#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const ll nx=1e5+5, inf=1e17;
ll area[nx], L=0, R=1e12+5, df[nx];
stack<ll> s;
pair<ll, ll> res;
struct point
{
ll x, y;
bool operator< (const point &o) const {
if (x==o.x) return y>o.y;
return x<o.x;
}
} v[nx], p[nx];
struct line
{
ll m, c, idx;
double p;
line(ll m, ll c, ll idx, ll p): m(m), c(c), idx(idx), p(p){}
};
struct convexhull
{
deque<line> dq;
void add(ll m, ll c, ll idx)
{
line nw=line(m, c, idx, inf);
while (dq.size()>=2&&(double)(nw.c-dq[dq.size()-2].c)/(dq[dq.size()-2].m-nw.m)<=dq[dq.size()-2].p) dq.pop_back();
if (!dq.empty()) dq.back().p=((double)(nw.c-dq.back().c)/(dq.back().m-nw.m));
dq.push_back(nw);
}
pair<ll, ll> query(ll x)
{
while (x>dq.front().p) dq.pop_front();
return {dq.front().m*x+dq.front().c, dq.front().idx};
}
} cvh;
pair<ll, ll> solve(ll x, int sz)
{
vector<pair<ll, ll>> dp(nx);
while (cvh.dq.size()>0) cvh.dq.pop_back();
for (int i=1; i<=sz; i++)
{
dp[i]={df[i]+x, -1};
if (i!=1) cvh.add(-2*p[i].y, p[i].y*p[i].y-2*p[i].y+1-area[i]+dp[i-1].first, i);
if (!cvh.dq.empty())
{
auto tmp=cvh.query(p[i].x);
tmp.first=tmp.first+p[i].x*p[i].x+2*p[i].x+x;
tmp.second=dp[tmp.second-1].second-1;
dp[i]=min(dp[i], tmp);
}
}
return dp[sz];
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
for (int i=0; i<n; i++) if (r[i]>c[i]) swap(r[i], c[i]);
for (int i=1; i<=n; i++) v[i].x=c[i-1], v[i].y=r[i-1];
sort(v+1, v+n+1);
for (int i=1; i<=n; i++)
{
while (!s.empty()&&v[s.top()].y>=v[i].y) s.pop();
s.push(i);
}
n=s.size();
while (!s.empty()) p[s.size()]=v[s.top()], s.pop();
for (int i=2; i<=n; i++) if (p[i-1].x>=p[i].y) area[i]=(p[i-1].x-p[i].y+1)*(p[i-1].x-p[i].y+1);
for (int i=1; i<=n; i++) df[i]=(p[i].x-p[1].y+1)*(p[i].x-p[1].y+1);
k=min(k, n);
while (L<R)
{
ll md=(L+R)/2;
res=solve(md, n);
if (-res.second<=k) R=md;
else L=md+1;
}
//cout<<"sz "<<n<<'\n';
//cout<<"here "<<L<<' '<<solve(L, n).first<<' '<<solve(L, n).second<<'\n';
return solve(L, n).first-k*L;
}
