結果
| 問題 | No.1294 マウンテン数列 |
| ユーザー |
 jell
|
| 提出日時 | 2020-11-21 16:26:15 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,041 ms / 2,000 ms |
| コード長 | 64,578 bytes |
| コンパイル時間 | 2,929 ms |
| コンパイル使用メモリ | 279,004 KB |
| 実行使用メモリ | 4,384 KB |
| 最終ジャッジ日時 | 2023-09-30 21:57:38 |
| 合計ジャッジ時間 | 10,775 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge12 |
（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
4,376 KB |
| testcase_01 | AC | 2 ms
4,384 KB |
| testcase_02 | AC | 2 ms
4,376 KB |
| testcase_03 | AC | 2 ms
4,376 KB |
| testcase_04 | AC | 2 ms
4,380 KB |
| testcase_05 | AC | 86 ms
4,376 KB |
| testcase_06 | AC | 120 ms
4,376 KB |
| testcase_07 | AC | 1 ms
4,376 KB |
| testcase_08 | AC | 1 ms
4,380 KB |
| testcase_09 | AC | 2 ms
4,380 KB |
| testcase_10 | AC | 1,031 ms
4,376 KB |
| testcase_11 | AC | 1,038 ms
4,380 KB |
| testcase_12 | AC | 1,041 ms
4,376 KB |
| testcase_13 | AC | 1,034 ms
4,376 KB |
| testcase_14 | AC | 818 ms
4,376 KB |
| testcase_15 | AC | 949 ms
4,376 KB |
| testcase_16 | AC | 821 ms
4,376 KB |
ソースコード
#line 1 "Library/yu2.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/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>
template <typename T, class = void> struct is_complete : std::false_type {};
template <typename T>
struct is_complete<T, decltype(void(sizeof(T)))> : std::true_type {};
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 = 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;
};
#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 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/io/stream.hpp"
/*
* @file stream.hpp
* @brief Stream
*/
#include <cxxabi.h>
#line 13 "Library/src/utils/io/stream.hpp"
namespace workspace {
/*
* @class istream
* @brief A wrapper class for std::istream.
*/
class istream : std::istream {
template <class Tp, typename = std::nullptr_t> struct helper {
helper(std::istream &is, Tp &x) {
for (auto &&e : x) helper<decltype(e)>(is, e);
}
};
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;
// operator<< overloads
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 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 "Library/yu2.cc"
int main() { workspace::iterate_main(); }
unsigned workspace::case_number() {
// return -1; // unspecified
// int t; std::cin >> t; std::cin.ignore(); return t; // given
return 1;
}
#line 3 "Library/src/data_structure/convex_hull_trick/Li_Chao_tree.hpp"
template <class T = long long, class Comp = std::less<T>, T infty = std::numeric_limits<T>::max()>
class Li_Chao_tree
{
struct line
{
T slop = 0, icpt = infty;
line *lch = nullptr, *rch = nullptr;
~line() { delete lch; delete rch; }
line *swap(line &rhs) { std::swap(slop, rhs.slop); std::swap(icpt, rhs.icpt); return this; }
T eval(const T x) const { return slop * x + icpt; }
}; // struct line
T lower, upper, eps;
Comp comp;
line *root = nullptr;
// // insert a line for the interval [l, r).
line *insert(line *const p, const T l, const T r, line ln)
{
if(!p) return new line(ln);
bool lcmp = comp(ln.eval(l), p->eval(l));
bool rcmp = comp(ln.eval(r - eps), p->eval(r - eps));
if(lcmp == rcmp) return lcmp ? p->swap(ln) : p;
if(r - l <= eps) return p;
T mid = (l + r) / 2;
if(comp(ln.eval(mid), p->eval(mid)))
{
p->swap(ln);
lcmp = !lcmp;
}
if(lcmp) p->lch = insert(p->lch, l, mid, ln);
else p->rch = insert(p->rch, mid, r, ln);
return p;
}
// // insert a segment for the interval [l, r).
