#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
const int M = 1e6 + 5;
int n, m, k;
int at[M];
vector<int> ats;
vector<ll> a, b;
const ll is_query = -(1LL<<62);
struct Line {
ll m, b;
int cnt;
mutable function<const Line*()> succ;
bool operator<(const Line& rhs) const {
if (rhs.b != is_query) return m < rhs.m;
const Line* s = succ();
if (!s) return 0;
ll x = rhs.m;
return b - s->b < (s->m - m) * x;
}
};
struct HullDynamic : public multiset<Line> { // will maintain upper hull for maximum
bool bad(iterator y) {
auto z = next(y);
if (y == begin()) {
if (z == end()) return 0;
return y->m == z->m && y->b <= z->b;
}
auto x = prev(y);
if (z == end()) return y->m == x->m && y->b <= x->b;
return (x->b - y->b)*(z->m - y->m) >= (y->b - z->b)*(y->m - x->m);
}
void insert_line(ll m, ll b, int cnt) {
m *= -1;
b *= -1;
auto y = insert({ m, b, cnt });
y->succ = [=] { return next(y) == end() ? 0 : &*next(y); };
if (bad(y)) { erase(y); return; }
while (next(y) != end() && bad(next(y))) erase(next(y));
while (y != begin() && bad(prev(y))) erase(prev(y));
}
pair<ll, int> eval(ll x) {
auto l = *lower_bound((Line) { x, is_query });
return {-(l.m * x + l.b), l.cnt};
}
};
vector<int> go;
tuple<ll, int, ll> get(ll discourage) {
vector<ll> dp(m + 1, 1e18);
dp[0] = 0;
vector<ll> cost(m + 1);
HullDynamic trick;
for(int i = 1; i <= m; i++) {
ll len = max(0LL, b[i - 1] - a[i]);
cost[i] = dp[i - 1] + a[i] * a[i] - len * len;
trick.insert_line(- 2 * a[i], cost[i], go[i - 1] + 1);
auto [res, cnt] = trick.eval(b[i]);
dp[i] = res + b[i] * b[i] + discourage;
go[i] = cnt;
}
// printf("discourage = %.3lf cnt = %d dp = %.3lf real = %lll\n", discourage, cnt, dp[m], ans);
ll ans = dp[m] - go[m] * discourage;
return {dp[m], go[m], ans};
}
ll take_photos(int nn, int mm, int kk, vector<int> rr, vector<int> cc) {
n = nn;
m = mm;
k = kk;
for(int i = 0; i < n; i++) {
if(rr[i] > cc[i]) {
swap(rr[i], cc[i]);
}
at[rr[i] + 1] = max(at[rr[i] + 1], cc[i] + 2);
}
a.push_back(0);
b.push_back(0);
for(int i = 1; i <= m + 1; i++) {
if(at[i]) {
if(!ats.empty() and ats.back() >= at[i]) {
continue;
}
ats.push_back(at[i]);
a.push_back(i);
b.push_back(at[i]);
}
}
m = (int) a.size() - 1;
k = min(k, m);
if(k == 1 or m == 1) {
return (b.back() - a[1]) * (b.back() - a[1]);
}
go.resize(m + 1);
ll l = 0, r = 1e13;
ll ans = 1e18;
while(l < r) {
ll m = (l + r) / 2;
auto [_, used, res] = get(m);
if(used > k) {
l = m + 1;
}
else {
ans = min(ans, res);
r = m;
}
}
auto [_, used, res] = get(l);
ans = res;
return ans;
}
