#include "aliens.h"
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
#define x first
#define y second
ll sq(ll a) { return a * a; }
bool cmp(pair<int, int> a, pair<int, int> b) {
if (a.x == b.x) return (a.y > b.y);
return a.x < b.y;
}
ll dp[100001], cnt[100001]{1};
vector<pair<int, int>> useful;
float slope(int i, int j) {
return (sq(useful[j + 1].y) - sq(useful[i + 1].y) + dp[j] - dp[i] +
sq(max(useful[i].x - useful[i + 1].y + 1, 0)) -
sq(max(useful[j].x - useful[j + 1].y + 1, 0))) /
(float)(useful[j + 1].y - useful[i + 1].y);
}
void compute(int lambda, int k) {
deque<int> dq;
dq.push_back(0);
dp[0] = lambda + sq(useful[0].y - useful[0].x + 1);
for (int i = 1; i < useful.size(); i++) {
while (dq.size() > 1 && slope(dq[0], dq[1]) <= 2 * (useful[i].x + 1)) dq.pop_front();
int opt = dq.front();
dp[i] = sq(useful[i].y - useful[opt + 1].x + 1) + dp[opt] -
sq(max(0, useful[opt].y - useful[opt + 1].x + 1)) + lambda;
cnt[i] = cnt[opt] + 1;
while (dq.size() > 1 && slope(dq[dq.size() - 2], dq.back()) >= slope(dq.back(), i)) dq.pop_back();
dq.push_back(i);
}
}
ll take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
vector<pair<int, int>> points;
for (int i = 0; i < n; i++) {
int x = r[i], y = c[i];
if (x > y) swap(x, y);
points.push_back({x, y});
}
sort(points.begin(), points.end(), cmp);
for (int i = 0; i < n; i++)
if (useful.empty() || useful.back().y < points[i].y)
useful.push_back(points[i]);
ll l = 0, u = INT_MAX;
while (l != u) {
ll mid = (l + u) / 2;
compute(mid, k);
if (cnt[useful.size() - 1] <= k) u = mid;
else l = mid + 1;
}
compute(l, k);
return dp[useful.size() - 1] - l * cnt[useful.size() - 1];
}