line *insert(line *const p, const T l, const T r, line ln, const T s, const T t)
{
if(t - eps < l || r - eps < s) return p;
T mid = (l + r) / 2;
if(l < s or t < r)
{
line *np = p ? p : new line;
np->lch = insert(np->lch, l, mid, ln, s, t);
np->rch = insert(np->rch, mid, r, ln, s, t);
return np;
}
if(!p) return new line(ln);
bool lcmp = comp(ln.eval(l), p->eval(l));
bool rcmp = comp(ln.eval(r - eps), p->eval(r - eps));
if(lcmp == rcmp) return lcmp ? p->swap(ln) : p;
if(r - l <= eps) return p;
if(comp(ln.eval(mid), p->eval(mid)))
{
p->swap(ln);
lcmp = !lcmp;
}
if(lcmp) p->lch = insert(p->lch, l, mid, ln, s, t);
else p->rch = insert(p->rch, mid, r, ln, s, t);
return p;
}
public:
// domain set to be the interval [lower, upper).
Li_Chao_tree(const T lower, const T upper, const T eps = 1, Comp comp = Comp())
: lower(lower), upper(upper), eps(eps), comp(comp) {}
~Li_Chao_tree() { delete root; }
bool empty() const { return !root; }
// insert a line whose slope is p and inception is q.
void insert(const T p, const T q) { root = insert(root, lower, upper, line{p, q}); }
// insert a line(segment) whose slope is p, inception is q,
// and domain is the interval [s, t).
void insert(const T p, const T q, const T s, const T t) { if(s < t) root = insert(root, lower, upper, line{p, q}, s, t); }
T get(const T x) const
{
line *p = root;
T l = lower, r = upper;
T res = infty;
while(p)
{
T nval = p->eval(x);
if(comp(nval, res)) res = nval;
if(r - l <= eps) return res;
T mid = (l + r) / 2;
if(x < mid)
{
p = p->lch;
r = mid;
}
else
{
p = p->rch;
l = mid;
}
}
return res;
}
}; // class Li_Chao_tree
#line 4 "Library/src/data_structure/convex_hull_trick/monotone.hpp"
template <class T> class lower_convex_monotone {
struct line {
T slop, icpt;
T eval(const T x) const { return slop * x + icpt; }
};
std::vector<line> lines;
typename std::vector<line>::iterator lp, rp;
void realloc() {
if (rp != lines.end()) return;
std::vector<line> copy((rp - lp) * 2 + 1);
copy.swap(lines);
rp = copy(lp, rp, lines.begin());
lp = lines.begin();
}
public:
lower_convex_monotone() : lines(2), lp(lines.begin()), rp(lp) {}
bool empty() const { return lp == rp; }
void clear() { rp = lp = lines.begin(); }
void add(const T a, const T b) {
while (rp - lp > 1) {
auto [a1, b1] = *(rp - 1);
auto [a2, b2] = *(rp - 2);
if ((b - b1) * (a2 - a) > (b - b2) * (a1 - a)) break;
--rp;
}
if (rp == lp) rp = lp = lines.begin();
realloc();
*rp++ = {a, b};
}
T get(const T x) {
assert(!empty());
while (rp - lp > 1 && lp->eval(x) > (lp + 1)->eval(x)) ++lp;
return lp->eval(x);
}
}; // class lower_convex_monotone
#line 4 "Library/src/data_structure/deque_aggregation.hpp"
// implementation with dynamic memory allocation.
template <class monoid>
class deque_aggregation
{
template <bool left_operand_added>
class stack_aggregation
{
friend deque_aggregation;
struct data { monoid value, acc; };
size_t capacity;
data *stack, *end, *itr;
bool top_referred;
void recalc()
{
if(top_referred)
{
assert(itr != stack);
top_referred = false;
monoid top_val{top().value};
pop();
push(top_val);
}
}
public:
stack_aggregation() : capacity(1), stack(new data[1]), end(std::next(stack)), itr(stack), top_referred() {}
~stack_aggregation() { delete[] stack; }
bool empty() const { return stack == itr; }
size_t size() const { return itr - stack; }
// copy of the element at the index.
