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:heavy_check_mark: test_atcoder/abc266h_2.test.cpp

Depends on

Code

#define PROBLEM "https://atcoder.jp/contests/abc266/tasks/abc266_Ex"
#include "my_template.hpp"
#include "other/io.hpp"
#include "ds/fenwicktree/fenwicktree_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;
  });

  vi X1(N), Y1(N), X2(N), Y2(N);
  FOR(i, N) {
    auto [t, x, y, v] = dat[i];
    X1[i] = x;
    X2[i] = -x;
    Y1[i] = t - x - y;
    Y2[i] = x - y + t;
  }
  FenwickTree_2D<Mono, ll, false> seg1(X1, Y1);
  FenwickTree_2D<Mono, ll, false> seg2(X2, Y2);

  ll ANS = 0;
  FOR(i, N) {
    const auto [t, x, y, v] = dat[i];
    const ll a = x, b = y, c = t;
    if (i == 0) {
      seg1.add(a, c - a - b, 0);
      seg2.add(-a, a - b + c, 0);
      continue;
    }
    ll best = -infty<ll>;
    chmax(best, seg1.prefix_sum(x + 1, t - x - y + 1));
    chmax(best, seg2.prefix_sum((-x) + 1, x - y + t + 1));
    if (best < 0) continue;
    best += v;
    chmax(ANS, best);
    seg1.add(a, c - a - b, best);
    seg2.add(-a, a - b + c, best);
  }
  print(ANS);
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}
#line 1 "test_atcoder/abc266h_2.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 u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
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 FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#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_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (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 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;
}
#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;

#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); }
#line 2 "alg/monoid/add.hpp"

template <typename E>
struct Monoid_Add {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 2 "ds/fenwicktree/fenwicktree_2d.hpp"

template <typename Monoid, typename XY, bool SMALL_X = false>
struct FenwickTree_2D {
  using G = Monoid;
  using E = typename G::value_type;
  static_assert(G::commute);
  int N;
  vc<XY> keyX;
  XY min_X;
  vc<int> indptr;
  vc<XY> keyY;
  vc<E> dat;

  FenwickTree_2D(vc<XY>& X, vc<XY>& Y, vc<E> wt) { build(X, Y, wt); }
  FenwickTree_2D(vc<XY>& X, vc<XY>& Y) { build(X, Y); }

  inline int xtoi(XY x) {
    if constexpr (SMALL_X) {
      return clamp<int>(x - min_X, 0, N);
    } else {
      return LB(keyX, x);
    }
  }
  inline int nxt(int i) { return i + ((i + 1) & -(i + 1)); }
  inline int prev(int i) { return i - ((i + 1) & -(i + 1)); }

  void build(vc<XY> X, vc<XY> Y, vc<E> wt) {
    assert(len(X) == len(Y));
    if constexpr (!SMALL_X) {
      keyX = X;
      UNIQUE(keyX);
      N = len(keyX);
    } else {
      min_X = (len(X) == 0 ? 0 : MIN(X));
      N = (len(X) == 0 ? 0 : MAX(X)) - min_X + 1;
      keyX.resize(N);
      FOR(i, N) keyX[i] = min_X + i;
    }

    auto I = argsort(Y);
    X = rearrange(X, I), Y = rearrange(Y, I), wt = rearrange(wt, I);

    FOR(i, len(X)) X[i] = xtoi(X[i]);

    vc<XY> last_y(N, -infty<XY> - 1);
    indptr.assign(N + 1, 0);
    FOR(i, len(X)) {
      int ix = X[i];
      XY y = Y[i];
      while (ix < N) {
        if (last_y[ix] == y) break;
        last_y[ix] = y, indptr[ix + 1]++, ix = nxt(ix);
      }
    }
    FOR(i, N) indptr[i + 1] += indptr[i];
    keyY.resize(indptr.back());
    dat.assign(indptr.back(), G::unit());
    fill(all(last_y), -infty<XY> - 1);
    vc<int> prog = indptr;
    FOR(i, len(X)) {
      int ix = X[i];
      XY y = Y[i];
      E w = wt[i];
      while (ix < N) {
        if (last_y[ix] != y) {
          last_y[ix] = y, keyY[prog[ix]] = y, dat[prog[ix]] = w;
          prog[ix]++;
        } else {
          dat[prog[ix] - 1] = G::op(dat[prog[ix] - 1], w);
        }
        ix = nxt(ix);
      }
    }
    FOR(i, N) {
      int n = indptr[i + 1] - indptr[i];
      FOR(j, n - 1) {
        int k = nxt(j);
        if (k < n)
          dat[indptr[i] + k] = G::op(dat[indptr[i] + k], dat[indptr[i] + j]);
      }
    }
  }

  void build(vc<XY> X, vc<XY> Y) {
    assert(len(X) == len(Y));
    if constexpr (!SMALL_X) {
      keyX = X;
      UNIQUE(keyX);
      N = len(keyX);
    } else {
      min_X = (len(X) == 0 ? 0 : MIN(X));
      N = (len(X) == 0 ? 0 : MAX(X)) - min_X + 1;
      keyX.resize(N);
      FOR(i, N) keyX[i] = min_X + i;
    }

    auto I = argsort(Y);
    X = rearrange(X, I), Y = rearrange(Y, I);

