#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
int n1, k1; vector<long long> lr, rr;
struct l
{
long long m, b, f;
};
struct ch
{
deque<l>dq;
long long ev(const l& li, long long x){return li.m*x+li.b;}
bool ba(const l& l1, const l& l2, const l& l3)
{
return (l3.b-l1.b)*(l1.m-l2.m)<=(l2.b-l1.b)*(l1.m-l3.m);
}
void add(l li)
{
while(dq.size()>=2&&ba(dq[dq.size()-2], dq.back(), li)) dq.pop_back();
dq.push_back(li);
}
pair<long long, int> query(long long x)
{
while(dq.size()>=2&&ev(dq[0], x)>=ev(dq[1], x)) dq.pop_front();
return {ev(dq[0], x), dq[0].f};
}
};
pair<long long, int> p(long long pen)
{
auto adj=[&](long long i)
{
if(i==1) return 0LL; return max(0LL, rr[i-1]-lr[i]+1)*max(0LL, rr[i-1]-lr[i]+1);
};
vector<long long> g(n1+1, 0); vector<int> mf(n1+1, 0); g[0]=0; mf[0]=0;
ch hull; hull.add({0, pen, 0});
for(long long i=1; i<=n1; i++)
{
long long ans=rr[i-1];
pair<long long, int> uj=hull.query(ans);
g[i]=ans*ans+uj.first;
mf[i]=mf[uj.second]+1;
long long mt=-2LL*(lr[i]-1), nt=g[i]+(lr[i]-1)*(lr[i]-1)-adj(i)+pen;
hull.add({mt, nt, i});
}
return {g[n1], mf[n1]};
}
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
k1=k; long long jk=-1;
if(n==0) return 0; vector<pair<long long, long long>> a(n);
vector<long long> ul, tra;
for(long long i=0; i<n; i++)
{
a[i]={min(r[i], c[i]),max(r[i], c[i])};
}
sort(a.begin(), a.end(), [](const auto& a, const auto& b)
{
if(a.first!=b.first) return a.first<b.first; return a.second>b.second;
});
for(auto &x: a)
{
if(x.second<=jk) continue; ul.push_back(x.first); tra.push_back(x.second);
jk=x.second;
}
n1=ul.size(); lr.assign(n1+1, 0); rr.assign(n1+1, 0);
for(long long i=1; i<=n1; i++)
{
lr[i]=ul[i-1]; rr[i]=tra[i-1];
}
rr[0]=0;
auto adj=[&](long long i)
{
if(i==1) return 0LL; return max(0LL, rr[i-1]-lr[i]+1)*max(0LL, rr[i-1]-lr[i]+1);
};
long long l1=1, r2=1e9+7;
while(l1<r2)
{
long long m=(l1+r2)/2; pair<long long, int> u=p(m);
if(u.second>=k){l1=m+1;} else r2=m;
}
vector<long long> dp(n1+1,LLONG_MAX), cu(n1+1, LLONG_MAX);
dp[0]=0;
for(long long i=1; i<=k1; i++)
{
ch hull; hull.add({0, 0, 0});
for(int j=1; j<=n1; j++)
{
long long bt=hull.query(rr[j-1]).first;
cu[j]=(rr[j-1])*(rr[j-1])+bt;
if(dp[j]!=LLONG_MAX)
{
long long mt=-2LL*(lr[j]-1), nt=dp[j]+(lr[j]-1)*(lr[j]-1)-adj(j);
hull.add({mt, nt, j});
}
}
swap(dp, cu); fill(cu.begin(), cu.end(), LLONG_MAX);
}
return dp[n1];
}
