#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
#define block_of_code if(true)
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ll mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
const ll INF = 1e18 + 69;
ll sqr(ll x){return x * x;}
vector<pair<int, int>> compress(vector<pair<int, int>> a){
vector<pair<int, int>> tmp = a;
a.clear();
for(pair<int, int> i: tmp){
if (a.empty() || a.back().second != i.second) a.push_back(i);
else minimize(a.back().first, i.first);
}
return a;
}
struct CHT{
#define Node pair<ll, ll>
vector<Node> a;
vector<int> cnt;
vector<double> bubble;
bool flag;
// if flag = 0: if inserted in decreasing order, return min, otherwise return max
// flag = 1: the opposite
CHT(bool _flag){
flag = _flag;
}
double getInter(Node a, Node b){
double x = (double) (b.second - a.second) / (a.first - b.first);
return x;
}
void add(Node x, int c, bool isMin = 1){
if (a.empty()) {a.push_back(x); cnt.push_back(c); return;}
if (a.back().first == x.first){
if (isMin) {
if (minimize(a.back().second, x.second)) cnt.back() = c;
}
else {
if (maximize(a[a.size() - 1].second, x.second)) cnt.back() = c;
}
if (a.back().second == x.second )
minimize(cnt.back(), c);
return;
}
while(a.size() >= 2){
double x1 = getInter(a.back(), x), x2 = bubble.back();
if (flag){
if (x1 >= x2) break;
}
else{
if (x1 <= x2) break;
}
a.pop_back(); bubble.pop_back(); cnt.pop_back();
}
bubble.push_back(getInter(a.back(), x));
a.push_back(x);
cnt.push_back(c);
}
pair<ll, int> get(ll x){
if (a.empty()) return make_pair(INF, 0);
long idx;
if (flag) idx = lower_bound(ALL(bubble),x) - bubble.begin();
else idx = lower_bound(ALL(bubble), x, greater<double>()) - bubble.begin();
return make_pair(a[idx].first * x + a[idx].second, cnt[idx]);
}
};
int n;
vector<pair<int, int>> point;
vector<int> suff_min, nxt;
pair<ll, ll> go(ll x){
vector<ll> dp(n+1, INF);
vector<int> cnt(n+1);
dp[0] = 0;
CHT hull_min(1);
int j = 1;
for(int i = 1; i<=n; ++i) {
while(j <= nxt[i+1]){
if (dp[j-1] != INF)
hull_min.add({-2 * suff_min[j], sqr(suff_min[j]) + dp[j-1]}, cnt[j-1]);
j++;
}
int L = suff_min[i+1];
ll lmao = 0;
if (L <= point[i].second) lmao = sqr(point[i].second - L + 1);
tie(dp[i], cnt[i]) = hull_min.get(point[i].second + 1);
cnt[i]++;
if (dp[i] != INF){
dp[i] += sqr(point[i].second + 1) - lmao + x;
}
}
// cout << "Mid = " << x << "\n";
// printArr(dp); printArr(cnt);
return make_pair(dp.back(), cnt.back());
}
ll take_photos(int _n, int m, int k, vector<int> R, vector<int> C) {
n = _n;
for(int i = 0; i<n; ++i) {
R[i]++; C[i]++;
if (R[i] > C[i]) swap(R[i], C[i]);
point.push_back({R[i], C[i]});
}
point.push_back({0, 0});
sort(ALL(point), [](pair<int, int> x, pair<int, int> y){return x.second < y.second;});
point = compress(point);
n = point.size() - 1;
suff_min = vector<int>(n+2, m+1);
for(int i = n; i>=0; --i)
suff_min[i] = min(point[i].first, suff_min[i+1]);
nxt = vector<int>(n+2);
for(int i = 1; i<=n+1; ++i){
if (suff_min[i] != suff_min[i-1]) nxt[i] = i-1;
else nxt[i] = nxt[i-1];
}
ll l = 0, r = 1e14;
while(l < r){
ll mid = (l + r) >> 1;
if (go(mid).second <= k) r = mid;
else l = mid + 1;
}
return go(l).first - k * l;
}
// int main(void){
// ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
// clock_t start = clock();
// int n, m, k; cin >> n >> m >> k;
// vector<int> r(m), c(m);
// for(int i = 0; i<n; ++i) cin >> r[i] >> c[i];
// cout << take_photos(n, m, k, r, c) << "\n";
// cerr << "Time elapsed: " << clock() - start << " ms\n";
// return 0;
// }
