#include "aliens.h"
#include <cstdio>
#include <cassert>
#include <vector>
#include <iostream>
using namespace std;
int maxim[1000005];
int until[1000005];
int maximpref[1000005];
vector<int>pozitii;
pair<long long,pair<int,int>>dp[1000005];
pair<long long,pair<int,int>> solve(int n,long long mij)
{
for(int i=1;i<=n;i++)
{
dp[i].first=1ll*n*n+mij*n;
dp[i].second.first=0;
dp[i].second.second=0;
if(maxim[i]==n+1)
{
dp[i]=dp[i-1];
continue;
}
for(auto lower:pozitii)
{
if(lower>min(until[i],maxim[i]))
{
break;
}
int nxt=maximpref[lower-1];
long long add;
if(nxt>=lower)
{
add=1ll*(nxt-lower+1)*(nxt-lower+1);
}
else
{
add=0;
}
if(dp[nxt].first+1ll*(i+1)*(i+1)+1ll*lower*lower-1ll*2*(i+1)*lower-add+mij<dp[i].first)
{
dp[i].first=dp[nxt].first+1ll*(i+1)*(i+1)+1ll*lower*lower-1LL*2*(i+1)*lower-add+mij;
dp[i].second.first=dp[nxt].second.first+1;
dp[i].second.second=dp[nxt].second.second+1;
}
else if(dp[nxt].first+1ll*(i+1)*(i+1)+1ll*lower*lower-1ll*2*(i+1)*lower-add+mij==dp[i].first)
{
dp[i].second.second=max(dp[i].second.second,dp[nxt].second.second+1);
dp[i].second.first=min(dp[i].second.first,dp[nxt].second.first+1);
}
}
}
return dp[n];
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
swap(n,m);
for(int i=0;i<=n;i++)
{
maxim[i]=n+1;
until[i]=n+1;
maximpref[i]=0;
}
for(int i=0;i<m;i++)
{
r[i]++;
c[i]++;
maxim[max(r[i],c[i])]=min(maxim[max(r[i],c[i])],min(r[i],c[i]));
maximpref[min(r[i],c[i])]=max(maximpref[min(r[i],c[i])],max(r[i],c[i]));
}
for(int i=1;i<=n;i++)
{
if(maxim[i]!=n+1 || maximpref[i]!=0)
{
pozitii.push_back(i);
}
}
for(int i=1;i<=n;i++)
{
if(maximpref[i]>maximpref[i-1])
{
for(int j=maximpref[i-1]+1;j<=maximpref[i];j++)
{
until[j]=i;
}
}
maximpref[i]=max(maximpref[i],maximpref[i-1]);
}
long long st=0,dr=1e12,best=n*n;
while(st<=dr)
{
long long mij=(st+dr)/2;
pair<long long,pair<int,int> >rez=solve(n,mij);
if(rez.second.first<=k && rez.second.second>=k)
{
//cout<<rez.first<<" "<<rez.second.first<<" "<<rez.second.second<<" "<<mij<<'\n';
best=min(best,rez.first-k*mij);
break;
}
if(rez.second.second<k)
{
best=min(best,rez.first-mij*rez.second.second);
}
if(rez.second.second>k)
{
st=mij+1;
}
else
{
dr=mij-1;
}
}
return best;
}
