#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<long long, long long>;
const ll inf = 1e18;
const int N = 1e5 + 10;
const int M = 1e6 + 10;
ll n, f[N], mx, minR[M], bestR[M], mxC[M], bestC[M], x[N], y[N];
vector<pll> v, a;
pll dp[N];
struct CHT {
struct line {
ll m, c, cnt;
ll eval(ll x) { return m * x + c; }
};
double intersectX(line a, line b) { return (a.c - b.c) / (b.m - a.m); }
deque<line> dq;
void add(ll m, ll c, ll cnt) {
line l = {m, c, cnt};
while (dq.size() > 1 && intersectX(l, dq[0]) <= intersectX(dq[0], dq[1])) dq.pop_front();
dq.push_front(l);
}
pll get(ll x) {
while (dq.size() > 1 && dq.back().eval(x) > dq.end()[-2].eval(x)) dq.pop_back();
return {dq.back().eval(x), dq.back().cnt};
}
};
pll solve(ll lambda) {
CHT cht;
for (int i = 1; i <= n; i++) dp[i] = {inf, 0};
for (int i = 1; i <= n; i++) {
ll c = x[i] * x[i] + dp[i-1].first;
if (i > 1 && y[i-1] >= x[i]) c -= (y[i-1] - x[i]) * (y[i-1] - x[i]);
cht.add(-2 * x[i], c, dp[i-1].second);
auto [v, cnt] = cht.get(y[i]);
dp[i] = {y[i] * y[i] + lambda + v, cnt + 1};
}
return dp[n];
}
ll take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
for (int i = 0; i < n; i++) if (r[i] > c[i]) swap(r[i], c[i]);
for (int i = 0; i < n; i++) v.push_back({r[i], c[i]});
sort(v.begin(), v.end());
v.resize(unique(v.begin(), v.end()) - v.begin());
n = v.size();
//for (auto [x, y] : v) cout << x << " " << y << "\n";
for (int i = 0; i < m; i++) minR[i] = m;
for (int i = 0; i < m; i++) mxC[i] = bestR[i] = bestC[i] = -1;
for (int i = 0; i < n; i++) {
auto [x, y] = v[i];
if (minR[y] > x) minR[y] = x, bestR[y] = i;
if (mxC[x] < y) mxC[x] = y, bestC[x] = i;
}
//for (int i = 0; i < m; i++) cout << bestR[i] << " "; cout << "\n";
//for (int i = 0; i < m; i++) cout << bestC[i] << " "; cout << "\n";
for (int i = 0; i < m; i++) if (bestR[i] != -1) f[bestR[i]]++;
for (int i = 0; i < m; i++) if (bestC[i] != -1) f[bestC[i]]++;
//for (int i = 0; i < n; i++) cout << f[i] << " "; cout << "\n";
for (int i = 0; i < n; i++) if (f[i] == 2) a.push_back({v[i].first, v[i].second});
//for (auto [x, y] : a) cout << x << " " << y << "\n";
sort(a.begin(), a.end());
n = a.size();
mx = -1;
for (int i = 0; i < n; i++) f[i] = 0;
for (int i = 0; i < n; i++) {
auto [x, y] = a[i];
if (mx < y) mx = y, f[i] = 1;
}
v.clear();
for (int i = 0; i < n; i++) if (f[i]) v.push_back({a[i].first, a[i].second});
n = v.size();
::n = n;
for (int i = 1; i <= n; i++) x[i] = v[i-1].first, y[i] = v[i-1].second + 1;
//cout << "\n" << n << "\n"; for (int i = 1; i <= n; i++) cout << x[i] << " " << y[i] << "\n";
// solve
ll b = 0, e = 1e18;
while (b < e) {
ll mid = (b + e) / 2;
if (solve(mid).second > k) b = mid + 1;
else e = mid;
}
//for (int i = 1; i <= n; i++) cout << dp[i] << " ";
return solve(b).first - b * k;
}
