#include <bits/stdc++.h>
#include "aliens.h"
//#include "grader.cpp"
using namespace std;
typedef long long ll;
#define F first
#define S second
#define sz(x) int(x.size())
#define all(x) x.begin(),x.end()
#define pb push_back
const int N = 1e5+5, M = 1e6+1;
pair<ll, int> dp[N];
//ll dp[N][2];
vector<int> R[M];
struct Line {
long long m, c;
int cnt;
Line() {}
Line(long long _m, long long _c, int _cnt) : m(_m), c(_c), cnt(_cnt) {}
long long eval(long long x) const { return m * x + c; }
};
struct CHT {
deque <Line> lines;
bool is_invalid(const Line &l1, const Line &l2, const Line &l3) {
return (l3.c - l1.c) * (l1.m - l2.m) <= (l2.c - l1.c) * (l1.m - l3.m);
}
void add(ll m, ll c, int ctr) {
Line new_line(m, c, ctr);
while(sz(lines) >= 2 && is_invalid(lines[sz(lines) - 2], lines.back(), new_line)) lines.pop_back();
lines.push_back(new_line);
}
pair<ll, int> query(long long x) {
while(sz(lines) >= 2 && lines[0].eval(x) > lines[1].eval(x)) lines.pop_front();
return {lines[0].eval(x), lines[0].cnt + 1};
}
};
ll l[N], r[N];
long long take_photos(int n, int m, int k, std::vector<int> roo, std::vector<int> co) {
vector<ll> ro, c;
for (auto &i : roo)ro.push_back(i);
for (auto &i : co)c.push_back(i);
vector<pair<ll, ll>> rng;
for (int i = 0; i < n; i++) {
ll l = min(ro[i], c[i]), rr = max(ro[i], c[i]);
R[rr].push_back(l);
}
int mnl = 1e9;
for (int i = m; i >= 0; i--) {
sort(all(R[i]));
for (auto &l : R[i]) {
if (mnl > l)rng.push_back({l, i});
mnl = min(mnl, l);
}
R[i].clear();
}
sort(all(rng));
n = sz(rng);
k = min(k, sz(rng));
ll st = 0, ed = ll(m) * ll(m), ans = 1e18;
for (int i = 0; i < n; i++) {
l[i] = rng[i].F;
r[i] = rng[i].S;
}
while (st <= ed) {
ll md = (st + ed) / 2ll;
CHT ch;
for (int i = 0; i < n; i++) {
ll cc = 0;
if (i) {
ll xx = max(0ll, r[i-1]-l[i]+1);
cc = dp[i-1].F - (xx * xx);
}
//cout << "bad: " << 2ll * l[i] << " " << -2ll * l[i] + (l[i] * l[i]) + cc << "\n";
ch.add(-2ll * l[i], -2ll * l[i] + (l[i] * l[i]) + cc, (i == 0 ? 0 : dp[i-1].S));
pair<ll, int> xx = ch.query(r[i]);
dp[i] = {md + (r[i] * r[i]) + (2ll * r[i]) + 1ll + xx.F, xx.S};
//cout << l[i] << " " << r[i] << " " << md << " " << dp[i].F << " " << dp[i].S << " ez2\n";
}
if (dp[n-1].S <= k) {
ans = dp[n-1].F - md * ll(k);
ed = md - 1;
} else {
st = md + 1;
}
}
/*int cur = 0, prv = 1;
for (int i = 0; i < n; i++) {
l[i] = rng[i].F, r[i] = rng[i].S;
dp[i][cur] = (r[i] - l[0] + 1ll) * (r[i] - l[0] + 1ll);
//cout << l[i] << " " << r[i] << " " << dp[i][cur] << " ez\n";
}
for (int ii = 0; ii+1 < k; ii++) {
cur ^= 1;
prv ^= 1;
CHT LC;
for (int i = 0; i <= ii; i++) {
ll cc = 0;
if (i) {
ll xx = max(0ll, r[i-1]-l[i]+1);
cc = dp[i-1][prv] - (xx * xx);
}
LC.add(-2ll * l[i], -2ll * l[i] + (l[i] * l[i]) + cc, 0);
dp[i][cur] = dp[i][prv];
//cout << l[i] << " " << r[i] << " " << dp[i][cur] << " ez\n";
}
for (int i = ii+1; i < n; i++) {
ll cc = 0;
if (i) {
ll xx = max(0ll, r[i-1]-l[i]+1);
cc = dp[i-1][prv] - (xx * xx);
}
LC.add(-2ll * l[i], -2ll * l[i] + (l[i] * l[i]) + cc, 0);
dp[i][cur] = (r[i] * r[i]) + (2ll * r[i]) + 1ll + LC.query(r[i]).F;
//cout << l[i] << " " << r[i] << " " << dp[i][cur] << " ez\n";
}
}
ans = dp[n-1][cur];*/
return ans;
}
