#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define ALL(x) (x).begin(), (x).end()
#define REP(i, l, r) for (int i = (l); i < (r); ++i)
#define len(x) int(x.size())
ll pow2(ll v) { return v * v; }
struct Line {
ll a, b;
ll eval(ll x) { return a * x + b; }
};
struct CHT {
// add: decrease
// query: increase
// query: min
deque<Line> deq;
void add(Line line) {
if (not deq.empty() and deq.front().a == line.a) {
if (deq.front().b < line.b) {
return;
} else {
deq.pop_front();
}
}
while (len(deq) >= 2) {
if (__int128_t(deq[0].a - line.a) *
__int128_t(deq[1].b - deq[0].b) <=
__int128_t(deq[0].b - line.b) *
__int128_t(deq[1].a - deq[0].a)) {
deq.pop_front();
} else {
break;
}
}
deq.push_front(line);
}
ll query(ll x) {
while (len(deq) >= 2) {
if (deq[len(deq) - 1].eval(x) >= deq[len(deq) - 2].eval(x)) {
deq.pop_back();
} else {
break;
}
}
return deq.back().eval(x);
ll mn = 1ll << 60;
for (auto &line : deq)
mn = min(mn, line.eval(x));
return mn;
}
};
long long take_photos(int n, int m, int K, std::vector<int> r,
std::vector<int> c) {
vector<pair<int, int>> pts(n);
REP(i, 0, n) {
if (r[i] > c[i]) {
swap(r[i], c[i]);
}
pts[i] = make_pair(r[i], c[i]);
}
sort(ALL(pts));
{
vector<pair<int, int>> pts2;
REP(i, 0, n) {
if (i != n - 1 and pts[i].first == pts[i + 1].first) {
continue;
}
pts2.push_back(pts[i]);
}
pts = pts2;
n = len(pts);
}
{
vector<pair<int, int>> pts2;
int mx_c = -1;
REP(i, 0, n) {
if (pts[i].second <= mx_c) {
continue;
}
pts2.push_back(pts[i]);
mx_c = max(mx_c, pts[i].second);
}
pts = pts2;
n = len(pts);
}
auto relax = [&](ll lambda) {
vector<ll> dp(n + 1, 1ll << 60);
dp[0] = 0;
CHT cht;
REP(i, 0, n + 1) {
if (i != 0) {
ll x = pts[i - 1].second;
ll mn = cht.query(x);
ll res = mn + x * x + lambda;
dp[i] = res;
}
if (i == n) {
continue;
}
ll a = 2 * (-pts[i].first + 1);
ll diff = pow2(max(0ll, i == 0 ? 0ll : (pts[i - 1].second - pts[i].first + 1)));
ll b = dp[i] + pow2(-pts[i].first + 1) - diff;
cht.add({a, b});
}
return dp[n] - lambda * K;
};
ll lo = -(1ll << 40), hi = 1ll << 40;
while (hi - lo > 3) {
ll m1 = (2 * lo + hi) / 3;
ll m2 = (lo + 2 * hi) / 3;
if (relax(m1) > relax(m2)) {
hi = m2 - 1;
} else {
lo = m1 + 1;
}
}
ll ans = -1;
for (ll lambda = lo; lambda <= hi; ++lambda) {
ans = max(ans, relax(lambda));
}
return ans;
}