data operator[](size_t index) const
{
assert(index < size());
recalc();
return stack[index];
}
// reference to the last element
data &top()
{
assert(itr != stack);
top_referred = true;
return *std::prev(itr);
}
void pop()
{
assert(itr != stack);
--itr;
top_referred = false;
}
void push(const monoid &mono)
{
recalc();
if(itr == end)
{
data *tmp = new data[capacity << 1];
std::swap(stack, tmp);
end = (itr = std::copy(tmp, tmp + capacity, stack)) + capacity;
capacity <<= 1;
delete[] tmp;
}
if(left_operand_added) *itr = data{mono, mono + fold()};
else *itr = data{mono, fold() + mono};
++itr;
}
monoid fold()
{
if(itr == stack) return monoid();
recalc();
return std::prev(itr)->acc;
}
}; // class stack_aggregation
stack_aggregation<true> left;
stack_aggregation<false> right;
void balance_to_left()
{
if(!left.empty() || right.empty()) return;
left.recalc(); right.recalc();
size_t mid = (right.size() + 1) >> 1;
auto *itr = right.stack + mid;
do { left.push((--itr)->value); } while(itr != right.stack);
monoid acc;
for(auto *p = right.stack + mid; p != right.itr; ++p, ++itr)
{
*itr = {p->value, acc = acc + p->value};
}
right.itr = itr;
}
void balance_to_right()
{
if(!right.empty() || left.empty()) return;
left.recalc(); right.recalc();
size_t mid = (left.size() + 1) >> 1;
auto *itr = left.stack + mid;
do { right.push((--itr)->value); } while(itr != left.stack);
monoid acc;
for(auto *p = left.stack + mid; p != left.itr; ++p, ++itr)
{
*itr = {p->value, acc = p->value + acc};
}
left.itr = itr;
}
public:
bool empty() const { return left.empty() && right.empty(); }
size_t size() const { return left.size() + right.size(); }
// reference to the first element.
monoid &front() { assert(!empty()); balance_to_left(); return left.top().value; }
// reference to the last element.
monoid &back() { assert(!empty()); balance_to_right(); return right.top().value; }
// copy of the element at the index.
monoid operator[](size_t index) const
{
assert(index < left.size() + right.size());
return index < left.size() ? left[index].value : right[index - left.size()].value;
}
void push_front(const monoid &mono) { left.push(mono); }
void push_back(const monoid &mono) { right.push(mono); }
void pop_front()
{
assert(!empty());
balance_to_left();
left.pop();
}
void pop_back()
{
assert(!empty());
balance_to_right();
right.pop();
}
monoid fold() { return left.fold() + right.fold(); }
}; // class deque_aggregation
#line 2 "Library/src/data_structure/Mo.hpp"
/*
* @file Mo.hpp
* @brief Mo's Algorithm
*/
#line 13 "Library/src/data_structure/Mo.hpp"
namespace workspace {
/*
* @class Mo
* @brief process queries about contiguous subarray
* @tparam Push_back
* @tparam Pop_back
* @tparam Push_front Push_back as default
* @tparam Pop_front Pop_back as default
*/
template <class Push_back, class Pop_back, class Push_front = Push_back,
class Pop_front = Pop_back>
class Mo {
Push_front push_front;
Pop_front pop_front;
Push_back push_back;
Pop_back pop_back;
std::vector<size_t> lft, rgt, ord;
std::vector<size_t>::iterator itr;
size_t lpos, rpos;
public:
/*
* @param push_back
* @param pop_back
*/
Mo(Push_back push_back, Pop_back pop_back)
: Mo(push_back, pop_back, push_back, pop_back) {}
/*
* @param push_front
* @param pop_front
* @param push_back
* @param pop_back
*/
Mo(Push_front push_front, Pop_front pop_front, Push_back push_back,
Pop_back pop_back)
: push_front(push_front),
pop_front(pop_front),
push_back(push_back),
pop_back(pop_back),
lpos(),
rpos() {}
/*
* @return number of queries
*/
size_t size() const { return lft.size(); }
/*
* @brief add query
* @param l left end, inclusive
* @param r right end, exclusive
*/
void set(size_t l, size_t r) {
assert(!(r < l));
lft.emplace_back(l), rgt.emplace_back(r);
}
/*
* @brief sort queries
*/
void make() {
assert(size());
ord.resize(size());
iota(ord.begin(), ord.end(), 0);
const size_t width = sqrt(*max_element(rgt.begin(), rgt.end()));
std::sort(ord.begin(), ord.end(), [&](size_t x, size_t y) {
if (lft[x] / width != lft[y] / width) return lft[x] < lft[y];
return rgt[x] < rgt[y];
});
itr = ord.begin();
}
/*
* @brief process one query
* @return index of query
*/
