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 pb push_back
#define fi first
#define se second
#define sz(a) a.size()
#define all(a) a.begin(),a.end()
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
typedef pair<int,int> pii;
typedef long long int ll;
const int MAXN = 5e5;
array<ll,3>pts1[MAXN],pts2[MAXN];
vector<int>crd[3];
//i have rectangle queries but i cant do it offline?
//i can but its double log on 2s
//ok try n^2 first
int main()
{
owo
int n;
cin>>n;
vector<array<ll,3>>a(n);
for(int i=0;i<n;i++){
for(int j=0;j<3;j++){
cin>>a[i][j];
crd[j].pb(a[i][j]);
}
}
sort(all(a),[&](array<ll,3>i,array<ll,3>j){return j[0] > i[0];});
for(int j=0;j<3;j++){
sort(all(crd[j]));
crd[j].resize(unique(all(crd[j])) - crd[j].begin());
}
//cout<<"sorted"<<'\n';
//for(int i=0;i<n;i++)cout<<a[i][0]<<" "<<a[i][1]<<" "<<a[i][2]<<'\n';
for(int i=0;i<n;i++){
pts1[i][0] = pts2[i][0] = -2e9;
pts1[i][1] = a[i][1]; //i has bigger b
pts2[i][2] = a[i][2]; //i has bigger c
for(int j=0;j<i;j++){
if(a[j][1] < a[i][1])pts1[i][2] = max(pts1[i][2],a[j][2]);
if(a[j][2] < a[i][2])pts2[i][1] = max(pts2[i][1],a[j][1]);
}
if(pts1[i][2] > a[i][2])pts1[i][0] = pts1[i][1] + pts1[i][2];
if(pts2[i][1] > a[i][1])pts2[i][0] = pts2[i][1] + pts2[i][2];
}
ll ans = -1;
for(int i=0;i<n;){
int k = i;
while(k+1<n && a[k][0] == a[k+1][0])k++;
for(int x=i;x<=k;x++){
for(int j=0;j<x;j++){
if(a[x][0] == a[j][0])break;
if(pts1[j][1] > a[x][1] && pts1[j][2] >a[x][2])ans = max(ans,a[x][0] + pts1[j][0]);
if(pts2[j][1] > a[x][1] && pts2[j][2] >a[x][2])ans = max(ans,a[x][0] + pts2[j][0]);
}
}
i = k+1;
}
cout<<ans;
}
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