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test/3_yukicoder/1826.test.cpp
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- Last update: 2025-09-05 13:42:28+09:00
- Problem: https://yukicoder.me/problems/no/1826
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Code
#define PROBLEM "https://yukicoder.me/problems/no/1826"
#include "my_template.hpp"
#include "other/io.hpp"
#include "ds/segtree/dynamic_segtree.hpp"
#include "alg/monoid/max.hpp"
void solve() {
LL(N);
vi X, Y, V;
FOR(N) {
LL(t, x, v);
X.eb(t - x), Y.eb(t + x), V.eb(v);
}
auto I = argsort(X);
X = rearrange(X, I), Y = rearrange(Y, I), V = rearrange(V, I);
ll LIM = 1LL << 31;
Dynamic_SegTree<Monoid_Max<ll>, false> seg(-LIM, LIM);
auto root = seg.new_node(-LIM, LIM);
root = seg.set(root, 0, 0);
FOR(i, N) {
ll x = X[i], y = Y[i], v = V[i];
if (x < 0) continue;
ll t = seg.prod(root, -LIM, y + 1) + v;
root = seg.multiply(root, y, t);
}
print(seg[root].x);
}
signed main() {
solve();
return 0;
}#line 1 "test/3_yukicoder/1826.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1826"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#endif
#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> = numeric_limits<double>::infinity();
template <>
constexpr long double infty<long double> =
numeric_limits<long double>::infinity();
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 pq_max = priority_queue<T>;
template <class T>
using pq_min = 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) {}
UINT 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};
}
constexpr ll TEN[] = {
1LL,
10LL,
100LL,
1000LL,
10000LL,
100000LL,
1000000LL,
10000000LL,
100000000LL,
1000000000LL,
10000000000LL,
100000000000LL,
1000000000000LL,
10000000000000LL,
100000000000000LL,
1000000000000000LL,
10000000000000000LL,
100000000000000000LL,
1000000000000000000LL,
};
template <typename T, typename U>
T SUM(const U &A) {
return std::accumulate(A.begin(), A.end(), T{});
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#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 <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &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 (llabs(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>
vc<T> cumsum(const vc<U> &A, int off = 1) {
int N = A.size();
vc<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>
vc<int> argsort(const vc<T> &A) {
vc<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
// 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() {
memmove(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;
}
}
template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> rd(
T &x) {
rd_integer(x);
}
template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> rd(T &x) {
rd_real(x);
}
template <class T, class U>
void rd(pair<T, U> &p) {
rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < tuple_size<T>::value) {
auto &x = 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...);
}
// 先に用意（既出なら不要）
inline void wt_range(const char *s, size_t n) {
size_t i = 0;
while (i < n) {
if (por == SZ) flush();
size_t chunk = min(n - i, (size_t)(SZ - por));
memcpy(obuf + por, s + i, chunk);
por += chunk;
i += chunk;
}
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const char *s) { wt_range(s, strlen(s)); }
void wt(const string &s) { wt_range(s.data(), s.size()); }
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>
inline void wt_real(T x) {
char buf[64];
// 有効数字 15 桁、通常/指数を自動選択（printf("%.15g") 相当）
int n = std::snprintf(buf, sizeof(buf), "%.15g", (double)x);
// （任意）-0 を 0 に正規化
if (n == 2 && buf[0] == '-' && buf[1] == '0') {
buf[0] = '0';
n = 1;
}
wt_range(buf, (size_t)n);
}
template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> wt(
T x) {
wt_integer(x);
}
template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> wt(T x) {
wt_real(x);
}
inline void wt(bool b) { wt(static_cast<char>('0' + (b ? 1 : 0))); }
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 < tuple_size<T>::value) {
if constexpr (N > 0) wt(' ');
wt(get<N>(t));
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(const 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::flush;
using fastio::print;
using fastio::read;
#if defined(LOCAL)
#define HDR "[DEBUG:", __func__, __LINE__, "]"
#define SHOW(...) \
SHOW_IMPL(__VA_ARGS__, SHOW8, SHOW7, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, \
SHOW1) \
(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, _7, _8, NAME, ...) NAME
#define SHOW1(x) print(HDR, #x, "=", (x)), flush()
#define SHOW2(x, y) print(HDR, #x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v)), \
flush()
#define SHOW6(x, y, z, w, v, u) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v), #u, "=", (u)), \
flush()
#define SHOW7(x, y, z, w, v, u, t) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v), #u, "=", (u), #t, "=", (t)), \
flush()
#define SHOW8(x, y, z, w, v, u, t, s) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v), #u, "=", (u), #t, "=", (t), #s, "=", (s)), \
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) { YA(!t); }
#line 1 "alg/default_prod.hpp"
template <class Monoid>
struct DefaultUnitProd {
using X = typename Monoid::value_type;
static constexpr bool unit_only = true;
X operator()(long long, long long) const { return Monoid::unit(); }
};
#line 2 "ds/segtree/dynamic_segtree.hpp"
/*
要素数の管理が面倒なので, vector<int> を使うようにした.
