#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
struct LINE{
ld m, c, ocpt; ll chosennumbers;
bool operator !=(const LINE& l)const{
return l.m!=m||l.c!=c||l.ocpt!=ocpt||l.chosennumbers!=chosennumbers;
}
};
deque<LINE>q;
ll outc[100005],outr[100005],outn,outm,outk,getmin[1000005];
pair<ld,ll> dp[1000005];
vector<pair<ll,ll> >need;
pair<ld,ld> int_pt(LINE a, LINE b){
ld x=(b.c-a.c)/(a.m-b.m);
ld y=a.m*x+a.c;
return {x,y};
}
void insert(LINE l){
while(!q.empty()&&int_pt(l,q.back()).first<=q.back().ocpt){
q.pop_back();
}
l.ocpt=int_pt(q.back(),l).first;
q.push_back(l);
}
pair<ld,ll> qry(ld x){
LINE store={-1e18,-1e18,-1e18,-10000000000000},comp=store;
while(!q.empty()&&q.front().ocpt<=x){
store=q.front();
q.pop_front();
}
if(store!=comp){
q.push_front(store);
}
LINE ans=q.front();
return {ans.m*x+ans.c,ans.chosennumbers};
}
bool ck(ld lambda){
// I から j まで の一番小さい 解決の後 は I−１ が 解決 すること出来るかな
// from i to j (i-smallest+1)*(i-smallest+1)+dp[minimum-1]
// i^2 - i*smallest + i + smallest^2 - smallest + i -smallest +1 +dp[i-1]
// i^2 + 2*i + smallest^2 - 2* smallest + 1 + dp[i-1] - smallest*i
// same for all: i^2 + 2*i
// slope: -smallest (x = i)
// constant: smallest^2 - 2*smallest + 1 + dp[i-1]
// もしかしたら、小さいの数は変わってば、dp[0]が使えます
// じゃないなら、slope が入ります
// 一番小さいから、 Alienの cost は ＋cost です
for(int i=0;i<need.size();i++){
// (need[i].first-(cur-1))^2
// need[i].first^2 - 2*(cur-1)*need[i].first + (cur-1)^2
// slope: -2*(cur-1)
// x: need[i].first
// constant: (cur-1)^2 - (need[i+1].second-need[i].first+1)^2 only if need[i+1].second-need[i].first>=0 + dp[cur]
// always part: need[i].first^2
if(i==0){
dp[i]={(need[i].first-need[i].second+1)*(need[i].first-need[i].second+1)+lambda,1};
if(i!=need.size()-1){
// insert part
ld slo=-2*(need[i+1].second-1);
ld con=(need[i+1].second-1)*(need[i+1].second-1);
if(need[i].first-need[i+1].second>=0){
con-=(need[i].first-need[i+1].second+1)*(need[i].first-need[i+1].second+1);
}
con+=dp[i].first;
q.push_back({slo,con,-1e18,dp[i].second});
}
}
else{
pair<ld,ll> take=qry((ld)need[i].first);
take.first= take.first+lambda+need[i].first*need[i].first;
take.second++;
dp[i]=take;
pair<ld,ll>anotheroption={(need[i].first-need[0].second+1)*(need[i].first-need[0].second+1)+lambda,1};
dp[i]=min(dp[i],anotheroption);
if(i!=need.size()-1){
// insert part
ld slo=-2*(need[i+1].second-1);
ld con=(need[i+1].second-1)*(need[i+1].second-1);
if(need[i].first-need[i+1].second>=0){
con-=(need[i].first-need[i+1].second+1)*(need[i].first-need[i+1].second+1);
}
con+=dp[i].first;
insert({slo,con,0,dp[i].second});
}
}
}
while(q.size()){
q.pop_back();
}
return dp[need.size()-1].second<=outk;
// dp[need.size()-1].
}
ld Aliens(){
ld l=0,r=(ld)1000000*(ld)1000000;
while(r-l>=1e-4){
ld mid=(l+r)/2;
// minimum grids
// cout<<mid<<'\n';
if(ck(mid)){
r=mid;
}
else{
l=mid;
}
}
l=r;
ck(l);
// cout<<l<<" ";
// cout<<dp[need.size()-1].first-l*(ld)outk<<"\n";
return dp[need.size()-1].first-l*(ld)outk;
}
ll take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c){
//convert back to array 1-based and cell 1-based
outn=n,outm=m,outk=k;
int storer[n+5], storec[n+5];
for(int i=1;i<=m;i++){
getmin[i]=1e18;
}
vector<ll>lol;
for(int i=1;i<=n;i++){
storer[i]=r[i-1]+1;
storec[i]=c[i-1]+1;
outc[i]=storec[i];
outr[i]=storer[i];
getmin[max(outc[i],outr[i])]=min(getmin[max(outc[i],outr[i])],min(outc[i],outr[i]));
lol.push_back(max(outc[i],outr[i]));
}
outn=n,outm=m,outk=k;
// solve the q find for all m points the minimum size of the square needed
//
// need push backs id then occupy pt
sort(lol.begin(),lol.end());
need.push_back({lol[0],getmin[lol[0]]});
for(int i=1;i<lol.size();i++){
if(lol[i]==lol[i-1]){
continue;
}
while(need.size()){
if(need.back().second>=getmin[lol[i]]){
need.pop_back();
}
else{
break;
}
}
if(getmin[lol[i]]!=1e18){
need.push_back({lol[i],getmin[lol[i]]});
}
}
outk=min(outk,(ll)need.size());
// for(auto u: lol){
// cout<<u<<" ";
// }
// cout<<"\n";
// for(auto u: need){
// cout<<u.first<<" "<<u.second<<"\n";
// }
ld ans=Aliens();
// cout<<ans<<"\n";
// cout<<dp[need.size()-1].second<<"\n";
// cout<<outk<<'\n';
// for(int i=0;i<need.size()-1;i++){
// cout<<dp[i].first<<"\n";
// }
return (ll)round(ans);
}
// #ifndef ONLINE_JUDGE
// int main() {
// int n, m, k;
// assert(3 == scanf("%d %d %d", &n, &m, &k));
// std::vector<int> r(n), c(n);
// for (int i = 0; i < n; i++) {
// assert(2 == scanf("%d %d", &r[i], &c[i]));
// }
// long long ans = take_photos(n, m, k, r, c);
// printf("%lld\n", ans);
// return 0;
// }
// #endif
