#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
const int MAX = 1000005;
struct Line {
long long k, n;
Line() {}
Line(long long _k, long long _n) : k(_k), n(_n) {}
long long get(long long x) {
return k * x + n;
}
};
int root, ls[4 * MAX], rs[4 * MAX], tsz;
Line st[4 * MAX];
void modify(int& node, int l, int r, Line k) {
if (!node) {
node = ++tsz;
st[node] = k;
return;
}
long long a = st[node].get(l);
long long b = k.get(l);
long long c = st[node].get(r);
long long d = k.get(r);
if (a >= b && c >= d) {
return;
}
if (a <= b && c <= d) {
st[node] = k;
return;
}
int mid = l + r >> 1;
if (a <= b) {
swap(st[node], k);
}
if (st[node].get(mid) >= k.get(mid)) {
modify(rs[node], mid + 1, r, k);
} else {
swap(st[node], k);
modify(ls[node], mid, l, k);
}
}
long long query(int node, int l, int r, int i) {
if (!node) {
return -1e18;
}
if (l == r) {
return st[node].get(i);
}
long long val = st[node].get(i);
int mid = l + r >> 1;
if (i <= mid) {
val = max(val, query(ls[node], l, mid, i));
} else {
val = max(val, query(rs[node], mid + 1, r, i));
}
return val;
}
void build() {
for (int i = 1; i <= tsz; i++) {
ls[i] = 0;
rs[i] = 0;
}
root = 0;
tsz = 0;
}
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
for (int i = 0; i < n; i++) {
if (r[i] > c[i]) {
swap(r[i], c[i]);
}
}
vector<int> order(n);
iota(order.begin(), order.end(), 0);
sort(order.begin(), order.end(), [&](int i, int j) {
if (r[i] != r[j]) {
return r[i] < r[j];
} else {
return c[i] > c[j];
}
});
vector<pair<int, int>> pts;
int mx = -1;
for (int id = 0; id < n; id++) {
int i = order[id];
if (c[i] <= mx) {
continue;
} else {
mx = max(mx, c[i]);
pts.emplace_back(r[i], c[i]);
}
}
n = (int) pts.size();
for (int i = 0; i < n; i++) {
r[i] = pts[i].first;
c[i] = pts[i].second;
}
vector<long long> w(n);
for (int i = 1; i < n; i++) {
long long d = c[i - 1] - r[i] + 1;
if (d < 0) {
continue;
}
w[i - 1] = d * d;
}
const long long inf = (long long) 1e18;
vector<long long> dp(n, inf);
for (int t = 0; t < k; t++) {
vector<long long> new_dp(n, inf);
build();
for (int i = 0; i < n; i++) {
new_dp[i] = -query(1, 0, MAX, c[i] + 1) + (c[i] + 1) * 1LL * (c[i] + 1);
long long ft = 0;
if (i > 0) {
ft = dp[i - 1] - w[i - 1];
}
new_dp[i] = min(new_dp[i], ft + (c[i] - r[i] + 1) * 1LL * (c[i] - r[i] + 1));
modify(root, 0, MAX, Line(2 * r[i], -(r[i] * 1LL * r[i] + (i == 0 ? 0LL : ft))));
/*
ft = (c[i] + 1 - r[j]) ^ 2 - w[j]
ft = (c[i] + 1) ^ 2 - 2 * (c[i] + 1) * r[j] + r[j] ^ 2
*/
}
/* for (int i = 0; i < n; i++) {
for (int j = 0; j <= i; j++) {
long long d = c[i] - r[j] + 1;
long long ft = d * d;
if (j > 0) {
ft += dp[j - 1] - w[j - 1];
}
new_dp[i] = min(new_dp[i], ft);
}
} */
swap(dp, new_dp);
}
return dp[n - 1];
}
/*
5 7 2
0 3
4 4
4 6
4 5
4 6
*/
