#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
bool cmp(const pair<int, int>& a, const pair<int, int>& b) {
if (a.first != b.first) {
return a.first < b.first;
}
return a.second > b.second;
}
const long long inf = 2e18;
long long div_up(long long a, long long b) {
if (a < 0) {
return a / b;
}
return (a + b - 1) / b;
}
long long take_photos(int n, int m, int k, vector<int> x, vector<int> y) {
for (int i = 0; i < n; i++) {
if (x[i] > y[i]) {
swap(x[i], y[i]);
}
}
vector<pair<int, int>> pairs;
for (int i = 0; i < n; i++) {
pairs.push_back({x[i], y[i]});
}
sort(pairs.begin(), pairs.end(), cmp);
vector<pair<int, int>> new_pairs;
new_pairs.push_back({-1, -1});
int max_y = -1;
for (int i = 0; i < n; i++) {
if (max_y < pairs[i].second) {
max_y = pairs[i].second;
new_pairs.push_back(pairs[i]);
}
}
n = new_pairs.size();
vector<long long> l(n), r(n);
for (int i = 0; i < n; i++) {
l[i] = new_pairs[i].first;
r[i] = new_pairs[i].second + 1;
}
k = min(k, n - 1);
vector<long long> dp(n, inf);
dp[0] = 0;
for (int jumps = 0; jumps < k; jumps++) {
vector<long long> a(n), b(n);
for (int i = 0; i + 1 < n; i++) {
a[i] = dp[i] + l[i + 1] * l[i + 1] - max(0LL, r[i] - l[i + 1]) * max(0LL, r[i] - l[i + 1]);
b[i] = 2 * l[i + 1];
}
vector<long long> new_dp(n, inf);
vector<pair<long long, int>> ch;
ch.push_back({-1, jumps});
for (int i = jumps + 1; i < n; i++) {
int from = ch[upper_bound(ch.begin(), ch.end(), make_pair(r[i], n)) - ch.begin() - 1].second;
new_dp[i] = r[i] * r[i] + a[from] - b[from] * r[i];
if (i + 1 == n) {
break;
}
if (jumps == 0) {
continue;
}
while (!ch.empty()) {
int last = ch.back().second;
long long x = ch.back().first;
if (a[last] - b[last] * x < a[i] - b[i] * x) {
break;
}
ch.pop_back();
}
int last = ch.back().second;
long long x = div_up(a[i] - a[last], b[i] - b[last]);
ch.push_back({x, i});
}
dp = new_dp;
}
return dp[n - 1];
}
