#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
bool comp_points(const pair<long long, long long>& a, const pair<long long, long long>& b) {
if (a.first != b.first) {
return a.first < b.first;
}
return a.second > b.second;
}
long long div_up(long long a, long long b) {
if (b < 0) {
a = -a;
b = -b;
}
if (a < 0) {
return a / b;
}
return (a + b - 1) / b;
}
long long take_photos(int n, int m, int k, vector<int> points_x, vector<int> points_y) {
vector<pair<long long, long long>> points;
for (int i = 0; i < n; i++) {
if (points_x[i] > points_y[i]) {
swap(points_x[i], points_y[i]);
}
points.push_back({points_x[i], points_y[i]});
}
sort(points.begin(), points.end(), comp_points);
vector<pair<long long, long long>> points_fin;
points_fin.push_back({-1, -1});
long long cur_largest_y = -2e9;
for (int i = 0; i < n; i++) {
if (points[i].second <= cur_largest_y) {
continue;
}
cur_largest_y = points[i].second;
points_fin.push_back(points[i]);
}
points = points_fin;
n = points.size();
vector<long long> b(n);
for (int i = 0; i < n - 1; i++) {
b[i] = 2 * points[i + 1].first;
}
vector<long long> dp(n, 2e12);
dp[0] = 0;
long long ans = 2e12;
for (int p = 0; p < k; p++) {
vector<long long> new_dp(n, 2e12);
vector<long long> a(n);
for (int i = 0; i < n - 1; i++) {
a[i] = dp[i] + points[i + 1].first * points[i + 1].first -
max(0ll, points[i].second - points[i + 1].first + 1) *
max(0ll, points[i].second - points[i + 1].first + 1);
}
vector<pair<long long, long long>> ch;
ch.push_back({-4e12 - 10, p});
for (int i = p + 1; i < n; i++) {
int j = ch[upper_bound(ch.begin(), ch.end(), make_pair(points[i].second + 1, (long long)(2e18))) - ch.begin() - 1].second;
new_dp[i] = (points[i].second + 1) * (points[i].second + 1) + a[j] - b[j] * (points[i].second + 1);
if (i == n - 1) {
continue;
}
while (true) {
long long x = ch.back().first;
int j = ch.back().second;
if (a[j] - b[j] * x < a[i] - b[i] * x) {
break;
}
ch.pop_back();
}
j = ch.back().second;
long long x = div_up(a[i] - a[j], b[i] - b[j]);
ch.push_back({x, i});
}
dp = new_dp;
ans = min(ans, dp.back());
}
return ans;
}
