#include "aliens.h"
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
#define ll long long
#define pb push_back
#define mp make_pair
#define ld long double
#define F first
#define S second
#define pii pair<ll,ll>
#define pdd pair<ld,ld>
using namespace :: std;
const ll maxn=3e5+500;;
const ll inf=1e12+900;
ld tav2(ld x){return x*x;}
vector<pair<pdd,ll> > khat;
vector<pair<ld,ll> > cht;
ll poi;
ld barkhord(ll a,ll b){
return (khat[a].F.F-khat[b].F.F)/(khat[b].F.S-khat[a].F.S);
}
void clearr(){
poi=0;
khat.clear();
cht.clear();
}
void add(ld x,ld v,ll h){
khat.pb(mp(mp(x,v),h));
ll i=khat.size()-1;
while(cht.size() && barkhord(cht.back().S,i)<=cht.back().F)cht.pop_back();
if(cht.empty()){
cht.pb(mp(0,i));
}else{
cht.pb(mp(barkhord(cht.back().S,i),i));
}
}
pair<ld,ll> findMinAt(ld t){
if(cht.size()<=1)poi=0;
else poi=min(poi,(ll)cht.size()-2);
while(poi<cht.size()-1 && cht[poi+1].F<=t)poi++;
ll v=cht[poi].S;
return mp(khat[v].F.F+khat[v].F.S*t,khat[v].S);
}
vector<pii> vec;
ll X[maxn];
ll V[maxn];
const ll maxm=1e6+100;
ll mx[maxm];
ll cnt[maxn];
ld dp[maxn];
pair<ld,ll> solve(vector<pii> vec,ld mid){
clearr();
add(X[0],V[0],0);
for(ll i=0;i<vec.size();i++){
pair<ld,ll> e=findMinAt(vec[i].F);
dp[i]=e.F+tav2(vec[i].F)+mid;
cnt[i]=e.S+1;
add(X[i+1]+dp[i],V[i+1],cnt[i]);
}
return mp(dp[vec.size()-1],cnt[vec.size()-1]);
}
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
swap(n,m);
fill(mx,mx+maxm,inf);
for(ll i=0;i<m;i++){
if(c[i]>r[i]){
swap(c[i],r[i]);
}
mx[r[i]]=min(mx[r[i]],(ll)c[i]);
}
stack<ll> stk;
for(ll i=0;i<n;i++){
while(stk.size() && mx[stk.top()]>=mx[i]){
stk.pop();
}
if(mx[i]!=inf){
stk.push(i);
}
}
while(stk.size()){
vec.pb(mp(stk.top(),mx[stk.top()]));
stk.pop();
}
sort(vec.begin(),vec.end());
X[0]=tav2(vec[0].S);
V[0]=vec[0].S*-2;
for(ll i=0;i+1<vec.size();i++){
X[i+1]=-tav2(max((ll)0,vec[i].F-vec[i+1].S+1))+tav2(vec[i+1].S);
V[i+1]=vec[i+1].S*-2;
}
for(ll i=0;i<vec.size();i++){
vec[i].F++;
}
ld b=0;
ld e=1e13;
for(ll i=0;i<100;i++){
ld mid=(e+b)/2;
pair<ld,ll> r=solve(vec,mid);
if(r.S<=k){
e=mid;
}else{
b=mid;
}
}
pair<ld,ll> rr=solve(vec,e);
return round(rr.F-k*e);
}
