#include <bits/stdc++.h>
#include "aliens.h"
#define ar array
using namespace std;
using ll = long long;
int n;
vector<ar<ll, 2>> p;
vector<ll> ul, dr;
ar<ll, 2> go(ll penalty) {
//cerr << penalty << '\n';
ll real_cost = 0;
ll total_used = 1;
ll cur_ul = ul[0], cur_dr = dr[0];
ll cur_w = cur_dr-cur_ul+1;
for (int i = 1; i < n; ++i) {
ll extend_ul = min(cur_ul, ul[i]);
ll extend_dr = max(cur_dr, dr[i]);
ll extend_w = extend_dr - extend_ul + 1;
ll extend_cost = extend_w*extend_w - cur_w*cur_w;
ll new_w = dr[i]-ul[i]+1;
ll new_cost = new_w*new_w + penalty;
if (extend_cost < new_cost) {
cur_ul = extend_ul;
cur_dr = extend_dr;
cur_w = extend_w;
} else {
//cerr << cur_w << ' ';
real_cost += cur_w * cur_w;
++total_used;
cur_ul = ul[i];
cur_dr = dr[i];
cur_w = new_w;
}
}
real_cost += cur_w * cur_w;
//cerr << cur_w << '\n';
//cerr << real_cost << ' ' << total_used << '\n';
//cerr << '\n';
return {real_cost, total_used};
}
long long take_photos(int n_, int m, int k, vector<int> r, vector<int> c) {
n = n_;
p.resize(n);
ul.resize(n);
dr.resize(n);
for (int i = 0; i < n; ++i)
p[i] = {r[i], c[i]};
sort(p.begin(), p.end(), [&](auto a, auto b) { return a[0] + a[1] < b[0] + b[1]; });
for (int i = 0; i < n; ++i)
ul[i] = min(p[i][0], p[i][1]);
for (int i = 0; i < n; ++i)
dr[i] = max(p[i][0], p[i][1]);
/*
cerr << "ul: ";
for (int i = 0; i < n; ++i)
cerr << ul[i] << " \n"[i==n-1];
cerr << "dr: ";
for (int i = 0; i < n; ++i)
cerr << dr[i] << " \n"[i==n-1]; // */
const ll INF = 1LL<<50;
ll ans = INF;
ll lo = 0, hi = INF;
while (lo != hi) {
ll ce = lo + (hi-lo)/2;
auto [cost, used] = go(ce);
if (used > k) lo = ce+1;
else hi = ce;
}
hi = INF;
while (lo < hi) {
ll ce1 = lo + (hi-lo)/2;
ll ce2 = ce1+1;
auto [cost1, used1] = go(ce2);
auto [cost2, used2] = go(ce2);
ans = min({ans, cost1, cost2});
if (cost1 > cost2) lo = ce1+1;
else hi = ce2-1;
}
return ans;
}