size_t process() {
if (itr == ord.end()) return ord.size();
const size_t id = *itr++, l = lft[id], r = rgt[id];
while (lpos > l) push_front(--lpos);
while (rpos < r) push_back(rpos++);
while (lpos < l) pop_front(lpos++);
while (rpos > r) pop_back(--rpos);
return id;
}
};
} // namespace workspace
#line 5 "Library/src/data_structure/segment_tree/basic.hpp"
#line 2 "Library/algebra/system/monoid.hpp"
/*
* @file monoid.hpp
* @brief Monoid
*/
#line 9 "Library/algebra/system/monoid.hpp"
namespace workspace {
template <class T, class E = T> struct min_monoid {
using value_type = T;
static T min, max;
T value;
min_monoid() : value(max) {}
min_monoid(const T &value) : value(value) {}
operator T() const { return value; }
min_monoid operator+(const min_monoid &rhs) const {
return value < rhs.value ? *this : rhs;
}
min_monoid operator*(const E &rhs) const;
};
template <class T, class E>
T min_monoid<T, E>::min = std::numeric_limits<T>::min() / 2;
template <class T, class E>
T min_monoid<T, E>::max = std::numeric_limits<T>::max() / 2;
template <class T, class E = T> struct max_monoid : min_monoid<T, E> {
using base = min_monoid<T, E>;
using base::min_monoid;
max_monoid() : base(base::min) {}
max_monoid operator+(const max_monoid &rhs) const {
return !(base::value < rhs.value) ? *this : rhs;
}
max_monoid operator*(const E &rhs) const;
};
} // namespace workspace
#line 3 "Library/src/data_structure/segment_tree/waitlist.hpp"
namespace internal {
struct waitlist : std::queue<size_t> {
waitlist(size_t n) : in(n) {}
bool push(size_t index) {
assert(index < in.size());
if (in[index]) return false;
emplace(index);
return (in[index] = true);
}
size_t pop() {
assert(!empty());
auto index = front();
std::queue<size_t>::pop();
in[index] = false;
return index;
}
private:
std::vector<int_least8_t> in;
};
}
#line 9 "Library/src/data_structure/segment_tree/basic.hpp"
template <class Monoid, class Container = std::vector<Monoid>>
class segment_tree {
static_assert(std::is_same<Monoid, mapped_type<Container>>::value);
size_t size_orig, height, size_ext;
Container data;
internal::waitlist wait;
void repair() {
while (!wait.empty()) {
const size_t index = wait.pop() >> 1;
if (index && wait.push(index)) pull(index);
}
}
void pull(const size_t node) {
data[node] = data[node << 1] + data[node << 1 | 1];
}
template <class Pred>
size_t left_partition_subtree(size_t index, const Pred pred,
Monoid mono) const {
assert(index);
while (index < size_ext) {
const Monoid tmp = data[(index <<= 1) | 1] + mono;
if (pred(tmp))
mono = tmp;
else
++index;
}
return ++index -= size_ext;
}
template <class Pred>
size_t right_partition_subtree(size_t index, const Pred pred,
Monoid mono) const {
assert(index);
while (index < size_ext) {
const Monoid tmp = mono + data[index <<= 1];
if (pred(tmp)) ++index, mono = tmp;
}
return (index -= size_ext) < size_orig ? index : size_orig;
}
public:
using value_type = Monoid;
segment_tree(const size_t n = 0)
: size_orig{n},
height(n > 1 ? 32 - __builtin_clz(n - 1) : 0),
size_ext{1u << height},
data(size_ext << 1),
wait(size_ext << 1) {}
segment_tree(const size_t n, const Monoid &init) : segment_tree(n) {
std::fill(std::next(std::begin(data), size_ext), std::end(data), init);
for (size_t i{size_ext}; --i;) pull(i);
}
template <class iter_type, class value_type = typename std::iterator_traits<
iter_type>::value_type>
segment_tree(iter_type first, iter_type last)
: size_orig(std::distance(first, last)),
height(size_orig > 1 ? 32 - __builtin_clz(size_orig - 1) : 0),
size_ext{1u << height},
data(size_ext << 1),
wait(size_ext << 1) {
static_assert(std::is_constructible<Monoid, value_type>::value,
"Monoid(iter_type::value_type) is not constructible.");
for (auto iter{std::next(std::begin(data), size_ext)};
iter != std::end(data) && first != last; ++iter, ++first)
*iter = Monoid{*first};
for (size_t i{size_ext}; --i;) pull(i);
}
template <class Cont, typename = typename Cont::value_type>
segment_tree(const Cont &cont)
: segment_tree(std::begin(cont), std::end(cont)) {}
size_t size() const { return size_orig; }
size_t capacity() const { return size_ext; }
// reference to the element at the index.
