#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
#define sz(v) ((int)(v).size())
typedef long long lint;
typedef pair<int,int> pii;
vector<pii>Vtmp,V;
lint sq(int L)
{
return 1ll*L*L;
}
int a[500004],b[500004];
struct Line{
lint a,b;
};
vector<Line>CHT[4004];
int piv[500004];
int N;
lint D[500004];
bool cmp(pii A,pii B){
return A.second!=B.second?A.second<B.second:A.first>B.first;
}
bool check1(Line A,Line B,Line C)
{
if((__int128)(B.b-A.b)*(B.a-C.a) >= (__int128)(C.b-B.b)*(A.a-B.a))return 1;
else return 0;
}
bool check2(Line A,Line B,lint x)
{
if((__int128)(B.b-A.b) < (__int128) x*(A.a-B.a)) return 1;
else return 0;
}
void insert_line(int num,Line L)
{
while((int)CHT[num].size()>2 && check1(CHT[num][(int)CHT[num].size()-2],CHT[num][(int)CHT[num].size()-1],L)){
CHT[num].pop_back();
}
CHT[num].push_back(L);
piv[num]=min(piv[num],(int)CHT[num].size()-1);
}
lint gets(int num,lint x)
{
int q=sz(CHT[num])-1,h;
while(q!=0 && !check2(CHT[num][q-1],CHT[num][q],x))q--;
return CHT[num][q].a * x + CHT[num][q].b;
}
lint take_photos(int n, int m, int K, std::vector<int> r, std::vector<int> c) {
for(int i=0;i<n;i++)
{
if(r[i]>c[i])swap(r[i],c[i]);
Vtmp.push_back({r[i],c[i]});
}
sort(Vtmp.begin(),Vtmp.end(),cmp);
int N=0;
for(auto &z:Vtmp)
{
while(N && a[N]>=z.first)N--;
a[N+1]=z.first;
b[N+1]=z.second+1;
N++;
}
n=N;
insert_line(0,{-2*a[1],sq(a[1])});
K=min(K,n);
for(int i=0;i<=K;i++)piv[i]=0;
for(int i=1;i<=n;i++)
{
for(int k=min(K,i);k>=1;k--)
{
D[k]=gets(k-1,b[i])+sq(b[i]);
if(i!=n)insert_line(k,{-2*a[i+1],D[k]+sq(a[i+1])-sq(b[i]-min(b[i],a[i+1]))});
}
}
lint ans=1e18;
for(int k=1;k<=K;k++)ans=min(ans,D[k]);
return ans;
}
