#include "bits/stdc++.h"
#include "aliens.h"
using namespace std;
bool query = 0;
struct line{
long long m ,b;
mutable function <const line*()> succ;
bool operator<(const line&rhs) const{
if(!query)
return m < rhs.m;
const line *s = succ();
return s ? (b-s->b) < rhs.m*(s->m-m) : 0;
}
};
struct hull:vector<line>{
bool bad(iterator y){
auto z = next(y);
if(y == begin()){
if(z == end())
return 0;
return (y->m==z->m) && (y->b<=z->b);
}
auto x = prev(y);
if(z == end())
return (y->m==x->m) && (y->b<=x->b);
return (1.0)*(x->b-y->b)*(z->m-y->m) >= (1.0)*(y->b-z->b)*(y->m-x->m);
}
void add(long long m ,long long b){
push_back({-m ,-b}); //remove - for max
auto it = prev(end());
it -> succ = [=]{ return next(it)==end() ? 0:&*next(it); };
if(bad(it)){
erase(it);
return;
}
while(next(it) != end() && bad(next(it))) erase(next(it));
while(it != begin() && bad(prev(it))) erase(prev(it));
}
long long eval(long long x){
if(empty())
return -LLONG_MAX;
query = 1;
auto l = *lower_bound(begin() ,end() ,line{x,0});
query = 0;
return -(l.m*x+l.b); //remove - for max
}
};
long long sqr(long long num){
return num*num;
}
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
vector <pair<int ,int>> rngs ,po;
for(int i=0; i<n; i++){
if(r[i] < c[i])
swap(r[i] ,c[i]);
rngs.push_back({c[i] ,-r[i]});
}
sort(rngs.begin() ,rngs.end());
int mx = -1;
for(auto&r : rngs) if(-r.second > mx){
po.push_back({r.first ,-r.second+1});
mx = -r.second;
}
po.insert(po.begin() ,make_pair(-1 ,0));
n = po.size();
vector <long long> dp(n ,1e18) ,exdp(n ,1e18);
dp[0] = 0 ,exdp[0] = 0;
while(k--){
swap(dp ,exdp);
hull h;
for(int i=1; i<n; i++){
h.add(-2*po[i].first ,exdp[i-1] + sqr(po[i].first) - sqr(max(0 ,po[i-1].second-po[i].first)));
dp[i] = sqr(po[i].second) + h.eval(po[i].second);
///for(int j=0; j<i; j++)
/// dp[i] = min(dp[i] ,exdp[j] + sqr(po[i].second-po[j+1].first+1) - sqr(max(0 ,po[j].second-po[j+1].first+1)));
}
}
return dp.back();
}