Monoid &operator[](size_t index) {
assert(index < size_orig);
wait.push(index |= size_ext);
return data[index];
}
// const reference to the element at the index.
const Monoid &operator[](size_t index) const {
assert(index < size_orig);
return data[index |= size_orig];
}
Monoid fold(size_t first, size_t last) {
assert(last <= size_orig);
repair();
Monoid leftval{}, rightval{};
first += size_ext, last += size_ext;
while (first < last) {
if (first & 1) leftval = leftval + data[first++];
if (last & 1) rightval = data[--last] + rightval;
first >>= 1, last >>= 1;
}
return leftval + rightval;
}
Monoid fold() { return fold(0, size_orig); }
template <class Pred> size_t left_partition(size_t right, Pred pred) {
assert(right <= size_orig);
repair();
right += size_ext;
Monoid mono{};
for (size_t left{size_ext}; left != right; left >>= 1, right >>= 1) {
if ((left & 1) != (right & 1)) {
const Monoid tmp = data[--right] + mono;
if (!pred(tmp)) return left_partition_subtree(right, pred, mono);
mono = tmp;
}
}
return 0;
}
template <class Pred> size_t right_partition(size_t left, Pred pred) {
assert(left <= size_orig);
repair();
left += size_ext;
Monoid mono{};
for (size_t right{size_ext << 1}; left != right; left >>= 1, right >>= 1) {
if ((left & 1) != (right & 1)) {
const Monoid tmp = mono + data[left];
if (!pred(tmp)) return right_partition_subtree(left, pred, mono);
mono = tmp;
++left;
}
}
return size_orig;
}
}; // class segment_tree
#line 5 "Library/src/data_structure/segment_tree/lazy.hpp"
#line 9 "Library/src/data_structure/segment_tree/lazy.hpp"
template <class Monoid, class Endomorphism,
class Monoid_container = std::vector<Monoid>,
class Endomorphism_container = std::vector<Endomorphism>>
class lazy_segment_tree {
static_assert(std::is_same<Monoid, mapped_type<Monoid_container>>::value);
static_assert(
std::is_same<Endomorphism, mapped_type<Endomorphism_container>>::value);
static_assert(std::is_same<Monoid, decltype(Monoid{} + Monoid{})>::value,
"\'Monoid\' has no proper binary operator+.");
static_assert(std::is_same<Endomorphism,
decltype(Endomorphism{} * Endomorphism{})>::value,
"\'Endomorphism\' has no proper binary operator*.");
static_assert(
std::is_same<Monoid, decltype(Monoid{} * Endomorphism{})>::value,
"\'Endomorphism\' is not applicable to \'Monoid\'.");
size_t size_orig, height, size_ext;
Monoid_container data;
Endomorphism_container lazy;
internal::waitlist wait;
void repair() {
while (!wait.empty()) {
const size_t index = wait.pop() >> 1;
if (index && wait.push(index)) pull(index);
}
}
void apply(size_t node, const Endomorphism &endo) {
data[node] = data[node] * endo;
if (node < size_ext) lazy[node] = lazy[node] * endo;
}
void push(size_t node) {
if (!(node < size_ext)) return;
apply(node << 1, lazy[node]);
apply(node << 1 | 1, lazy[node]);
lazy[node] = Endomorphism{};
}
void pull(size_t node) { data[node] = data[node << 1] + data[node << 1 | 1]; }
template <class Pred>
size_t left_partition_subtree(size_t node, Pred pred, Monoid mono) {
assert(node);
while (node < size_ext) {
push(node);
const Monoid &tmp = data[(node <<= 1) | 1] + mono;
if (pred(tmp))
mono = tmp;
else
++node;
}
return ++node -= size_ext;
}
template <class Pred>
size_t right_partition_subtree(size_t node, Pred pred, Monoid mono) {
assert(node);
while (node < size_ext) {
push(node);
const Monoid &tmp = mono + data[node <<= 1];
if (pred(tmp)) ++node, mono = tmp;
}
return (node -= size_ext) < size_orig ? node : size_orig;
}
public:
using value_type = Monoid;
lazy_segment_tree(size_t n = 0)
: size_orig{n},
height(n > 1 ? 32 - __builtin_clz(n - 1) : 0),
size_ext{1u << height},
data(size_ext << 1),
lazy(size_ext),
wait(size_ext << 1) {}