    FOR(i, len(X)) X[i] = xtoi(X[i]);

    vc<XY> last_y(N, -infty<XY> - 1);
    indptr.assign(N + 1, 0);
    FOR(i, len(X)) {
      int ix = X[i];
      XY y = Y[i];
      while (ix < N) {
        if (last_y[ix] == y) break;
        last_y[ix] = y, indptr[ix + 1]++, ix = nxt(ix);
      }
    }
    FOR(i, N) indptr[i + 1] += indptr[i];
    keyY.resize(indptr.back());
    dat.assign(indptr.back(), G::unit());
    fill(all(last_y), -infty<XY> - 1);
    vc<int> prog = indptr;
    FOR(i, len(X)) {
      int ix = X[i];
      XY y = Y[i];
      while (ix < N) {
        if (last_y[ix] == y) break;
        last_y[ix] = y, keyY[prog[ix]++] = y, ix = nxt(ix);
      }
    }
  }

  void add(XY x, XY y, E val) { multiply(x, y, val); }
  void multiply(XY x, XY y, E val) {
    int i = xtoi(x);
    assert(keyX[i] == x);
    while (i < N) { multiply_i(i, y, val), i = nxt(i); }
  }

  E sum(XY lx, XY rx, XY ly, XY ry) { return prod(lx, rx, ly, ry); }
  E prod(XY lx, XY rx, XY ly, XY ry) {
    E pos = G::unit(), neg = G::unit();
    int L = xtoi(lx) - 1, R = xtoi(rx) - 1;
    while (L < R) { pos = G::op(pos, prod_i(R, ly, ry)), R = prev(R); }
    while (R < L) { neg = G::op(neg, prod_i(L, ly, ry)), L = prev(L); }
    return G::op(pos, G::inverse(neg));
  }

  E prefix_sum(XY rx, XY ry) { return prefix_prod(rx, ry); }
  E prefix_prod(XY rx, XY ry) {
    E pos = G::unit();
    int R = xtoi(rx) - 1;
    while (R >= 0) { pos = G::op(pos, prefix_prod_i(R, ry)), R = prev(R); }
    return pos;
  }

private:
  void multiply_i(int i, XY y, E val) {
    int LID = indptr[i], n = indptr[i + 1] - indptr[i];
    auto it = keyY.begin() + LID;
    int j = lower_bound(it, it + n, y) - it;
    while (j < n) { dat[LID + j] = G::op(dat[LID + j], val), j = nxt(j); }
  }

  E prod_i(int i, XY ly, XY ry) {
    E pos = G::unit(), neg = G::unit();
    int LID = indptr[i], n = indptr[i + 1] - indptr[i];
    auto it = keyY.begin() + LID;
    int L = lower_bound(it, it + n, ly) - it - 1;
    int R = lower_bound(it, it + n, ry) - it - 1;
    while (L < R) { pos = G::op(pos, dat[LID + R]), R = prev(R); }
    while (R < L) { neg = G::op(neg, dat[LID + L]), L = prev(L); }
    return G::op(pos, G::inverse(neg));
  }

  E prefix_prod_i(int i, XY ry) {
    E pos = G::unit();
    int LID = indptr[i], n = indptr[i + 1] - indptr[i];
    auto it = keyY.begin() + LID;
    int R = lower_bound(it, it + n, ry) - it - 1;
    while (R >= 0) { pos = G::op(pos, dat[LID + R]), R = prev(R); }
    return pos;
  }
};
#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_atcoder/abc266h_2.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;
  });

  vi X1(N), Y1(N), X2(N), Y2(N);
  FOR(i, N) {
    auto [t, x, y, v] = dat[i];
    X1[i] = x;
    X2[i] = -x;
    Y1[i] = t - x - y;
    Y2[i] = x - y + t;
  }
  FenwickTree_2D<Mono, ll, false> seg1(X1, Y1);
  FenwickTree_2D<Mono, ll, false> seg2(X2, Y2);

  ll ANS = 0;
  FOR(i, N) {
    const auto [t, x, y, v] = dat[i];
    const ll a = x, b = y, c = t;
    if (i == 0) {
      seg1.add(a, c - a - b, 0);
      seg2.add(-a, a - b + c, 0);
      continue;
    }
    ll best = -infty<ll>;
    chmax(best, seg1.prefix_sum(x + 1, t - x - y + 1));
    chmax(best, seg2.prefix_sum((-x) + 1, x - y + t + 1));
    if (best < 0) continue;
    best += v;
    chmax(ANS, best);
    seg1.add(a, c - a - b, best);
    seg2.add(-a, a - b + c, best);
  }
  print(ANS);
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}
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