
* @file stream.hpp
* @brief Input Stream
*/
#include <cxxabi.h>
#line 13 "Library/src/utils/io/istream.hpp"
#line 15 "Library/src/utils/io/istream.hpp"
namespace workspace {
/*
* @class istream
* @brief A wrapper class for std::istream.
*/
class istream : public std::istream {
template <class Tp, typename = std::nullptr_t> struct helper {
helper(std::istream &is, Tp &x) {
if constexpr (has_begin<Tp>::value)
for (auto &&e : x) helper<decltype(e)>(is, e);
else
static_assert(has_begin<Tp>::value, "istream unsupported type.");
}
};
template <class Tp>
struct helper<
Tp,
decltype(std::declval<std::decay<decltype(
std::declval<std::istream &>() >> std::declval<Tp &>())>>(),
nullptr)> {
helper(std::istream &is, Tp &x) { is >> x; }
};
template <class T1, class T2> struct helper<std::pair<T1, T2>> {
helper(std::istream &is, std::pair<T1, T2> &x) {
helper<T1>(is, x.first), helper<T2>(is, x.second);
}
};
template <class... Tps> struct helper<std::tuple<Tps...>> {
helper(std::istream &is, std::tuple<Tps...> &x) { iterate(is, x); }
private:
template <class Tp, size_t N = 0> void iterate(std::istream &is, Tp &x) {
if constexpr (N == std::tuple_size<Tp>::value)
return;
else
helper<typename std::tuple_element<N, Tp>::type>(is, std::get<N>(x)),
iterate<Tp, N + 1>(is, x);
}
};
public:
template <typename Tp> istream &operator>>(Tp &x) {
helper<Tp>(*this, x);
if (std::istream::fail()) {
static auto once = atexit([] {
std::cerr << "\n\033[43m\033[30mwarning: failed to read \'"
<< abi::__cxa_demangle(typeid(Tp).name(), 0, 0, 0)
<< "\'.\033[0m\n\n";
});
assert(!once);
}
return *this;
}
};
namespace internal {
auto *const cin_ptr = (istream *)&std::cin;
}
auto &cin = *internal::cin_ptr;
} // namespace workspace
#line 2 "Library/src/utils/io/ostream.hpp"
/*
* @file ostream.hpp
* @brief Output Stream
*/
#line 10 "Library/src/utils/io/ostream.hpp"
namespace workspace {
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
return os << p.first << ' ' << p.second;
}
template <class tuple_t, size_t index> struct tuple_os {
static std::ostream &apply(std::ostream &os, const tuple_t &t) {
tuple_os<tuple_t, index - 1>::apply(os, t);
return os << ' ' << std::get<index>(t);
}
};
template <class tuple_t> struct tuple_os<tuple_t, 0> {
static std::ostream &apply(std::ostream &os, const tuple_t &t) {
return os << std::get<0>(t);
}
};
template <class tuple_t> struct tuple_os<tuple_t, SIZE_MAX> {
static std::ostream &apply(std::ostream &os, const tuple_t &t) { return os; }
};
template <class... T>
std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
return tuple_os<std::tuple<T...>,
std::tuple_size<std::tuple<T...>>::value - 1>::apply(os, t);
}
template <class Container,
typename = decltype(std::begin(std::declval<Container>()))>
typename std::enable_if<
!std::is_same<typename std::decay<Container>::type, std::string>::value &&
!std::is_same<typename std::decay<Container>::type, char *>::value,
std::ostream &>::type
operator<<(std::ostream &os, const Container &cont) {
bool head = true;
for (auto &&e : cont) head ? head = 0 : (os << ' ', 0), os << e;
return os;
}
} // namespace workspace
#line 3 "Library/src/utils/io/read.hpp"
namespace workspace {
namespace internal {
struct cast_read {
template <class T> operator T() const {
T value;
workspace::cin >> value;
return value;
}
};
} // namespace internal
/*
* @fn read
* @tparam Tp The type of input.
* @brief Read from stdin.
*/
template <class Tp = void> auto read() {
typename std::remove_const<Tp>::type value;
cin >> value;
return value;
}
/*
* @fn read
* @brief Read from stdin on type casting.