lazy_segment_tree(size_t n, const Monoid &init) : lazy_segment_tree(n) {
std::fill(std::next(std::begin(data), size_ext), std::end(data), init);
for (size_t i{size_ext}; --i;) pull(i);
}
template <class iter_type, class value_type = typename std::iterator_traits<
iter_type>::value_type>
lazy_segment_tree(iter_type first, iter_type last)
: size_orig(std::distance(first, last)),
height(size_orig > 1 ? 32 - __builtin_clz(size_orig - 1) : 0),
size_ext{1u << height},
data(size_ext << 1),
lazy(size_ext),
wait(size_ext << 1) {
static_assert(std::is_constructible<Monoid, value_type>::value,
"Monoid(iter_type::value_type) is not constructible.");
for (auto iter{std::next(std::begin(data), size_ext)};
iter != std::end(data) && first != last; ++iter, ++first)
*iter = Monoid(*first);
for (size_t i{size_ext}; --i;) pull(i);
}
template <class Container, typename = element_type<Container>>
lazy_segment_tree(const Container &cont)
: lazy_segment_tree(std::begin(cont), std::end(cont)) {}
size_t size() const { return size_orig; }
size_t capacity() const { return size_ext; }
Monoid &operator[](size_t index) {
assert(index < size_orig);
index |= size_ext;
wait.push(index);
for (size_t i = height; i; --i) push(index >> i);
return data[index];
}
void update(size_t index, const Endomorphism &endo) {
update(index, index + 1, endo);
}
void update(size_t first, size_t last, const Endomorphism &endo) {
assert(last <= size_orig);
repair();
if (first >= last) return;
first += size_ext, last += size_ext - 1;
for (size_t i = height; i; --i) push(first >> i), push(last >> i);
for (size_t l = first, r = last + 1; last; l >>= 1, r >>= 1) {
if (l < r) {
if (l & 1) apply(l++, endo);
if (r & 1) apply(--r, endo);
}
if (first >>= 1, last >>= 1) {
pull(first), pull(last);
}
}
}
Monoid fold() { return fold(0, size_orig); }
Monoid fold(size_t first, size_t last) {
assert(last <= size_orig);
repair();
if (first >= last) return Monoid{};
first += size_ext, last += size_ext - 1;
Monoid left_val{}, right_val{};
for (size_t l = first, r = last + 1; last; l >>= 1, r >>= 1) {
if (l < r) {
if (l & 1) left_val = left_val + data[l++];
if (r & 1) right_val = data[--r] + right_val;
}
if (first >>= 1, last >>= 1) {
left_val = left_val * lazy[first];
right_val = right_val * lazy[last];
}
}
return left_val + right_val;
}
template <class Pred> size_t left_partition(size_t right, Pred pred) {
assert(right <= size_orig);
repair();
right += size_ext - 1;
for (size_t i{height}; i; --i) push(right >> i);
++right;
Monoid mono{};
for (size_t left{size_ext}; left != right; left >>= 1, right >>= 1) {
if ((left & 1) != (right & 1)) {
const Monoid &tmp = data[--right] + mono;
if (!pred(tmp)) return left_partition_subtree(right, pred, mono);
mono = tmp;
}
}
return 0;
}
template <class Pred> size_t right_partition(size_t left, Pred pred) {
assert(left <= size_orig);
repair();
left += size_ext;
for (size_t i{height}; i; --i) push(left >> i);
Monoid mono{};
for (size_t right{size_ext << 1}; left != right; left >>= 1, right >>= 1) {
if ((left & 1) != (right & 1)) {
const Monoid &tmp = mono + data[left];
if (!pred(tmp)) return right_partition_subtree(left, pred, mono);
mono = tmp;
++left;
}
}
return size_orig;
}
}; // class lazy_segment_tree
#line 2 "Library/src/data_structure/union_find/basic.hpp"
/*
* @file basic.hpp
* @brief Basic Union-Find
*/
#line 11 "Library/src/data_structure/union_find/basic.hpp"
namespace workspace {
template <typename Tp> struct union_find {
protected:
using signed_t = typename std::make_signed<Tp>::type;
using unsigned_t = typename std::make_unsigned<Tp>::type;
std::vector<signed_t> link;
public:
/*
* @param n The number of nodes.
