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 pair<int,int> pii;
const int INF=1e9;
int n;
struct point
{
int x,y,z;
} v[150005];
bool byx(point a,point b)
{
return a.x<b.x;
}
bool byy(pii a,pii b)
{
if(a.first!=b.first)
return a.first>b.first;
return a.second<b.second;
}
bool byz(pii a,pii b)
{
if(a.second!=b.second)
return a.second>b.second;
return a.first<b.first;
}
vector<pii> myy,myz;
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
myy.push_back({-INF,INF});
myz.push_back({INF,-INF});
cin>>n;
for(int i=1;i<=n;i++)
cin>>v[i].x>>v[i].y>>v[i].z;
int ans=-1;
sort(v+1,v+n+1,byx);
for(int i=1;i<=n;i++)
{
vector<point> a;
int j=i;
while(j<=n&&v[j].x==v[i].x)
{
a.push_back(v[j]);
j++;
}
for(point p:a)
{
for(pii ymax:myy)
{
if(ymax.first<=p.y)
continue;
int z=-1;
for(pii a:myz)
if(a.first<ymax.first&&a.second>ymax.second)
z=max(z,a.second);
if(z>p.z)
ans=max(ans,ymax.first+z+p.x);
}
for(pii zmax:myz)
{
if(zmax.second<=p.z)
continue;
int y=-1;
for(pii a:myy)
if(a.second<zmax.second&&a.first>zmax.first)
y=max(y,a.first);
if(y>p.y)
ans=max(ans,zmax.second+y+p.x);
}
}
for(point p:a)
{
myy.push_back({p.y,p.z});
sort(myy.begin(),myy.end(),byy);
myy.erase(unique(myy.begin(),myy.end()),myy.end());
if(myy.size()>100)
myy.pop_back();
myz.push_back({p.y,p.z});
sort(myz.begin(),myz.end(),byz);
myz.erase(unique(myz.begin(),myz.end()),myz.end());
if(myz.size()>100)
myz.pop_back();
}
i=j-1;
}
cout<<ans;
return 0;
}
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