#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 20;
const long long inf = 1e18L + 20;
const long long max_cost = 1e12L + 20;
long long lt[maxn];
long long rt[maxn];
long long over[maxn];
pair<long long, int> dp[maxn];
long long cost;
int n;
struct line {
long long a, b;
int cnt;
line(long long _a, long long _b, int _cnt): a(_a), b(_b), cnt(_cnt) {};
long long eval(long long x) {
return a * x + b;
};
};
struct CHT {
vector<line> Q;
void add(line L) {
Q.push_back(L);
}
pair<long long, int> get(long long x) {
line best = Q[0];
for (auto L: Q) {
if (L.eval(x) < best.eval(x)) {
best = L;
}
}
return {best.eval(x) + x * x, best.cnt + 1};
}
};
void solve() {
CHT C;
dp[0] = {0, 0};
for (int i = 1; i <= n; i++) {
dp[i] = {inf, -1};
for (int j = 0; j < i; j++) {
dp[i] = min(dp[i], {dp[j].first + rt[i] * (2 - lt[j + 1] * 2) + (lt[j + 1] * lt[j + 1] - lt[j + 1] * 2 - over[j] + cost + 1), dp[j].second + 1});
}
dp[i].first += rt[i] * rt[i];
//Q.add(line(2 - lt[i + 1] * 2, lt[i + 1] * lt[j + 1] - lt[j + 1] * 2 - over[j] + cost + 1, dp[j].second))
}
}
long long take_photos(int _n, int m, int k, std::vector<int> rows, std::vector<int> cols) {
n = _n;
vector<pair<int, int>> p, q;
for (int i = 0; i < n; i++) {
if (rows[i] > cols[i]) {
swap(rows[i], cols[i]);
}
p.push_back({rows[i], -cols[i]});
}
sort(p.begin(), p.end());
for (auto x: p) {
if (q.empty() || x.second < q.back().second) {
q.push_back(x);
}
}
n = q.size();
k = min(k, n);
for (int i = 0; i < n; i++) {
lt[i + 1] = q[i].first;
rt[i + 1] = -q[i].second;
}
over[0] = 0;
for (int i = 1; i <= n - 1; i++) {
long long sz = max(rt[i] - lt[i + 1] + 1, 0LL);
over[i] = sz * sz;
}
long long cost_l = 0;
long long cost_r = max_cost;
long long res = inf;
while (cost_l <= cost_r) {
cost = (cost_l + cost_r) / 2;
solve();
if (dp[n].second <= k) {
res = dp[n].first - cost * k;
cost_r = cost - 1;
}
else {
cost_l = cost + 1;
}
}
return res;
}
