#include "aliens.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,int> pli;
const int maxn=100010;
struct Section{
int l,r;
Section(int _l=0,int _r=0):l(_l),r(_r){}
inline bool operator<(const Section& rhs) const{
return l!=rhs.l?l<rhs.l:r>rhs.r;
}
inline bool operator==(const Section& rhs) const{
return l==rhs.l && r==rhs.r;
}
};
vector<Section> sec;
pli dp[maxn];
inline pli calc_dp(ll ext){
dp[0]=pli(0,0);
for(int i=1;i<=(int)sec.size();i++){
dp[i]=pli(1ll<<62,100001);
for(int j=1;j<=i;j++){
pli pr=pli(dp[j-1].first+(ll)(sec[i-1].r-sec[j-1].l)*(sec[i-1].r-sec[j-1].l)+ext,dp[j-1].second+1);
if(pr<dp[i]) dp[i]=pr;
}
}
return dp[(int)sec.size()];
}
long long 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]);
sec.push_back(Section(r[i],c[i]+1));
}
sort(sec.begin(),sec.end());
sec.erase(unique(sec.begin(),sec.end()),sec.end());
int mx=-1,sz=0;
for(int i=0;i<(int)sec.size();i++){
if(sec[i].r>mx) sec[sz++]=sec[i],mx=sec[i].r;
}
sec.erase(sec.begin()+sz,sec.end());
k=min(k,(int)sec.size());
ll L=0,R=(ll)m*m+10;
while(L!=R){
ll mid=(L+R)>>1;
if(calc_dp(mid).second<=k) R=mid;
else L=mid+1;
}
return calc_dp(R).first-R*k;
}
