#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
struct line
{
long long a,b,id;
line() {}
line(long long _a,long long _b,int _id)
{
a=_a;
b=_b;
id=_id;
}
long long data(long long x)
{
return a*x+b;
}
};
deque<line> cht,cht2;
int num;
pair<int,int> p[200001];
bool cmp(pair<int,int> p1,pair<int,int> p2)
{
if(p1.second==p2.second)return p1.first<p2.first;
return p1.second<p2.second;
}
long long sq(long long x)
{
return x*x;
}
double pt(line l1,line l2)
{
return (double)(l2.b-l1.b)/(double)(l1.a-l2.a);
}
void insert_(line l)
{
//cout<<l.a<<" - "<<l.b<<endl;
while(cht.size()>=2&&pt(cht[cht.size()-1],l)<pt(cht[cht.size()-2],l))cht.pop_back();
cht.push_back(l);
}
int s,ch;
long long dp[200001];
int cnt[200001];
long long value(long long x,int id)
{
s=min(s,(int)cht.size()-1);
int h=s;
long long ans=1e18;
for(int i=s; i<cht.size(); i++)
if(cht[i].id<id)
{
//cout<<cht[i].data(x)<<" ";
if(ans>cht[i].data(x))
ch=cnt[cht[i].id];
ans=min(ans,cht[i].data(x));
if(ans==cht[i].data(x))h=i,ch=min(ch,cnt[cht[i].id]);
else break;
}
else break;
s=h;
//cout<<endl;
return ans;
}
void compute(long long c)
{
cht.clear();
dp[0]=sq(p[0].second-p[0].first+1)+c;
cnt[0]=1;
long long b=-2*p[1].first+dp[0]-sq(max(0,p[0].second-p[1].first+1))+sq(p[1].first);
insert_({-2*p[1].first,b,0});
s=0;
//cout<<"! "<<c<<" !!!"<<endl;
for(int i=1; i<num; i++)
{
dp[i]=sq(p[i].second+1)+value(p[i].second,i)+c;
//cout<<". "<<dp[i]<<endl;
cnt[i]=ch+1;
if(dp[i]>sq(p[i].second-p[0].first+1)+c)
{
dp[i]=sq(p[i].second-p[0].first+1)+c;
//cout<<"? "<<dp[i]<<endl;
cnt[i]=1;
b=-2*p[i+1].first+dp[i]-sq(max(0,p[i].second-p[i+1].first+1))+sq(p[i+1].first);
insert_({-2*p[i+1].first,b,i});
continue;
}
b=-2*p[i+1].first+dp[i]-sq(max(0,p[i].second-p[i+1].first+1))+sq(p[i+1].first);
insert_({-2*p[i+1].first,b,i});
}
//for(int i=0;i<num;i++)
// cout<<dp[i]<<" "<<cnt[i]<<endl;
}
long long dp2[4001][4001];
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c)
{
num=0;
for(int i=0; i<n; i++)
p[i]= {min(r[i],c[i]),max(r[i],c[i])};
sort(p,p+n,cmp);
for(int i=0; i<n; i++)
{
if(i!=0&&p[i].second==p[i-1].second)continue;
while(num!=0&&p[num-1].first>=p[i].first)num--;
p[num++]=p[i];
}
long long ans=1e18;
long long lf=0,rt=1e12;
long long x=0;
while(lf<=rt)
{
int x=(lf+rt)/2;
compute(x);
if(cnt[num-1]<=k)
{
rt=x-1;
ans=x;
}
else lf=x+1;
}
compute(ans);
ans=dp[num-1]-k*ans;
/*long long ans2=1e18;
for(int i=0;i<num;i++)
{
dp2[i][1]=sq(p[i].second-p[0].first+1);
if(i==num-1)ans2=min(ans,dp2[i][1]);
for(int j=2;j<=k;j++)
{
dp2[i][j]=1e18;
for(int l=1;l<=i;l++)
{
//dp[i][j]=min(dp[i][j],dp[l-1][j-1]+sq(p[i].second-p[l].first+1)-sq(max(0,p[l-1].second-p[l].first+1)));
dp2[i][j]=min(dp2[i][j],sq(p[i].second+1)+
(-2*p[l].first*p[i].second-2*p[l].first+dp2[l-1][j-1]-sq(max(0,p[l-1].second-p[l].first+1))+sq(p[l].first)));
}
if(i==num-1)ans2=min(ans2,dp2[i][j]);
}
}
cout<<ans<<" "<<ans2<<endl;
if(ans!=ans2)return -1;*/
return ans;
}
