#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = 1e12;
struct CHT {
struct line {
ll a, b, i;
ll f(ll x) { return a * x + b; };
};
ll intersect(line f1, line f2) {
assert(f1.a != f2.a);
return ceil(((double)f2.b - f1.b) / ((double)f1.a - f2.a));
}
vector<line> st;
vector<ll> p;
void insert(line t) {
if (st.empty()) {
st.push_back(t);
p.push_back(-INF);
return;
}
while (!st.empty() && intersect(st.back(), t) <= p.back()) {
p.pop_back();
st.pop_back();
}
p.push_back(intersect(st.back(), t));
st.push_back(t);
}
int opt = 0;
// for every 0 <= i < q x[i] < x[i+1]
line query(ll x) {
int l = 0, r = (int)st.size();
while (r - l > 1) {
int mid = (l + r) / 2;
if (p[mid] <= x) l = mid;
else r = mid;
}
return st[l];
}
};
template<typename T1, typename T2>
pair<T1, T2> operator + (pair<T1, T2> a, pair<T1, T2> b) {
return make_pair(a.first + b.first, a.second + b.second);
};
int n;
vector<long long> l;
vector<long long> r;
long long take_photos(int _n, int m, int k, vector<int> _r, vector<int> _c) {
n = _n;
for (int i = 0; i < n; i++)
if (_r[i] > _c[i]) swap(_r[i], _c[i]);
vector<int> ord(n);
iota(ord.begin(), ord.end(), 0);
sort(ord.begin(), ord.end(), [&](int a, int b) {
if (_r[a] == _r[b]) return _c[a] > _c[b];
return _r[a] < _r[b];
});
l.push_back(-1);
r.push_back(-1);
for (int cur : ord) {
if (r.empty() || r.back() < _c[cur]) {
l.push_back(_r[cur]);
r.push_back(_c[cur]);
}
}
n = (int)l.size() - 1;
vector<ll> dp(n + 1, INF);
vector<ll> t(n + 1);
for (int i = 0; i < n; i++)
t[i] = max(0ll, r[i] - l[i + 1] + 1)
* max(0ll, r[i] - l[i + 1] + 1);
dp[0] = 0;
ll ans = INF;
for (int iter = 1; iter <= k; iter++) {
CHT convex;
vector<ll> newdp(n + 1, INF);
for (int i = 1; i <= n; i++) {
ll a = (-2) * (l[i] - 1);
ll b = (l[i] - 1) * (l[i] - 1) - t[i - 1] + dp[i - 1];
convex.insert({a, b, i});
newdp[i] = convex.query(r[i]).f(r[i]) + r[i] * r[i];
}
dp = newdp;
ans = min(ans, dp[n]);
}
return ans;
}
