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test/5_atcoder/abc266h.test.cpp
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- Last update: 2024-12-26 06:32:57+09:00
- Problem: https://atcoder.jp/contests/abc266/tasks/abc266_Ex
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Depends on
alg/monoid/max.hpp
Code
#define PROBLEM "https://atcoder.jp/contests/abc266/tasks/abc266_Ex"
#include "my_template.hpp"
#include "other/io.hpp"
#include "ds/segtree/segtree_2d.hpp"
#include "alg/monoid/max.hpp"
using Mono = Monoid_Max<ll>;
void solve() {
LL(N);
using T = tuple<ll, ll, ll, ll>;
VEC(T, dat, N);
dat.eb(0, 0, 0, 0);
++N;
sort(all(dat), [&](auto& a, auto& b) -> bool {
auto [at, ax, ay, aa] = a;
auto [bt, bx, by, bb] = b;
if (ay < by) return true;
if (ay > by) return false;
return at < bt;
});
SegTree_2D<Mono, ll, false> seg1(N, [&](int i) -> tuple<int, int, ll> {
auto [t, x, y, v] = dat[i];
return {x, x + y - t, Mono::unit()};
});
SegTree_2D<Mono, ll, false> seg2(N, [&](int i) -> tuple<int, int, ll> {
auto [t, x, y, v] = dat[i];
return {x, x - y + t, Mono::unit()};
});
ll ANS = 0;
FOR(i, N) {
const auto [t, x, y, v] = dat[i];
if (i == 0) {
seg1.multiply(i, 0);
seg2.multiply(i, 0);
continue;
}
ll best = -infty<ll>;
chmax(best, seg1.prod(-infty<ll>, x + 1, x + y - t, infty<ll>));
chmax(best, seg2.prod(x, infty<ll>, -infty<ll>, x - y + t + 1));
if (best < 0) continue;
best += v;
chmax(ANS, best);
seg1.multiply(i, best);
seg2.multiply(i, best);
}
print(ANS);
}
signed main() {
solve();
return 0;
}#line 1 "test/5_atcoder/abc266h.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/abc266/tasks/abc266_Ex"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
int operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YES(!t); }
#line 1 "ds/segtree/segtree_2d.hpp"
// 点の重複があっても別の点として set などがされる
template <typename Monoid, typename XY, bool SMALL_X = false>
struct SegTree_2D {
using MX = Monoid;
using S = typename MX::value_type;
static_assert(MX::commute);
int N;
// X to idx
vc<XY> keyX;
int minX;
// top node の点列
vc<XY> all_Y;
vc<int> pos;
// segtree data
int NX, log, size;
vc<int> indptr;
vc<S> dat;
// fractional cascading
vc<int> to_left;
SegTree_2D(vc<XY>& X, vc<XY>& Y)
: SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> {
return {X[i], Y[i], MX::unit()};
}) {}
SegTree_2D(vc<XY>& X, vc<XY>& Y, vc<S>& vals)
: SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> {
return {X[i], Y[i], vals[i]};
}) {}
// f(i) = (x,y,val)
template <typename F>
SegTree_2D(int N, F f) {
vc<XY> X(N), Y(N);
vc<S> wt(N);
FOR(i, N) {
auto [a, b, c] = f(i);
X[i] = a, Y[i] = b, wt[i] = c;
}
if (!SMALL_X) {
keyX = X;
UNIQUE(keyX);
NX = len(keyX);
} else {
minX = (X.empty() ? 0 : MIN(X));
NX = (X.empty() ? 1 : MAX(X) - minX + 1);
}
log = 0;
while ((1 << log) < NX) ++log;
size = (1 << log);
vc<int> IX(N);
FOR(i, N) IX[i] = xtoi(X[i]);
indptr.assign(2 * size, 0);
for (auto i: IX) {
i += size;
while (i) indptr[i]++, i /= 2;
}
indptr = cumsum<int>(indptr);
dat.assign(2 * indptr.back(), MX::unit());
to_left.assign(indptr[size], 0);
vc<int> ptr = indptr;
vc<int> I = argsort(Y);
pos.resize(N);
FOR(i, N) pos[I[i]] = i;
for (auto raw_idx: I) {
int i = IX[raw_idx] + size;
int j = -1;
while (i) {
int p = ptr[i];
ptr[i]++;
dat[indptr[i + 1] + p] = wt[raw_idx];
if (j != -1) { to_left[p] = (j % 2 == 0); }
j = i, i /= 2;
}
}
to_left = cumsum<int>(to_left);
FOR(i, 2 * size) {
int off = 2 * indptr[i], n = indptr[i + 1] - indptr[i];
FOR_R(j, 1, n) {
dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]);
}
}
all_Y = Y;
sort(all(all_Y));
}
// 最初に与えた点群の index
void multiply(int raw_idx, S val) {
int i = 1, p = pos[raw_idx];
while (1) {
multiply_i(i, p - indptr[i], val);
if (i >= size) break;
int lc = to_left[p] - to_left[indptr[i]];
int rc = (p - indptr[i]) - lc;
