#include "aliens.h"
#include <vector>
#include <utility>
#include <algorithm>
#include <cstdint>
using namespace std;
pair <int64_t , int> minim[100001] , temporar[100001];
pair < pair <int , int64_t> , int > stiva[100001];
inline pair <int64_t , int> Query (int& inceput , int& sfarsit , const int punct)
{
while (inceput < sfarsit && stiva[inceput + 1].first.second - stiva[inceput].first.second <= 1LL * punct * (stiva[inceput].first.first - stiva[inceput + 1].first.first))
{ inceput++; }
return {1LL * stiva[inceput].first.first * punct + stiva[inceput].first.second , stiva[inceput].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);
for (int indice = 1 ; indice <= dorit ; indice++)
{ minim[indice] = {100000000000000000LL , 0}; }
sir[0] = {-1 , -1};
int64_t inceput = 0 , sfarsit = 100000LL , rezultat = 0;
//while (inceput <= sfarsit)
for (int secvente = 1 ; secvente <= limita ; secvente++)
{
int __stanga = 1 , __dreapta = 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)// + cost
} , minim[dreapta - 1].second + 1
};
while (__stanga < __dreapta && (long double)(candidat.first.second - stiva[__dreapta - 1].first.second) * (stiva[__dreapta - 1].first.first - stiva[__dreapta].first.first) < (long double)(stiva[__dreapta].first.second - stiva[__dreapta - 1].first.second) * (stiva[__dreapta - 1].first.first - candidat.first.first))
{ __dreapta--; }
stiva[++__dreapta] = candidat;
temporar[dreapta] = Query(__stanga , __dreapta , sir[dreapta].second);
temporar[dreapta].first += 1LL * sir[dreapta].second * sir[dreapta].second;
}
for (int indice = 1 ; indice <= dorit ; indice++)
{ minim[indice] = temporar[indice]; }
//if (minim[dorit].second <= limita) { rezultat = minim[dorit].first - cost * limita; sfarsit = cost - 1; }
//else { inceput = cost + 1; }
}
rezultat = minim[dorit].first;
return rezultat;
}