参照を持っているときに eb が入ると破壊されることに気を付ける必要がある！
*/
template <typename Monoid, bool PERSISTENT,
class DefaultProd = DefaultUnitProd<Monoid>>
struct Dynamic_SegTree {
using MX = Monoid;
using X = typename MX::value_type;
struct Node {
int ch[2];
X x;
};
const ll L0, R0;
DefaultProd default_prod;
vc<Node> node;
static constexpr int NIL = 0;
Dynamic_SegTree(ll L0_, ll R0_, DefaultProd func = DefaultProd{})
: L0(L0_), R0(L0_ == R0_ ? R0_ + 1 : R0_), default_prod(std::move(func)) {
reset();
}
void reserve(int n) { node.reserve(n + 1); }
void reset() { node.clear(), node.eb(Node{NIL, NIL, MX::unit()}); }
inline X get_prod(int i, ll l, ll r) {
if constexpr (kUnitOnly) {
return node[i].x;
} else {
return (i == NIL ? default_prod(l, r) : node[i].x);
}
}
void update(int i, ll l, ll r) {
assert(l + 1 < r);
ll m = (l + r) / 2;
int L = node[i].ch[0], R = node[i].ch[1];
node[i].x = MX::op(get_prod(L, l, m), get_prod(R, m, r));
}
inline int new_root() { return new_node(L0, R0); }
inline int new_node(const X &x) {
node.emplace_back(Node{NIL, NIL, x});
return int(node.size()) - 1;
}
inline int new_node(ll l, ll r) { return new_node(default_prod(l, r)); }
inline int new_node() { return new_node(L0, R0); }
inline Node operator[](int i) const { return node[i]; }
int new_node(const vc<X> &dat) {
assert(L0 == 0 && R0 == len(dat));
auto dfs = [&](auto &dfs, ll l, ll r) -> int {
if (r == l + 1) return new_node(dat[l]);
ll m = (l + r) / 2;
int l_root = dfs(dfs, l, m), r_root = dfs(dfs, m, r);
X x = MX::op(node[l_root].x, node[r_root].x);
node.eb(Node{l_root, r_root, x});
return int(node.size()) - 1;
};
return dfs(dfs, 0, len(dat));
}
X prod(int root, ll l, ll r) {
assert(root != NIL && L0 <= l && l <= r && r <= R0);
if (l == r) return MX::unit();
X x = MX::unit();
prod_rec(root, L0, R0, l, r, x);
return x;
}
X prod_all(int root) { return node[root].x; }
int set(int root, ll i, const X &x) {
assert(root != NIL && L0 <= i && i < R0);
root = copy_node(root);
set_rec(root, L0, R0, i, x);
return root;
}
int multiply(int root, ll i, const X &x) {
assert(root != NIL && L0 <= i && i < R0);
root = copy_node(root);
multiply_rec(root, L0, R0, i, x);
return root;
}
template <typename F>
ll max_right(int root, F check, ll L) {
assert(root != NIL && L0 <= L && L <= R0 && check(MX::unit()));
X x = MX::unit();
return max_right_rec(root, check, L0, R0, L, x);
}
template <typename F>
ll min_left(int root, F check, ll R) {
assert(root != NIL && L0 <= R && R <= R0 && check(MX::unit()));
X x = MX::unit();
return min_left_rec(root, check, L0, R0, R, x);
}
// (idx, val)
template <typename F>
void enumerate(int root, F f) {
assert(root != NIL);
auto dfs = [&](auto &dfs, int c, ll l, ll r) -> void {
if (c == NIL) return;
if (r - l == 1) {
f(l, node[c].x);
return;
}
ll m = (l + r) / 2;
dfs(dfs, node[c].ch[0], l, m), dfs(dfs, node[c].ch[1], m, r);