*/
template <> auto read<void>() { return internal::cast_read(); }
} // namespace workspace
#line 2 "Library/src/utils/io/setup.hpp"
/*
* @file setup.hpp
* @brief I/O Setup
*/
#line 10 "Library/src/utils/io/setup.hpp"
namespace workspace {
/*
* @fn io_setup
* @brief Setup I/O before main process.
*/
__attribute__((constructor)) void io_setup() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(15);
#ifdef _buffer_check
atexit([] {
char bufc;
if (std::cin >> bufc)
std::cerr << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n";
});
#endif
}
} // namespace workspace
#line 2 "Library/src/utils/make_vector.hpp"
/*
* @file make_vector.hpp
* @brief Multi-dimensional Vector
*/
#if __cplusplus >= 201703L
#include <tuple>
#include <vector>
namespace workspace {
/*
* @brief Make a multi-dimensional vector.
* @tparam Tp type of the elements
* @tparam N dimension
* @tparam S integer type
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S>
constexpr auto make_vector(S* sizes, Tp const& init = Tp()) {
static_assert(std::is_convertible_v<S, size_t>);
if constexpr (N)
return std::vector(*sizes,
make_vector<Tp, N - 1, S>(std::next(sizes), init));
else
return init;
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S>
constexpr auto make_vector(const S (&sizes)[N], Tp const& init = Tp()) {
return make_vector<Tp, N, S>((S*)sizes, init);
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N, typename S, size_t I = 0>
constexpr auto make_vector(std::array<S, N> const& sizes,
Tp const& init = Tp()) {
static_assert(std::is_convertible_v<S, size_t>);
if constexpr (I == N)
return init;
else
return std::vector(sizes[I], make_vector<Tp, N, S, I + 1>(sizes, init));
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, size_t N = SIZE_MAX, size_t I = 0, class... Args>
constexpr auto make_vector(std::tuple<Args...> const& sizes,
Tp const& init = Tp()) {
using tuple_type = std::tuple<Args...>;
if constexpr (I == std::tuple_size_v<tuple_type> || I == N)
return init;
else {
static_assert(
std::is_convertible_v<std::tuple_element_t<I, tuple_type>, size_t>);
return std::vector(std::get<I>(sizes),
make_vector<Tp, N, I + 1>(sizes, init));
}
}
/*
* @brief Make a multi-dimensional vector.
* @param sizes The size of each dimension
* @param init The initial value
*/
template <typename Tp, class Fst, class Snd>
constexpr auto make_vector(std::pair<Fst, Snd> const& sizes,
Tp const& init = Tp()) {
static_assert(std::is_convertible_v<Fst, size_t>);
static_assert(std::is_convertible_v<Snd, size_t>);
return make_vector({(size_t)sizes.first, (size_t)sizes.second}, init);
}
} // namespace workspace
#endif
#line 3 "Library/src/utils/random_number_generator.hpp"
template <typename num_type> class random_number_generator {
typename std::conditional<std::is_integral<num_type>::value,
std::uniform_int_distribution<num_type>,
std::uniform_real_distribution<num_type>>::type
unif;
std::mt19937 engine;
public:
random_number_generator(num_type min = std::numeric_limits<num_type>::min(),
num_type max = std::numeric_limits<num_type>::max())
: unif(min, max), engine(std::random_device{}()) {}
num_type min() const { return unif.min(); }
num_type max() const { return unif.max(); }
// generate a random number in [min(), max()].
num_type operator()() { return unif(engine); }
};
#line 2 "Library/src/utils/round_div.hpp"
/*
* @file round_div.hpp
* @brief Round Integer Division
*/
#line 9 "Library/src/utils/round_div.hpp"
#line 11 "Library/src/utils/round_div.hpp"
namespace workspace {
/*
* @fn floor_div
* @brief floor of fraction.
* @param x the numerator
* @param y the denominator
* @return maximum integer z s.t. z <= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
floor_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? (x - y + 1) / y : x / y;
}
/*
* @fn ceil_div
* @brief ceil of fraction.
* @param x the numerator
* @param y the denominator
* @return minimum integer z s.t. z >= x / y
* @note y must be nonzero.
