#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;
};
Line st[500004];
int sz;
int N;
lint D[500004],E[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;
}
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;
K=min(K,n);
for(int i=1;i<=n;i++)D[i]=sq(b[i]-a[1]);
for(int k=2;k<=K;k++)
{
for(int i=1;i<=n;i++)E[i]=D[i];
int piv=1;
sz=0;
for(int i=k;i<=n;i++)
{
Line ne={-2*a[i],E[k]+sq(a[i])-sq(b[i-1]-min(b[i-1],a[i]))};
while(sz>=2 && check1(st[sz-1],st[sz],ne))sz--;
if(piv>sz)piv=sz;
st[++sz]=ne;
while(piv<sz && check2(st[piv-1],st[piv],b[i]))piv++;
Line j=st[piv];
D[i]=j.a*b[i]+j.b+sq(b[i]);
}
}
return D[n];
}
