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 <iostream>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;
struct CONT {
long long int a, b, c;
} a[150005], b[150005];
int za = 0, zb = 0, zc = 0, t[600005];
vector<int> va, vb, vc;
vector<CONT> g[150005];
long long int da[150005], db[150005], dc[150005];
map<int, int> ma, mb, mc;
bool cmp(CONT aa, CONT bb) {
return aa.a < bb.a;
}
bool cmp2(CONT aa, CONT bb) {
return aa.b < bb.b;
}
void Clear(int n) {
for (int i = 1; i <= n * 4; i++) t[i] = 0;
}
void update(int v, int tl, int tr, int x, int y) {
if (tl == tr) {
t[v] = y;
return;
}
int mid = (tl + tr) / 2;
if (mid >= x) update(v * 2, tl, mid, x, y);
else update(v * 2 + 1, mid + 1, tr, x, y);
t[v] = max(t[v * 2], t[v * 2 + 1]);
}
int sum(int v, int tl, int tr, int l, int r) {
if (l > r) return 0;
if (tl == l && tr == r) {
return t[v];
}
int mid = (tl + tr) / 2;
return max(sum(v * 2, tl, mid, l, min(r, mid)), sum(v * 2 + 1, mid + 1, tr, max(l, mid + 1), r));
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int n;
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> a[i].a >> a[i].b >> a[i].c;
va.push_back(a[i].a);
vb.push_back(a[i].b);
vc.push_back(a[i].c);
}
sort(va.begin(), va.end());
sort(vb.begin(), vb.end());
sort(vc.begin(), vc.end());
for (int w : va) {
if (!ma.count(w)) {
ma[w] = ++za;
da[za] = w;
}
}
for (int w : vb) {
if (!mb.count(w)) {
mb[w] = ++zb;
db[zb] = w;
}
}
for (int w : vc) {
if (!mc.count(w)) {
mc[w] = ++zc;
dc[zc] = w;
}
}
for (int i = 1; i <= n; i++) {
a[i].a = ma[a[i].a], a[i].b = mb[a[i].b], a[i].c = mc[a[i].c];
b[i] = a[i];
}
sort(a + 1, a + n + 1, cmp);
sort(b + 1, b + n + 1, cmp2);
long long int res = -1;
for (int i = 1; i <= n; i++) {
long long int h = sum(1, 1, zb, 1, a[i].b - 1);
if (h > a[i].c) g[a[i].b].push_back({a[i].a, a[i].b, h});
update(1, 1, zb, a[i].b, a[i].c);
}
Clear(zb);
for (int i = 1; i <= n; i++) {
long long int h = sum(1, 1, zc, 1, a[i].c - 1);
if (h > a[i].b) g[h].push_back({a[i].a, h, a[i].c});
update(1, 1, zc, a[i].c, a[i].b);
}
Clear(zc);
for (int i = 1; i <= n; i++) {
if (b[i].b != b[i - 1].b) {
for (auto w : g[b[i].b]) {
//cout << i << " " << w.a << " " << w.b << " " << w.c << '\n';
long long int h = sum(1, 1, zc, 1, w.c - 1);
//cout << h << '\n';
if (h > w.a) {
res = max(res, da[h] + db[w.b] + dc[w.c]);
}
}
}
update(1, 1, zc, b[i].c, b[i].a);
}
cout << res;
}
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