#include<bits/stdc++.h>
using namespace std;
#define all(fl) fl.begin(),fl.end()
#define pb push_back
#define fi first
#define se second
#define for1(i,j,k) for(int i=j;i<=k;i++)
#define for2(i,j,k) for(int i=j;i>=k;i--)
#define for3(i,j,k,l) for(int i=j;i<=k;i+=l)
#define lb lower_bound
#define ub upper_bound
#define sz(a) (int)a.size()
#define pii pair<int,int>
#define pli pair<long long,int>
#define gcd __gcd
#define lcm(x,y) x*y/__gcd(x,y)
#define pil pair<int,long long>
#define pll pair<long long,long long>
const int maxn=1e5+4e5+9;
struct tup{
int x,y,z;
bool operator < (const tup& p){
return x<p.x;
}
}a[maxn];
int n;
int ans=-1;
int rx[maxn],ry[maxn],rz[maxn];
void nenso(){
vector<int>n1,n2,n3;
n1.pb(0),n2.pb(0),n3.pb(0);
for1(i,1,n){
n1.pb(a[i].x);
n2.pb(a[i].y);
n3.pb(a[i].z);
}
sort(all(n1)),sort(all(n2)),sort(all(n3));
map<int,int>m1,m2,m3;
for1(i,1,n){
if (n1[i]>n1[i-1]){
m1[n1[i]]=m1[n1[i-1]]+1;
rx[m1[n1[i]]]=n1[i];
}
}
for1(i,1,n){
if (n2[i]>n2[i-1]){
m2[n2[i]]=m2[n2[i-1]]+1;
ry[m2[n2[i]]]=n2[i];
}
}
for1(i,1,n){
if (n3[i]>n3[i-1]){
m3[n3[i]]=m3[n3[i-1]]+1;
rz[m3[n3[i]]]=n3[i];
}
}
for1(i,1,n){
a[i].x=m1[a[i].x];
a[i].y=m2[a[i].y];
a[i].z=m3[a[i].z];
}
}
struct IT{
vector<int>st;
void resz(int _n){
st.resize(4*_n+9);
}
void rep(int id,int l,int r,int u,int val){
if (l>u||r<u)return;
if (l==r){
st[id]=val;
return;
}
int mid=(l+r)/2;
rep(id*2,l,mid,u,val);
rep(id*2+1,mid+1,r,u,val);
st[id]=max(st[id*2],st[id*2+1]);
}
void update(int id,int l,int r,int u,int val){
if (l>u||r<u)return;
if (l==r){
st[id]=max(st[id],val);
return;
}
int mid=(l+r)/2;
update(id*2,l,mid,u,val);
update(id*2+1,mid+1,r,u,val);
st[id]=max(st[id*2],st[id*2+1]);
}
int get(int id,int l,int r,int u,int v){
if (l>v||r<u||u>v)return 0;
if (u<=l&&r<=v)return st[id];
int mid=(l+r)/2;
return max(get(id*2,l,mid,u,v),get(id*2+1,mid+1,r,u,v));
}
int walk(int id,int l,int r,int val){
//max suffix >=val
if (l==r&&st[id]>=val)return l;
if (st[id]<val)return -1;
int mid=(l+r)/2;
if (st[id*2+1]>=val){
return walk(id*2+1,mid+1,r,val);
}
return walk(id*2,l,mid,val);
}
};
int best[maxn];
void yz(){
IT st1,st2,st3;
//st1 mean match for z
//st2 mean max z
//st3 mean max sum
st1.resz(n);
st2.resz(n);
st3.resz(n);
multiset<pii>bestpair;
multiset<pii>::iterator it;
for1(i,1,n)best[i]=0;
for1(i,1,n){
int p=i;
for1(j,i,n){
if (a[i].x==a[j].x){
p=j;
}
else break;
}
for1(j,i,p){
int checkpoint=st2.walk(1,1,n,a[j].z);
if (checkpoint>a[j].y){
ans=max(ans,rx[a[j].x]+st3.get(1,1,n,a[j].y+1,checkpoint));
}
}
for1(j,i,p){
int vl=st1.get(1,1,n,1,a[j].y-1);
if (vl>a[j].z){
//have pair {a[i].y,a[i].z}
if (best[a[j].y]==0){
pii tmp={a[j].y,vl};
bool canadd=true;
if (!bestpair.empty()){
while (!bestpair.empty()){//check for a[j].y<a[i].y and a[j].z<a[i].z
it=bestpair.upper_bound(tmp);
if (it==bestpair.begin())break;
it--;
auto temp=(*it);
if (temp.se<=tmp.se){
bestpair.erase(it);
st2.rep(1,1,n,temp.fi,0);
st3.rep(1,1,n,temp.fi,0);
best[temp.fi]=0;
}
else {
break;
}
}
if (!bestpair.empty()){
it=bestpair.upper_bound(tmp);
if (!bestpair.empty()&&it!=bestpair.end()){
auto temp=(*it);
if (temp.se>=tmp.se){
canadd=false;
}
}
}
}
if (canadd){
bestpair.insert(tmp);
best[a[j].y]=vl;
st2.rep(1,1,n,tmp.fi,tmp.se);
st3.rep(1,1,n,tmp.fi,ry[tmp.fi]+rz[tmp.se]);
}
}
else if (best[a[i].y]<vl){
bestpair.erase(bestpair.find({a[j].y,best[a[j].y]}));
st2.rep(1,1,n,a[j].y,0);
st3.rep(1,1,n,a[j].y,0);
best[a[j].y]=0;
pii tmp={a[j].y,vl};
bool canadd=true;
if (!bestpair.empty()){
while (!bestpair.empty()){//check for a[j].y<a[i].y and a[j].z<a[i].z
it=bestpair.upper_bound(tmp);
if (it==bestpair.begin())break;
it--;
auto temp=(*it);
