This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define maxim(X, Y) (X = max(X, Y))
#define all(X) begin(X), end(X)
const int INF = 2e9+5;
struct Fenwick {
int n, *a;
Fenwick(int N) : n(N), a(new int[N+1]) {
fill(a, a + N + 1, -INF);
}
void upd(int i, int v) {
for(++i; i <= n; i += i&-i) maxim(a[i], v);
}
int qry(int i) {
int v = -INF;
for(++i; i >= 1; i -= i&-i) maxim(v, a[i]);
return v;
}
};
int sI, sV;
struct ST {
#define m ((l + r) / 2)
int v;
ST *L = NULL, *R = NULL;
ST() : v(-INF) {};
void upd(int i, int val) {
sI = i, sV = val;
_upd(0, 1<<18);
}
void _upd(int l, int r) {
maxim(v, sV);
if(r - l > 1) {
if(sI < m) (L ? : L = new ST)->_upd(l, m);
if(sI >=m) (R ? : R = new ST)->_upd(m, r);
}
}
int qry(int i) {
sI = i + 1, sV = -INF;
return qry(0, 1<<18), sV;
}
void qry(int l, int r) {
if(r <= sI) return void(maxim(sV, v));
if(l < sI) {
if(L) L->qry(l, m);
if(R) R->qry(m, r);
}
}
};
struct BIT {
int n;
vector<ST*> a;
BIT(int N) : n(N), a(N+1) {
for(auto &i : a) i = new ST;
}
void update(int i, int j, int v) {
for(++i; i <= n; i += i&-i) a[i]->upd(j, v);
}
int query(int i, int j) {
sI = j + 1, sV = -INF;
for(++i; i >= 1; i -= i&-i) a[i]->qry(0, 1<<18);
return sV;
}
};
int main() {
ios::sync_with_stdio(0), cin.tie(0);
int N; cin >> N;
array<int, 3> a[N];
vector<int> C[2];
array<int, 2> sz, c[N];
for(auto &[x, y, z] : a) {
cin >> x >> y >> z;
C[0].push_back(x);
C[1].push_back(y);
}
Fenwick *f[2];
for(int i = 0; i < 2; ++i) {
sort(all(C[i]));
C[i].erase(unique(all(C[i])), end(C[i]));
f[i] = new Fenwick(sz[i] = size(C[i]));
}
sort(a, a + N, [&](const auto &i, const auto &j) {
return i[2] < j[2];
});
BIT b(sz[0]);
for(int i = 0; i < N; ++i)
for(int k = 0; k < 2; ++k)
c[i][k] = sz[k] - 1 - (lower_bound(all(C[k]), a[i][k]) - begin(C[k]));
int ans = -INF;
for(int l = 0, r; l < N; l = r) {
for(r = l + 1; r < N && a[l][2] == a[r][2]; ++r);
for(int i = l; i < r; ++i)
maxim(ans, a[i][2] + b.query(c[i][0] - 1, c[i][1] - 1));
for(int i = l; i < r; ++i) {
int j = f[0]->qry(sz[0] - 2 - c[i][0]);
if(j > sz[1] - 1 - c[i][1])
b.update(c[i][0], sz[1] - 1 - j, a[i][0] + C[1][j]);
j = f[1]->qry(sz[1] - 2 - c[i][1]);
if(j > sz[0] - 1 - c[i][0])
b.update(sz[0] - 1 - j, c[i][1], a[i][1] + C[0][j]);
for(int k = 0; k < 2; ++k)
f[k]->upd(sz[k] - 1 - c[i][k], sz[!k] - 1 - c[i][!k]);
}
}
cout << max(ans, int(-1));
}
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