#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef int INT;
#define pb push_back
#define FOR(i, l, r) for(int i = (l); i < (r); i++)
#define fst first
#define snd second
#define int long long
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef long long ll;
const ll INF = 1e15;
struct line{
int m, q;
line (int M, int Q) {
m = M;
q = Q;
}
bool operator< (const line &l){
return make_pair(m, q) < make_pair(l.m, l.q);
}
int eval(int x){
return m*x+q;
}
};
double intersect(const line &l1, const line &l2){
return (long double) (l1.q - l2.q) / (l2.m - l1.m);
}
bool bad(const line &l1, const line &l2, const line &l3){
return (l3.q-l2.q) * (l2.m - l1.m) < (l1.q - l2.q) * (l2.m - l3.m);
}
// MAX hull, slopes increasing
struct hull{
deque<line> slopes;
void insert(line l){
while(slopes.size() >= 2 and bad(*prev(slopes.end(), 2), slopes.back(), l)) slopes.pop_back();
slopes.push_back(l);
}
int get(int x){
while(slopes.size() != 1 and slopes[0].eval(x) <= slopes[1].eval(x)) slopes.pop_front();
return slopes[0].eval(x);
}
};
vi C, R;
vii points;
int sqr(int x) {return x*x;}
long long take_photos(INT n, INT m, INT k, std::vector<INT> r, std::vector<INT> c) {
FOR(i, 0, n) if(c[i] < r[i]) swap(r[i], c[i]);
FOR(i, 0, n) points.pb({r[i], c[i]});
points.pb({INF, INF});
sort(points.begin(), points.end());
FOR(i, 0, n){
if(points[i].fst != points[i+1].fst){
if(C.size() == 0 || points[i].snd > C.back()) {R.pb(points[i].fst); C.pb(points[i].snd);}
}
}
//FOR(i, 0, C.size()){
// cout << R[i] << " " << C[i] << endl;
//}
vector<vi> dp;
int N = C.size();
dp.assign(N+1, vi(k+1, -1));
FOR(i, 0, N) dp[i][0] = INF;
FOR(K, 0, k+1) dp[N][K] = 0;
FOR(K, 1, k+1){
hull h;
for(int i = N-1; i >= 0; i--){
h.insert({2*(C[i] +1), -sqr(C[i]+1) - dp[i+1][K-1]});
dp[i][K] = sqr(R[i]) - ( i == 0 ? 0 : sqr(max(0LL, C[i-1] + 1 - R[i])) ) - h.get(R[i]);
//int mi = INF;
//FOR(j, i+1, N+1) mi = min(mi, dp[j][K-1] + sqr(C[j-1]+1 - R[i]) - (i == 0 || C[i-1]+1-R[i] < 0 ? 0 : sqr(C[i-1]+1-R[i]) ) );
//dp[i][K] = mi;
}
}
//FOR(K, 0, k+1) {
// FOR(i, 0, N+1) cout << dp[i][K] << " ";
// cout<<endl;
//}
return dp[0][k];
}
/*
5 7 2
0 3
4 4
4 6
4 5
4 6
4 7 2
4 4
4 6
4 5
4 6
2 7 2
0 1
1 3
2 7 2
0 1
5 7
*/
