#include <bits/stdc++.h>
#include "aliens.h"
using namespace std;
#define int long long
const int inf = 2e18;
#ifdef LOCAL
#include "algo/debug.h"
#endif
#define f first
#define s second
template<class T> using V = vector<T>;
using vi = V<int>;
using vb = V<bool>;
using vs = V<string>;
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define pb push_back
#define lb lower_bound
#define ub upper_bound
template<class T> int lwb(V<T>& a, const T& b) { return lb(all(a),b)-begin(a); }
template<class T> int upb(V<T>& a, const T& b) { return ub(all(a),b)-begin(a); }
template<class T> bool ckmin(T& a, const T& b) { return a > b ? a=b, true : false; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a=b, true : false; }
using pt = complex<int>;
#define x real()
#define y imag()
template<class T> istream& operator>>(istream& in, complex<T>& o) {
T X, Y; in >> X >> Y; o.real(X); o.imag(Y); return in;
}
template<class T> bool operator<(const complex<T>& a, const complex<T>& b) {
if (a.x == b.x) return a.y > b.y;
return a.x < b.x;
}
template<class T> T sqr(const T& a) { return a*a; }
int cdiv(int a, int b) {return a/b + ((a^b)>0&&a%b);}
int n, m, k;
V<pt> inp, pts;
// void solve() {
// cin >> n >> m >> k;
#undef int
long long take_photos(int N, int M, int K, vector<int> XS, vector<int> YS) {
#define int long long
// n = N; m = M; k = K;
inp.resize(n);
for (int i = 0; i < n; i++) {
// cin >> inp[i];
inp[i] = {XS[i], YS[i]};
if (inp[i].x > inp[i].y) inp[i] = {inp[i].y, inp[i].x};
}
inp.pb({-1, -1}); n++;
sort(all(inp), [&](const pt& a, const pt& b) {return a < b;});
int max_y = -2;
for (int i = 0; i < n; i++) {
if (!ckmax(max_y, inp[i].y)) continue;
pts.pb(inp[i]);
}
n = pts.size();
k = min(n-1, k);
vi l(n), r(n);
for (int i = 0; i < n; i++) l[i] = pts[i].x, r[i] = pts[i].y+1;
vi dp(n, inf);
dp[0] = 0;
for (int p = 0; p < k; p++) {
vi a(n-1), b(n-1);
for (int i = 0; i < n-1; i++) {
int cpp = r[i]-l[i+1];
if (cpp < 0) cpp = 0;
a[i] = dp[i] + sqr(l[i+1]) - cpp;
b[i] = 2*l[i+1];
}
V<pt> ch = { {0, p} };
vi new_dp(n, inf);
int cur_entry = 0;
for (int i = p+1; i < n; i++) {
while (cur_entry+1 < ch.size() && ch[cur_entry+1].x <= r[i]) {
cur_entry++;
}
int j = ch[cur_entry].y;
new_dp[i] = sqr(r[i]) + a[j] - b[j]*r[i];
if (i == n-1 || p == 0) {
continue;
}
while (!ch.empty()) {
int j = ch.back().y;
int X = ch.back().x;
if (a[i]-b[i]*X <= a[j]-b[j]*X) {
ch.pop_back();
} else {
break;
}
}
if (ch.empty()) {
ch.pb({0ll, i});
} else {
int j = ch.back().y;
int X = cdiv(a[i]-a[j], b[i]-b[j]);
ch.pb({X, i});
}
if (cur_entry >= ch.size()) {
cur_entry = ch.size()-1;
}
}
dp = new_dp;
}
// cout << dp.back() << '\n';
return dp.back();
}
// signed main() {
// ios::sync_with_stdio(false);
// cin.tie(0); cout.tie(0);
// solve();
// return 0;
// }