*/
union_find(Tp n = 0) : link(n, 1) {}
/*
* @fn find
* @param x A node.
* @return The representative of the group.
*/
virtual unsigned_t find(unsigned_t x) {
assert(x < size());
return link[x] > 0 ? x : -(link[x] = -(signed_t)find(-link[x]));
}
/*
* @fn size
* @return The number of nodes.
*/
unsigned_t size() const { return link.size(); }
/*
* @fn size
* @param x A node.
* @return The number of nodes in the group.
*/
virtual unsigned_t size(unsigned_t x) {
assert(x < size());
return link[find(x)];
}
/*
* @fn same
* @param x 1st node.
* @param y 2nd node.
* @return Whether or not the two nodes belong to the same group.
*/
bool same(unsigned_t x, unsigned_t y) {
assert(x < size());
assert(y < size());
return find(x) == find(y);
}
/*
* @fn unite
* @param x 1st node.
* @param y 2nd node.
* @return Whether or not the two groups were merged anew.
*/
virtual bool unite(unsigned_t x, unsigned_t y) {
assert(x < size()), x = find(x);
assert(y < size()), y = find(y);
if (x == y) return false;
if (link[x] < link[y]) std::swap(x, y);
link[x] += link[y];
link[y] = -(signed_t)x;
return true;
}
};
} // namespace workspace
#line 2 "Library/src/data_structure/union_find/bipartite.hpp"
/*
* @file bipartite.hpp
* @brief Bipartite Union-Find
*/
#line 9 "Library/src/data_structure/union_find/bipartite.hpp"
namespace workspace {
class bipartite_union_find : public union_find<uint_least64_t> {
using base = union_find<uint_least64_t>;
using base::union_find;
constexpr static unsigned_t sgnb = unsigned_t(1) << 32, mask = sgnb - 1,
ubs = ~unsigned_t(0) ^ mask;
public:
unsigned_t find(unsigned_t x) override {
assert(x < base::size());
if (link[x] > 0) return x;
const auto p = -link[x] & mask, r = find(p);
if (r != p) link[x] = -(link[x] ^ p ^ link[p]);
return r;
}
bool diff(unsigned_t x) {
assert(x < base::size()), find(x);
return link[x] > 0 ? 0 : link[x] >> 32 & 1;
}
// bool diff(unsigned_t x, unsigned_t y) {}
unsigned_t size(size_t x, bool neq) {
assert(x < base::size()), x = find(x);
return neq ? link[x] >> 32 : link[x] & mask;
}
unsigned_t size(size_t x) override {
assert(x < base::size()), x = find(x);
return (link[x] >> 32) + (link[x] & mask);
}
/*
* @fn unite
* @param x 1st node.
* @param y 2nd node.
* @param flip
* @return Whether or not the relation is consistent.
