#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[4004];
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((B.b-A.b) < (__int128)x*(A.a-B.a)) return 1;
else return 0;
}
void insert_line(int num,Line L)
{
while(sz(CHT[num])>2 && check1(CHT[num][sz(CHT[num])-2],CHT[num][sz(CHT[num])-1],L))CHT[num].pop_back();
CHT[num].push_back(L);
}
lint get_min(int num,lint x)
{
if(CHT[num].empty())return 1e18;
if(piv[num]>=sz(CHT[num]))piv[num]=sz(CHT[num])-1;
while(piv[num]+1<sz(CHT[num]) && check2(CHT[num][piv[num]],CHT[num][piv[num]+1],x))piv[num]++;
return CHT[num][piv[num]].a * x + CHT[num][piv[num]].b;
}
lint take_photos(int n, int m, int K, std::vector<int> r, std::vector<int> c) {
lint D[n+1][K+1];
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());
int mini=1e9;
for(int i=sz(Vtmp)-1;i>=0;i--)
{
if(mini>-Vtmp[i].second)V.push_back({Vtmp[i].first,-Vtmp[i].second});
mini=min(mini,-Vtmp[i].second);
}
sort(V.begin(),V.end());
n=sz(V);
for(int i=1;i<=n;i++)
{
a[i]=V[i-1].second;
b[i]=V[i-1].first+1;
}
insert_line(0,{-2*a[1],sq(a[1])});
for(int i=1;i<=n;i++)
{
for(int k=K;k>=1;k--)
{
D[i][k]=get_min(k-1,b[i])+sq(b[i]);
insert_line(k,{-2*a[i+1],D[i][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[n][k]);
return ans;
}