if (to_left[p + 1] - to_left[p]) {
p = indptr[2 * i + 0] + lc;
i = 2 * i + 0;
} else {
p = indptr[2 * i + 1] + rc;
i = 2 * i + 1;
}
}
}
// 最初に与えた点群の index
void set(int raw_idx, S val) {
int i = 1, p = pos[raw_idx];
while (1) {
set_i(i, p - indptr[i], val);
if (i >= size) break;
int lc = to_left[p] - to_left[indptr[i]];
int rc = (p - indptr[i]) - lc;
if (to_left[p + 1] - to_left[p]) {
p = indptr[2 * i + 0] + lc;
i = 2 * i + 0;
} else {
p = indptr[2 * i + 1] + rc;
i = 2 * i + 1;
}
}
}
S prod(XY lx, XY rx, XY ly, XY ry) {
assert(lx <= rx && ly <= ry);
int L = xtoi(lx), R = xtoi(rx);
S res = MX::unit();
auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void {
if (a == b || R <= l || r <= L) return;
if (L <= l && r <= R) {
res = MX::op(res, prod_i(i, a, b));
return;
}
int la = to_left[indptr[i] + a] - to_left[indptr[i]];
int ra = a - la;
int lb = to_left[indptr[i] + b] - to_left[indptr[i]];
int rb = b - lb;
int m = (l + r) / 2;
dfs(dfs, 2 * i + 0, l, m, la, lb);
dfs(dfs, 2 * i + 1, m, r, ra, rb);
};
dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry));
return res;
}
// 矩形内の全点を数える, NlogN
int count(XY lx, XY rx, XY ly, XY ry) {
assert(lx <= rx && ly <= ry);
int L = xtoi(lx), R = xtoi(rx);
int res = 0;
auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void {
if (a == b || R <= l || r <= L) return;
if (L <= l && r <= R) {
res += b - a;
return;
}
int la = to_left[indptr[i] + a] - to_left[indptr[i]];
int ra = a - la;
int lb = to_left[indptr[i] + b] - to_left[indptr[i]];
int rb = b - lb;
int m = (l + r) / 2;
dfs(dfs, 2 * i + 0, l, m, la, lb);
dfs(dfs, 2 * i + 1, m, r, ra, rb);
};
dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry));
return res;
}
private:
inline int xtoi(XY x) {
if constexpr (SMALL_X) return clamp<XY>(x - minX, 0, NX);
return LB(keyX, x);
}
S prod_i(int i, int a, int b) {
int LID = indptr[i], n = indptr[i + 1] - indptr[i];
int off = 2 * LID;
int L = n + a, R = n + b;
S val = MX::unit();
while (L < R) {
if (L & 1) val = MX::op(val, dat[off + (L++)]);
if (R & 1) val = MX::op(dat[off + (--R)], val);
L >>= 1, R >>= 1;
}
return val;
}
void multiply_i(int i, int j, S val) {
int LID = indptr[i], n = indptr[i + 1] - indptr[i];
int off = 2 * LID;
j += n;
while (j) {
dat[off + j] = MX::op(dat[off + j], val);
j >>= 1;
}
}
void set_i(int i, int j, S val) {
int LID = indptr[i], n = indptr[i + 1] - indptr[i];
int off = 2 * LID;
j += n;
dat[off + j] = val;
while (j > 1) {
j /= 2;
dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]);
}
}
};
#line 2 "alg/monoid/max.hpp"
template <typename E>
struct Monoid_Max {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); }
static constexpr X unit() { return -infty<E>; }
static constexpr bool commute = true;
};
#line 6 "test/5_atcoder/abc266h.test.cpp"
using Mono = Monoid_Max<ll>;
void solve() {
LL(N);
using T = tuple<ll, ll, ll, ll>;
VEC(T, dat, N);
dat.eb(0, 0, 0, 0);
++N;
sort(all(dat), [&](auto& a, auto& b) -> bool {
auto [at, ax, ay, aa] = a;
auto [bt, bx, by, bb] = b;
if (ay < by) return true;
if (ay > by) return false;
return at < bt;
});
SegTree_2D<Mono, ll, false> seg1(N, [&](int i) -> tuple<int, int, ll> {
auto [t, x, y, v] = dat[i];
return {x, x + y - t, Mono::unit()};
});
SegTree_2D<Mono, ll, false> seg2(N, [&](int i) -> tuple<int, int, ll> {
auto [t, x, y, v] = dat[i];
return {x, x - y + t, Mono::unit()};
});
ll ANS = 0;
FOR(i, N) {
const auto [t, x, y, v] = dat[i];
if (i == 0) {
seg1.multiply(i, 0);
seg2.multiply(i, 0);
continue;
}
ll best = -infty<ll>;
chmax(best, seg1.prod(-infty<ll>, x + 1, x + y - t, infty<ll>));
chmax(best, seg2.prod(x, infty<ll>, -infty<ll>, x - y + t + 1));
if (best < 0) continue;
best += v;
chmax(ANS, best);
seg1.multiply(i, best);
seg2.multiply(i, best);
}
print(ANS);
}
signed main() {
solve();
return 0;
}