*/
template <typename T1, typename T2>
constexpr typename std::enable_if<(is_integral_ext<T1>::value &&
is_integral_ext<T2>::value),
typename std::common_type<T1, T2>::type>::type
ceil_div(T1 x, T2 y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x < 0 ? x / y : (x + y - 1) / y;
}
} // namespace workspace
#line 4 "Library/src/utils/trinary_search.hpp"
// trinary search on discrete range.
template <class iter_type, class comp_type>
iter_type trinary(iter_type first, iter_type last, comp_type comp)
{
assert(first < last);
intmax_t dist(last - first);
while(dist > 2)
{
iter_type left(first + dist / 3), right(first + dist * 2 / 3);
if(comp(left, right)) last = right, dist = dist * 2 / 3;
else first = left, dist -= dist / 3;
}
if(dist > 1 && comp(first + 1, first)) ++first;
return first;
}
// trinary search on real numbers.
template <class comp_type>
long double trinary(long double first, long double last, const long double eps, comp_type comp)
{
assert(first < last);
while(last - first > eps)
{
long double left{(first * 2 + last) / 3}, right{(first + last * 2) / 3};
if(comp(left, right)) last = right;
else first = left;
}
return first;
}
#line 2 "Library/src/utils/wrapper.hpp"
template <class Container> class reversed {
Container &ref, copy;
public:
constexpr reversed(Container &ref) : ref(ref) {}
constexpr reversed(Container &&ref = Container()) : ref(copy), copy(ref) {}
constexpr auto begin() const { return ref.rbegin(); }
constexpr auto end() const { return ref.rend(); }
constexpr operator Container() const { return ref; }
};
#line 12 "other/game.cc"
int main() { workspace::iterate_main(); }
unsigned workspace::case_number() {
// return -1; // unspecified
// int t; cin >> t, cin.ignore(); return t; // given
return 1;
}
#line 2 "Library/src/modular/inverse.hpp"
/*
* @file inverse.hpp
* @brief Inverse Table
*/
#line 9 "Library/src/modular/inverse.hpp"
#line 2 "Library/src/modular/modint.hpp"
/*
* @file modint.hpp
* @brief Modular Arithmetic
*/
#line 10 "Library/src/modular/modint.hpp"
#line 12 "Library/src/modular/modint.hpp"
namespace workspace {
namespace internal {
/*
* @struct modint_base
* @brief base of modular arithmetic.
* @tparam Mod identifier, which represents modulus if positive
*/
template <auto Mod> struct modint_base {
static_assert(is_integral_ext<decltype(Mod)>::value,
"Mod must be integral type.");
using mod_type =
typename std::conditional<0 < Mod,
typename std::add_const<decltype(Mod)>::type,
decltype(Mod)>::type;
static mod_type mod;
using value_type = typename std::decay<mod_type>::type;
constexpr operator value_type() const noexcept { return value; }
constexpr static modint_base one() noexcept { return 1; }
constexpr modint_base() noexcept = default;
template <class int_type,
typename std::enable_if<is_integral_ext<int_type>::value>::type * =
nullptr>
constexpr modint_base(int_type n) noexcept
: value((n %= mod) < 0 ? mod + n : n) {}
constexpr modint_base(bool n) noexcept : modint_base(int(n)) {}
constexpr modint_base operator++(int) noexcept {
modint_base t{*this};
return operator+=(1), t;
}
constexpr modint_base operator--(int) noexcept {
modint_base t{*this};
return operator-=(1), t;
}
constexpr modint_base &operator++() noexcept { return operator+=(1); }
constexpr modint_base &operator--() noexcept { return operator-=(1); }
constexpr modint_base operator-() const noexcept {
return value ? mod - value : 0;
}
constexpr modint_base &operator+=(const modint_base &rhs) noexcept {
return (value += rhs.value) < mod ? 0 : value -= mod, *this;
}
constexpr modint_base &operator-=(const modint_base &rhs) noexcept {
return (value += mod - rhs.value) < mod ? 0 : value -= mod, *this;
}
constexpr modint_base &operator*=(const modint_base &rhs) noexcept {
return value = (typename multiplicable_uint<value_type>::type)value *
rhs.value % mod,
*this;
}
constexpr modint_base &operator/=(const modint_base &rhs) noexcept {
return operator*=(rhs.inverse());
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator+(const int_type &rhs) const noexcept {
return modint_base{*this} += rhs;
