#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
pair <int64_t , int> minim[100001];
pair < pair <int , int64_t> , int > stiva[100001];
inline long double Intersectie (pair <int , int64_t> &dreapta_1 , pair <int , int64_t> &dreapta_2)
{
return (long double)(dreapta_2.second - dreapta_1.second) / (dreapta_1.first - dreapta_2.first);
}
inline pair <int64_t , int> Query (const int limita , const int punct)
{
int stanga = 2 , dreapta = limita;
while (stanga <= dreapta)
{
const int mijloc = (stanga + dreapta) >> 1;
if (Intersectie(stiva[mijloc].first , stiva[mijloc - 1].first) <= punct)
{ stanga = mijloc + 1; }
else
{ dreapta = mijloc - 1; }
}
return {1LL * stiva[dreapta].first.first * punct + stiva[dreapta].first.second , stiva[dreapta].second};
}
long long take_photos (int dorit , int lungime , int limita , vector <int> linie , vector<int> coloana)
{
vector < pair <int , int> > sir(dorit + 1);
for (int indice = 0 ; indice < dorit ; indice++)
{
if (coloana[indice] < linie[indice])
{ swap(linie[indice] , coloana[indice]); }
sir[indice + 1] = {linie[indice] , coloana[indice]};
}
sort(sir.begin() , sir.end());
int ramas = 1;
for (int indice = 2 ; indice <= dorit ; indice++)
{
if (sir[ramas].first == sir[indice].first)
{ sir[ramas].second = sir[indice].second; }
else
if (sir[ramas].second < sir[indice].second)
{ sir[++ramas] = sir[indice]; }
}
sir.resize(ramas + 1);
dorit = ramas;
limita = min(limita , dorit);
sir[0] = {-1 , -1};
int64_t inceput = 0 , sfarsit = 1000000000000LL , rezultat = 0;
while (inceput <= sfarsit)
{
int cantitate = 0;
const int64_t cost = (inceput + sfarsit) >> 1;
for (int dreapta = 1 ; dreapta <= dorit ; dreapta++)
{
pair < pair <int , int64_t> , int > candidat = {{
-2 * (sir[dreapta].first - 1) ,
minim[dreapta - 1].first + 1LL * (sir[dreapta].first - 1) * (sir[dreapta].first - 1) - 1LL * max(0 , sir[dreapta - 1].second - sir[dreapta].first + 1) * max(0 , sir[dreapta - 1].second - sir[dreapta].first + 1)
} , minim[dreapta - 1].second + 1
};
while (cantitate > 1 && (Intersectie(candidat.first , stiva[cantitate - 1].first) < Intersectie(stiva[cantitate - 1].first , stiva[cantitate].first) || (Intersectie(candidat.first , stiva[cantitate - 1].first) == Intersectie(stiva[cantitate - 1].first , stiva[cantitate].first) && candidat.second < stiva[cantitate].second)))
{ cantitate--; }
stiva[++cantitate] = candidat;
minim[dreapta] = Query(cantitate , sir[dreapta].second);
minim[dreapta].first += 1LL * sir[dreapta].second * sir[dreapta].second + cost;
}
if (minim[dorit].second <= limita) { rezultat = minim[dorit].first - cost * limita; sfarsit = cost - 1; }
else { inceput = cost + 1; }
}
return rezultat;
}