};
dfs(dfs, root, L0, R0);
}
private:
static constexpr bool kUnitOnly =
std::is_same_v<DefaultProd, DefaultUnitProd<Monoid>>;
int copy_node(int c) {
if constexpr (!PERSISTENT) return c;
if (c == NIL) return c;
node.eb(node[c]);
return int(node.size()) - 1;
}
int touch_child(int c, ll l, ll r) {
if constexpr (!PERSISTENT) {
return (c == NIL ? new_node(l, r) : c);
} else {
return (c == NIL ? new_node(l, r) : copy_node(c));
}
}
void set_rec(int c, ll l, ll r, ll i, const X &x) {
assert(c != NIL);
// もう c は新しくしてある
if (r == l + 1) {
node[c].x = x;
return;
}
ll m = (l + r) / 2;
int b = (m <= i);
ll nl = (b ? m : l), nr = (b ? r : m);
node[c].ch[b] = touch_child(node[c].ch[b], nl, nr);
set_rec(node[c].ch[b], nl, nr, i, x);
update(c, l, r);
}
void multiply_rec(int c, ll l, ll r, ll i, const X &x) {
assert(c != NIL);
// もう c は新しくしてある
if (r == l + 1) {
node[c].x = MX::op(node[c].x, x);
return;
}
ll m = (l + r) / 2;
int b = (m <= i);
ll nl = (b ? m : l), nr = (b ? r : m);
node[c].ch[b] = touch_child(node[c].ch[b], nl, nr);
multiply_rec(node[c].ch[b], nl, nr, i, x);
update(c, l, r);
}
void prod_rec(int c, ll l, ll r, ll ql, ll qr, X &x) {
chmax(ql, l), chmin(qr, r);
if (ql >= qr) return;
if (c == NIL || (l == ql && r == qr)) {
x = MX::op(x, get_prod(c, ql, qr));
return;
}
ll m = (l + r) / 2;
prod_rec(node[c].ch[0], l, m, ql, qr, x);
prod_rec(node[c].ch[1], m, r, ql, qr, x);
}
template <typename F>
ll max_right_rec(int c, const F &check, ll l, ll r, ll ql, X &x) {
if (r <= ql) return R0;
X myprod = get_prod(c, l, r);
if (ql <= l && check(MX::op(x, myprod))) {
x = MX::op(x, myprod);
return R0;
}
if (r == l + 1) return l;
ll m = (l + r) / 2;
ll k = max_right_rec(node[c].ch[0], check, l, m, ql, x);
if (k != R0) return k;
return max_right_rec(node[c].ch[1], check, m, r, ql, x);
}
// これ new node 作ってるのはさぼり
template <typename F>
ll min_left_rec(int c, const F &check, ll l, ll r, ll qr, X &x) {
if (qr <= l) return L0;
X myprod = get_prod(c, l, r);
if (r <= qr && check(MX::op(myprod, x))) {
x = MX::op(x, myprod);
return L0;
}
if (r == l + 1) return r;
ll m = (l + r) / 2;
ll k = min_left_rec(node[c].ch[1], check, m, r, qr, x);
if (k != L0) return k;
return min_left_rec(node[c].ch[0], check, l, m, qr, x);
}
};
#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/3_yukicoder/1826.test.cpp"
void solve() {
LL(N);
vi X, Y, V;
FOR(N) {
LL(t, x, v);
X.eb(t - x), Y.eb(t + x), V.eb(v);
}
auto I = argsort(X);
X = rearrange(X, I), Y = rearrange(Y, I), V = rearrange(V, I);
ll LIM = 1LL << 31;
Dynamic_SegTree<Monoid_Max<ll>, false> seg(-LIM, LIM);
auto root = seg.new_node(-LIM, LIM);
root = seg.set(root, 0, 0);
FOR(i, N) {
ll x = X[i], y = Y[i], v = V[i];
if (x < 0) continue;
ll t = seg.prod(root, -LIM, y + 1) + v;
root = seg.multiply(root, y, t);
}
print(seg[root].x);
}
signed main() {
solve();
return 0;
}