if (temp.se<=tmp.se){
bestpair.erase(it);
st2.rep(1,1,n,temp.fi,0);
st3.rep(1,1,n,temp.fi,0);
best[temp.fi]=0;
}
else {
break;
}
}
if (!bestpair.empty()){
it=bestpair.upper_bound(tmp);
if (!bestpair.empty()&&it!=bestpair.end()){
auto temp=(*it);
if (temp.se>=tmp.se){
canadd=false;
}
}
}
}
if (canadd){
bestpair.insert(tmp);
best[a[i].y]=vl;
st2.rep(1,1,n,tmp.fi,tmp.se);
st3.rep(1,1,n,tmp.fi,ry[tmp.fi]+rz[tmp.se]);
}
}
}
st1.update(1,1,n,a[j].y,a[j].z);
}
i=p;
}
//for (auto v:bestpair)cout<<v.fi<<" "<<v.se<<'\n';
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
//freopen("temp.INP","r",stdin);
//freopen("temp.OUT","w",stdout);
cin>>n;
for1(i,1,n){
cin>>a[i].x>>a[i].y>>a[i].z;
}
sort(a+1,a+1+n);
nenso();
yz();
for1(i,1,n){
swap(a[i].y,a[i].z);
swap(ry[i],rz[i]);
}
yz();
cout<<ans;
}
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
1 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
1 ms |
340 KB |
Output is correct |
5 |
Correct |
0 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Correct |
0 ms |
340 KB |
Output is correct |
12 |
Correct |
0 ms |
340 KB |
Output is correct |
13 |
Correct |
0 ms |
340 KB |
Output is correct |
14 |
Correct |
1 ms |
340 KB |
Output is correct |
15 |
Runtime error |
1 ms |
596 KB |
Execution killed with signal 6 |
16 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
1 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
1 ms |
340 KB |
Output is correct |
5 |
Correct |
0 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Correct |
0 ms |
340 KB |
Output is correct |
12 |
Correct |
0 ms |
340 KB |
Output is correct |
13 |
Correct |
0 ms |
340 KB |
Output is correct |
14 |
Correct |
1 ms |
340 KB |
Output is correct |
15 |
Runtime error |
1 ms |
596 KB |
Execution killed with signal 6 |
16 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
0 ms |
340 KB |
Output is correct |
5 |
Correct |
1 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Runtime error |
67 ms |
19836 KB |
Execution killed with signal 6 |
12 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
0 ms |
340 KB |
Output is correct |
5 |
Correct |
1 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Runtime error |
67 ms |
19836 KB |
Execution killed with signal 6 |
12 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
0 ms |
340 KB |
Output is correct |
5 |
Correct |
1 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Runtime error |
67 ms |
19836 KB |
Execution killed with signal 6 |
12 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
0 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
0 ms |
340 KB |
Output is correct |
5 |
Correct |
1 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Runtime error |
67 ms |
19836 KB |
Execution killed with signal 6 |
12 |
Halted |
0 ms |
0 KB |
- |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
0 ms |
340 KB |
Output is correct |
2 |
Correct |
1 ms |
340 KB |
Output is correct |
3 |
Correct |
0 ms |
340 KB |
Output is correct |
4 |
Correct |
1 ms |
340 KB |
Output is correct |
5 |
Correct |
0 ms |
340 KB |
Output is correct |
6 |
Correct |
0 ms |
340 KB |
Output is correct |
7 |
Correct |
0 ms |
340 KB |
Output is correct |
8 |
Correct |
0 ms |
340 KB |
Output is correct |
9 |
Correct |
0 ms |
340 KB |
Output is correct |
10 |
Correct |
0 ms |
340 KB |
Output is correct |
11 |
Correct |
0 ms |
340 KB |
Output is correct |
12 |
Correct |
0 ms |
340 KB |
Output is correct |
13 |
Correct |
0 ms |
340 KB |
Output is correct |
14 |
Correct |
1 ms |
340 KB |
Output is correct |
15 |
Runtime error |
1 ms |
596 KB |
Execution killed with signal 6 |
16 |
Halted |
0 ms |
0 KB |
- |