}
constexpr modint_base operator+(const modint_base &rhs) const noexcept {
return modint_base{*this} += rhs;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator-(const int_type &rhs) const noexcept {
return modint_base{*this} -= rhs;
}
constexpr modint_base operator-(const modint_base &rhs) const noexcept {
return modint_base{*this} -= rhs;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator*(const int_type &rhs) const noexcept {
return modint_base{*this} *= rhs;
}
constexpr modint_base operator*(const modint_base &rhs) const noexcept {
return modint_base{*this} *= rhs;
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator/(const int_type &rhs) const noexcept {
return modint_base{*this} /= rhs;
}
constexpr modint_base operator/(const modint_base &rhs) const noexcept {
return modint_base{*this} /= rhs;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator+(const int_type &lhs, const modint_base &rhs) noexcept {
return modint_base(lhs) + rhs;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator-(const int_type &lhs, const modint_base &rhs) noexcept {
return modint_base(lhs) - rhs;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator*(const int_type &lhs, const modint_base &rhs) noexcept {
return modint_base(lhs) * rhs;
}
template <class int_type>
constexpr friend typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
operator/(const int_type &lhs, const modint_base &rhs) noexcept {
return modint_base(lhs) / rhs;
}
constexpr modint_base inverse() const noexcept {
assert(value);
value_type a{mod}, b{value}, u{}, v{1}, t{};
while (b)
t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
return {u};
}
template <class int_type>
constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
power(int_type e) noexcept {
return pow(*this, e);
}
template <class int_type>
friend constexpr typename std::enable_if<is_integral_ext<int_type>::value,
modint_base>::type
pow(modint_base b, int_type e) noexcept {
modint_base res{1};
for (e < 0 ? b = b.inverse(), e = -e : 0; e; e >>= 1, b *= b)
if (e & 1) res *= b;
return res;
}
friend std::ostream &operator<<(std::ostream &os,
const modint_base &rhs) noexcept {
return os << rhs.value;
}
friend std::istream &operator>>(std::istream &is, modint_base &rhs) noexcept {
intmax_t value;
rhs = (is >> value, value);
return is;
}
protected:
value_type value = 0;
};
template <auto Mod>
typename modint_base<Mod>::mod_type modint_base<Mod>::mod = Mod;
} // namespace internal
/*
* @typedef modint
* @brief modular arithmetic.
* @tparam Mod modulus
*/
template <auto Mod, typename std::enable_if<(Mod > 0)>::type * = nullptr>
using modint = internal::modint_base<Mod>;
/*
* @typedef modint_runtime
* @brief runtime modular arithmetic.
* @tparam type_id uniquely assigned
*/
template <unsigned type_id = 0>
using modint_runtime = internal::modint_base<-(signed)type_id>;
// #define modint_newtype modint_runtime<__COUNTER__>
} // namespace workspace
#line 11 "Library/src/modular/inverse.hpp"
namespace workspace {
// Modulus must be prime.
template <class Modint> struct inverse_table {
static_assert(std::is_same<std::nullptr_t,
decltype((void *)Modint::mod, nullptr)>::value);
using value_type = Modint;
constexpr value_type operator()(int n) const {
constexpr int_fast64_t mod = value_type::mod;
assert(n %= mod);
if (n < 0) n += mod;
if (inv.empty()) inv = {1, mod != 1};
for (int m(inv.size()); m <= n; ++m)
inv.emplace_back(mod / m * -inv[mod % m]);
return inv[n];
}
private:
static std::vector<value_type> inv;
};
template <class Modint> std::vector<Modint> inverse_table<Modint>::inv;
} // namespace workspace
#line 22 "other/game.cc"
namespace workspace {
using mint = modint<998244353>;
void main() {
// start here!
int n;
cin >> n;
vector<mint> a(1 << n);
cin >> a;
for (auto i = 0; i < n; ++i) {
for (auto s = 0; s < size(a); ++s) {
if (s >> i & 1) a[s] += a[s ^ 1 << i];
}
}
mint ans;
for (auto s = 0; s + 1 < size(a); ++s) {
mint ctb = a.back() / (a.back() - a[s]);
if ((n - __popcount(s)) & 1)
ans += ctb;
else
ans -= ctb;
}
cout << ans << eol;
}
} // namespace workspace