#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
auto [fl, fr] = [&]() -> array<vector<long long>, 2> {
vector<array<int, 2>> fetch;
for (int i = 0; i < n; i++) {
fetch.push_back({min(r[i], c[i]), max(r[i], c[i]) + 1});
}
sort(fetch.begin(), fetch.end(), [&](array<int, 2> lr0, array<int, 2> lr1) {
if (lr0[0] != lr1[0]) return lr0[0] < lr1[0];
return lr0[1] > lr1[1];
});
vector<long long> fl, fr;
for (auto [l, r] : fetch) {
if (!fr.empty() && fr.back() >= r) continue;
fl.push_back(l);
fr.push_back(r);
}
return {fl, fr};
}();
n = fl.size();
k = min(n, k);
auto getExtremum = [&](long long lambda) -> pair<long long, int> {
auto cost = [&](int j, int i) -> long long {
long long d = max(0LL, j == 0 ? 0LL : fr[j - 1] - fl[j]);
return (fr[i - 1] - fl[j]) * (fr[i - 1] - fl[j]) - d * d + lambda;
};
vector<long long> dp(n + 1);
vector<int> arg(n + 1);
dp[0] = arg[0] = 0;
deque<array<int, 2>> deq = { {0, 1} };
for (int i = 1; i <= n; i++) {
if (deq.size() >= 2 && deq[1][1] == i) deq.pop_front();
int j = deq.front()[0];
dp[i] = dp[j] + cost(j, i);
arg[i] = arg[j] + 1;
if (i == n) break;
while (!deq.empty()) {
int j = deq.back()[0];
int k = max(i + 1, deq.back()[1]);
if (dp[i] + cost(i, k) < dp[j] + cost(j, k)) {
deq.pop_back();
} else {
break;
}
}
if (deq.empty()) {
deq.push_back({i, i + 1});
} else {
int l = max(i + 1, deq.back()[1]), r = n + 1;
int j = deq.back()[0];
while (l < r) {
int m = (l + r) >> 1;
if (dp[i] + cost(i, m) < dp[j] + cost(j, m)) {
r = m;
} else {
l = m + 1;
}
}
if (l <= n) {
deq.push_back({i, l});
}
}
}
return make_pair(dp[n], arg[n]);
};
long long lambda = [&]() -> long long {
long long l = 0, r = 1e18;
while (l < r) {
long long m = (l + r) >> 1;
auto [extre, arg] = getExtremum(m);
if (arg <= k) {
r = m;
} else {
l = m + 1;
}
}
return l;
}();
auto [extre, arg] = getExtremum(lambda);
return extre - lambda * k;
}
