#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;
class line{ public:
ll m, n;
int cnt;
line(ll m, ll n, int cnt) {
this -> m = m;
this -> n = n;
this -> cnt = cnt;
}
long double intersect(line oth) {
return (long double) (n - oth.n) / (oth.m - m);
}
};
class convex{ public:
int ptr;
vector < line > v;
void init() {
ptr = 0;
v.clear();
}
void add(ll m, ll n, int cnt) {
while(ptr + 1 < v.size()) {
line l1 = v[v.size() - 2];
line l2 = v[v.size() - 1];
line l3 = {m, n, cnt};
if(l1.intersect(l2) < l1.intersect(l3))
break;
v.pop_back();
}
v.push_back({m, n, cnt});
}
pair<ll, int> query(ll x) {
while(ptr + 1 < v.size()) {
line l1 = v[ptr];
line l2 = v[ptr + 1];
if(l1.intersect(l2) >= x)
break;
ptr++;
}
return {v[ptr].m * x + v[ptr].n, v[ptr].cnt};
}
};
vector<int> go;
tuple<ll, int, ll> get(ll discourage) {
vector<ll> dp(m + 1, (ll) 1e18);
dp[0] = 0;
vector<ll> cost(m + 1);
convex trick;
trick.init();
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.add(- 2 * a[i], cost[i], go[i - 1]);
auto [res, cnt] = trick.query(b[i]);
dp[i] = res + b[i] * b[i] + discourage;
go[i] = cnt + 1;
}
// printf("discourage = %.3lf cnt = %d dp = %.3lf real = %lll\n", discourage, cnt, dp[m], ans);
ll ans = dp[m] - k * 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 = 1e12;
ll ans = 1e18;
while(l < r) {
ll m = (l + r) / 2;
auto [_, used, res] = get(m);
if(used > k) {
l = m + 1;
}
else {
r = m;
}
}
auto [_, used, res] = get(l);
ans = res;
return ans;
}
