#include <bits/stdc++.h>
#include "aliens.h"
using namespace std;
#define f first
#define s second
#define pb push_back
#define ar array
#define all(x) x.begin(), x.end()
#define siz(x) (int) x.size()
#define uid(a, b) uniform_int_distribution<int>(a, b)(rng)
#define FOR(i, a, b) for(auto i=(a); i<(b); i++)
#define ROF(i, a, b) for(auto i=(b)-1; i>=(a); i--)
#define F0R(i, n) FOR(i, 0, n)
#define R0F(i, n) ROF(i, 0, n)
using ll=long long;
using ld=long double;
using pii=pair<int, int>;
using pll=pair<ll, ll>;
using vi=vector<int>;
using vl=vector<ll>;
using vpii=vector<pii>;
template<class T> bool ckmin(T&a, const T&b) {return b<a?a=b,1:0;}
template<class T> bool ckmax(T&a, const T&b) {return b>a?a=b,1:0;}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int mxN=1e5+10;
const int MOD=1e9+7;
const ll infLL=1e18;
const ld eps=1e-6;
ll n, m, k;
vi r, c;
vector<pair<ll, ll>> pts, pts2;
struct line{
ll M, B; int idx;
ll operator()(ll q)const{
assert(idx!=-1);
return M*q+B;
}
line(){M=-1, B=-1, idx=-1;}
line(ll m, ll b, int IDX):M(m), B(b), idx(IDX){}
};
int L, R;
// we can do convex hull in linear cause we only have x is decreasing order
line A[mxN];
ll ccw(line& o, line& p, line& q) {
return (o.M-p.M)*(o.B-q.B)-(o.B-p.B)*(o.M-q.M);
}
void add(line V){
while(R-L>1&&ccw(A[R-2], A[R-1], V)>=0) R--;
A[R]=V; R++;
}
pair<ll, ll> qry(ll X){
while(R-L>1&&A[L](X)>A[L+1](X)) L++;
assert(L!=R);
return {A[L](X), A[L].idx};
}
pair<ll, ll> solve(ll x){
pair<ll, ll> dp={0, 0};
L=0, R=0;
F0R(i, siz(pts)){
ll A=max(i?pts[i-1].f-pts[i].s+1:0LL, 0LL), B=pts[i].s;
add(line(-2*B, dp.f-A*A+B*B, dp.s));;
A=pts[i].f+1;
dp=qry(A);
dp.s++; dp.f+=A*A+x;
}
return dp;
}
ll take_photos(int N, int M, int K, vi R, vi C){
n=N, m=M, k=K, r=R, c=C;
pts2.clear(); pts.clear();
F0R(i, n){
pts.pb({r[i], c[i]});
if(pts[i].s>pts[i].f) swap(pts[i].s, pts[i].f);
}
sort(all(pts));
// F0R(i, n){
// cout << "PTS: " << pts[i].f << ' ' << pts[i].s << "\n";
// }
F0R(i, n){
while(!pts2.empty()&&pts[i].s<=pts2.back().s)
pts2.pop_back();
pts2.pb(pts[i]);
}
// for(auto v:pts2) cout << v.f << ' ' << v.s << "\n";
pts=pts2;
ll lo=0, hi=(ll)m*m; ll ans=0;
ckmin(k, (ll)siz(pts));
while(lo<=hi){
ll m=(lo+hi)/2;
auto cur=solve(m);
if(cur.s<=k)
ans=cur.f, hi=m-1;
else
lo=m+1;
}
return ans-lo*k;
}
/*
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*/
