//#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define pii pair<int, int>
#define pll pair<ll, ll>
#define all(x) (x).begin(), (x).end()
#define F first
#define S second
deque<pair<pll, int> > dq;
int o;
bool check (ll k, ll b){
auto [k0,b0]=dq[0].F;
auto [k1,b1]=dq[1].F;
// k1 * x + b1 = k0 * x + b0
// (b0 - b1) / (k1 - k0)
// k1 * x + b1 = k * x + b
// (b - b1) / (k1 - k)
//
// k < k0 < k1
//
// (b - b1) / (k1 - k) > (b0 - b1) / (k1 - k0)
// (b - b1) * (k1 - k0) - (b0 - b1) * (k1 - k) > 0
return (b - b1) * (k1 - k0) - (b0 - b1) * (k1 - k) > 0;
}
void add(ll k, ll b, int cnt){
while(dq.size()>1 && check(k, b))dq.pop_front(),o=max(o-1,0);
dq.push_front({{k,b},cnt});
}
pii get(int i, ll x, ll C){
auto [k,b]=dq[i].F;
// cout<<"[i, k, b, x]: "<<i<<" "<<dq.size()<<" "<<k<<" "<<b<<" "<<x<<endl;
return {k*x+b, dq[i].S};
}
ll take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
ll Ans=0;
vector<pll> v, V(n);
for (int i=0; i<n; i++){
if(c[i]<r[i])swap(r[i], c[i]);
V[i]={r[i], -c[i]};
}
sort(all(V));
ll rr=-1;
for (auto [l,r]:V){
r*=-1;
// cout<<r<<endl;
if(r>rr)v.pb({l,r+1});
rr=max(r, rr);
}
V.clear();
n=v.size();
// for (auto [l,r]:v){
// cout<<"[l, r]: "<<l<<" "<<r<<endl;
// }
ll L=0, R=1e18;
while(L<=R){
ll C=(L+R)>>1;
vector<pll> dp(n+1);
dp[0]={0,0};
add(-2*v[0].F, v[0].F*v[0].F, 0);
for (int i=1; i<=n; i++){
auto &[ans, cnt]=dp[i];
ll r=v[i-1].S;
ans=r*r+C;
// cout<<"[ans]: "<<ans<<endl;
cnt=1;
ll x=r;
while(i>1 && get(o,x,C)>get(o+1,x,C))o++;
auto [ans0, cnt0]=get(o,x,C);
// cout<<"[o]: "<<o<<" "<<dq.size()<<endl;
ans+=ans0;
cnt+=cnt0;
if(i==n)continue;
ll l=v[i].F;
add(-2*l, ans + l*l - max((ll)0, r-l)*max((ll)0, r-l), cnt);
}
// for (auto [x, y]:dp){
// cout<<"[dp]: "<<x<<" "<<y<<endl;
// }
if(dp[n].S>=k){
L=C+1;
Ans=dp[n].F-dp[n].S*C;
}else{
// cout<<"[C, Ans]: "<<C<<" "<<Ans<<endl;
R=C-1;
}
dq.clear();
o=0;
}
// dp + (r1-l)^2 - (r2-l)^2
// dp + r1*r1 + l*l - 2*r1*l - (r2-l)^2
// (-2*l) * r1 + (dp - r2*r2 + 2*r2*l)
return Ans;
}
