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;
typedef long long ll;
const int MX=2e5+5;
int N;
int X[MX],Y[MX],Z[MX],mn[MX];
vector<pair<int,int>> ops[MX];
priority_queue<int, vector<int>, greater<int>> pend[MX];
struct segtree {
pair<int,int> t[4 * MX];
void update(int v, int l, int r, int pos, int val) {
if(l > pos || r < pos) return;
if(l == r) {
t[v] = make_pair(val, pos);
return;
}
int mid = (l + r) >> 1;
update(v * 2 + 0, l, mid + 0, pos, val);
update(v * 2 + 1, mid + 1, r, pos, val);
t[v] = min(t[v * 2 + 0], t[v * 2 + 1]);
}
pair<int,int> query(int v, int l, int r, int ql, int qr) {
if(ql > r || qr < l) return make_pair(1e8, 1e8);
if(ql <= l && qr >= r) return t[v];
int mid = (l + r) >> 1;
return min(query(v * 2 + 0, l, mid + 0, ql, qr), query(v * 2 + 1, mid + 1, r, ql, qr));
}
void prep() {
for(int i=0;i<4*MX;i++) t[i]=make_pair(1e8,i);
}
} st, tt;
priority_queue<pair<int,int>> pts;
int rx[MX], ry[MX], rz[MX];
int main() {
cin.tie(0); ios_base::sync_with_stdio(0);
st.prep();
tt.prep();
cin>>N;
map<int,int> ix,iy,iz;
for(int i=0;i<N;i++) {
cin>>X[i]>>Y[i]>>Z[i];
ix[X[i]]=0;
iy[Y[i]]=0;
iz[Z[i]]=0;
}
int p=0;
for(auto &[x,y]:ix) y=p++, rx[y]=x;
p=0;
for(auto &[x,y]:iy) y=p++, ry[y]=x;
p=0;
for(auto &[x,y]:iz) y=p++, rz[y]=x;
for(int i=0;i<N;i++) {
ops[iz[Z[i]]].push_back({ix[X[i]],iy[Y[i]]});
pend[i].push(1e8);
mn[i]=1e8;
}
int ans=-1;
for(int z=0;z<N;z++) {
// evaluate
for(auto [x,y]:ops[z]) {
if(pts.empty()) continue;
auto [yy,xx]=pts.top();
// wanna get rightmost x
int l=xx+1,r=N,res=-1;
while(l<=r) {
int mid=(l+r)/2;
if(tt.query(1,0,N,mid,N).first<yy) {
res=mid,l=mid+1;
} else {
r=mid-1;
}
}
if(res<=x||yy<=y) continue;
ans=max(ans,rz[z]+ry[yy]+rx[res]);
}
// insert
for(auto [x,y]:ops[z]) {
if(tt.query(1,0,N,x+1,N).first>=y) {
pend[y].push(x);
st.update(1,0,N,y,pend[y].top());
} else {
pts.push({y,x});
}
mn[x]=min(mn[x],y);
tt.update(1,0,N,x,mn[x]);
}
for(auto [x,y]:ops[z]) {
while(true) {
auto [v,k]=st.query(1,0,N,y+1,N);
if(v<x) {
pts.push({k,v});
pend[k].pop();
st.update(1,0,N,k,pend[k].top());
} else {
break;
}
}
}
}
cout<<ans<<'\n';
}
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