#include "aliens.h"
#include <bits/stdc++.h>
#define x first
#define y second
#define all(v) v.begin(), v.end()
using namespace std;
typedef long long ll;
typedef pair<ll, ll> p;
int n, k;
ll dp[101010];
int cnt[101010];
p a[101010];
vector<p> v;
struct CHT{
struct Line{
ll a, b, c;
Line() : Line(0, 0, 0) {}
Line(ll a, ll b, ll c) : a(a), b(b), c(c) {}
ll f(ll x){ return a * x + b; }
};
Line v[101010]; int pv, top;
void init(){ pv = top = 0; }
int chk(const Line &a, const Line &b, const Line &c){
return (double)(a.b - b.b) / (b.a - a.a) >= (double)(c.b - b.b) / (b.a - c.a);
}
void update(Line l){
while(top >= pv+2 && chk(v[top-2], v[top-1], l)) top--;
v[top++] = l;
}
void update(ll a, ll b, ll c){ update({a, b, c}); }
p query(ll x){
while(pv+1 < top && v[pv].f(x) >= v[pv+1].f(x)) pv++;
return {v[pv].f(x), v[pv].c};
}
} cht;
void init(int N, int M, int K, const vector<int> &R, const vector<int> &C){
k = K; v.clear();
for(int i=0; i<N; i++) v.emplace_back(max(R[i], C[i]) + 1, min(R[i], C[i]));
sort(all(v));
for(int i=0; i<N; i++){
while(n && a[n].y >= v[i].y) n--;
a[++n] = v[i];
}
}
int chk(ll c){
cht.init(); cht.update(CHT::Line(-2 * a[1].y * 2, a[1].y * a[1].y * 2, 0));
for(int i=1; i<=n; i++){
auto t = cht.query(a[i].x);
dp[i] = t.x + a[i].x * a[i].x * 2 + c;
cnt[i] = cnt[t.y] + 1;
ll ta = a[i+1].y, tb = max(0LL, a[i].x - a[i+1].y);
ll aa = -2 * a[i+1].y * 2;
ll bb = dp[i] + ta*ta*2 - tb*tb*2;
cht.update(CHT::Line(aa, bb, i));
}
return cnt[n];
}
ll take_photos(int N, int M, int K, vector<int> R, vector<int> C){
init(N, M, K, R, C);
int q = min(n, k);
ll l = 0, r = 1e15;
while(l < r){
ll m = l + r >> 1;
if(chk(m << 1 | 1) <= q) r = m;
else l = m + 1;
}
chk(r << 1);
return dp[n] / 2 - r * q;
}