*/
bool unite(size_t x, size_t y, bool flip = true) {
assert(x < base::size()), flip ^= diff(x), x = find(x);
assert(y < base::size()), flip ^= diff(y), y = find(y);
if (x == y) return !flip;
if (link[x] < link[y]) std::swap(x, y);
link[x] += flip ? (unsigned_t)link[y] << 32 | link[y] >> 32 : link[y];
link[y] = flip ? (mask + 1) ^ -x : -x;
return true;
}
};
} // namespace workspace
#line 1 "Library/src/data_structure/union_find/partially_persistent_union_find.hpp"
// #line 2 "Partially_persistent_union_find.hpp"
// veryfied at https://atcoder.jp/contests/agc002/submissions/9514048
#ifndef Partially_persistent_union_find_hpp
#define Partially_persistent_union_find_hpp
#include <cstdint>
#include <cstddef>
#include <numeric>
#include <vector>
class partially_persistent_union_find
{
using time_type = uint32_t;
struct log_type { time_type time; size_t size; };
const size_t n;
std::vector<size_t> parent;
std::vector<time_type> last;
std::vector<std::vector<log_type>> size_log;
time_type clock;
public:
explicit partially_persistent_union_find(size_t _n) : n(_n), parent(n), last(n, UINT32_MAX), size_log(n, std::vector<log_type>(1, {0, 1})), clock()
{
std::iota(parent.begin(), parent.end(), 0);
}
size_t size(size_t x, time_type t = UINT32_MAX)
{
size_t root = find(x, t);
auto __ok{size_log[root].begin()}, __ng{size_log[root].end()};
auto dist = __ng - __ok;
while(dist > 1)
{
auto mid{__ok + (dist >> 1)};
if(mid->time > t) __ng = mid, dist >>= 1;
else __ok = mid, ++dist >>= 1;
}
return __ok->size;
}
size_t find(size_t x, size_t t = UINT32_MAX) { return last[x] >= t ? x : find(parent[x], t); }
bool same(size_t x, size_t y, time_type t = UINT32_MAX) { return find(x, t) == find(y, t); }
time_type unite(size_t x, size_t y)
{
if((x = find(x)) != (y = find(y)))
{
size_t size_x = size_log[x].back().size;
size_t size_y = size_log[y].back().size;
if(size_x < size_y) std::swap(x, y), std::swap(size_x, size_y);
size_log[x].push_back({clock + 1, size_x + size_y});
parent[y] = x;
last[y] = clock;
}
return ++clock;
}
}; // class partially_persistent_union_find
#endif
#line 1 "Library/src/data_structure/union_find/potentialized_union_find.hpp"
// #line 2 "potentialized_union_find.hpp"
// verified at https://atcoder.jp/contests/abc087/submissions/9511701
#ifndef Potentialized_union_find_hpp
#define Potentialized_union_find_hpp
#include <cassert>
#include <cstddef>
#include <vector>
template <class Abelian>
class potentialized_union_find
{
size_t n;
std::vector<int> link;
std::vector<Abelian> diff_weight;
public:
explicit potentialized_union_find(size_t _n) : n(_n), link(n, -1), diff_weight(n) {}
size_t find(const size_t x)
{
assert(x < n);
if(link[x] < 0) return x;
const size_t root = find(link[x]);
diff_weight[x] += diff_weight[link[x]];
return link[x] = root;
}
size_t size() const { return n; }
size_t size(const size_t x) { return -link[find(x)]; }
Abelian weight(size_t x) { return find(x), diff_weight[x]; }
Abelian diff(size_t x, size_t y) { return weight(y) - weight(x); }
bool same(const size_t x, const size_t y) { return find(x) == find(y); }
bool unite(size_t x, size_t y, Abelian w)
{
w += weight(x) - weight(y);
x = find(x), y = find(y);
if(x == y) return false;
if(link[x] > link[y]) std::swap(x, y), w = -w;
link[x] += link[y], link[y] = x;
diff_weight[y] = w;
return true;
}
}; // class potentialized_union_find
#endif
#line 2 "Library/src/data_structure/union_find/unbalanced.hpp"
/*
* @file unbalanced.hpp
* @brief Unbalanced Union-Find
*/
#line 9 "Library/src/data_structure/union_find/unbalanced.hpp"
namespace workspace {
class unbalanced_union_find : public union_find<uint_least32_t> {
using base = union_find<uint_least32_t>;
public:
using base::union_find;
bool unite(unsigned_t x, unsigned_t y) override {
assert(x < size()), x = find(x);
assert(y < size()), y = find(y);
if (x == y) return false;
link[x] += link[y];
link[y] = -(signed_t)x;
return true;
}
};
} // namespace workspace
#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 23 "Library/yu2.cc"
namespace workspace {
using mint = modint<998244353>;
void main() {
// start here!
int n;
cin >> n;
vector<int> a(n);
cin >> a;
const auto mx = a.back();
reverse(begin(a), end(a));
mint ans;
for (auto d = 1; d < mx; ++d) { // maxdiff <= d
if (d < a[0] - a[1]) continue;
segment_tree<mint> z(n);
bool fail = false;
z[0] = 1;
for (auto i = 2, j = 0; i < n; ++i) {
while (a[i] + d < a[j]) ++j;
if (i == j) {
fail = true;
break;
}
z[i - 1] = z.fold(j, i - 1);
}
if (!fail) ans += z.fold();
}
cout << mx * mint(2).power(n - 1) - ans * 2 << eol;
}
} // namespace workspace