#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef pair<long long,long long> pp;
#define f first
#define s second
pp a[500005];
long long dp[500005];
pair<pp,int> ss[500005];
int nn;
pp aa[500005];
int p[500005];
inline long double cr(pp x,pp y){
if(x.f==y.f)return 0;
return (long double)(y.s-x.s)/(long double)(x.f-y.f);
}
pair<long long,long long> CHT(long long c){
int i,j=1;
int t=0;
for(i=1 ; i<=nn ; i++){
pair<pp,int> k={{-2*aa[i].f,aa[i].f*aa[i].f+dp[i-1]+c-(long long)(i>=2)*max((long long)0,aa[i-1].s-aa[i].f)*max((long long)0,aa[i-1].s-aa[i].f)},p[i-1]};
while(t>=2 && cr(ss[t].f,ss[t-1].f)>=cr(ss[t].f,k.f))t--;
ss[++t]=k;
for( ; j<t && cr(ss[j].f,ss[j+1].f)<=(long double)aa[i].second ;j++);
/// cout<<j<<endl;
dp[i]=ss[j].f.f*aa[i].s+ss[j].f.s+aa[i].s*aa[i].s;
p[i]=ss[j].s+1;
}
return {p[nn],dp[nn]};
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
long long ans;
int i,j;
for(i=1 ; i<=n ; i++){
a[i]={r[i-1],c[i-1]};
if(a[i].s<a[i].f)swap(a[i].f,a[i].s);
}
sort(a+1,a+n+1);
j=0;
a[0].f=-1;
a[0].s=-1;
a[n+1].f=-1;
for(i=1 ; i<=n ; i++){
if(a[i].s<=a[j].s || a[i].f==a[i+1].f);
else{
aa[++nn]=a[i];
j=i;
}
}
n=nn;
for(i=1 ; i<=nn ; i++){
aa[i].f--;
// cout<<aa[i].f<<" "<<aa[i].s<<"\n";
}
ans=0;
long long lef=0;
long long rig=(long long)m*m;
while(rig>=lef){
long long mid=(lef+rig)/2;
pp v=CHT(mid);
/// cout<<mid<<" "<<v.f<<" "<<v.s<<endl;
if(v.f<=k){
ans=max(ans,-mid*k+v.s);
rig=mid-1;
}
else{
ans=max(ans,-mid*k+v.s);
lef=mid+1;
}
}
return ans;
}
