#include<bits/stdc++.h>
#include "aliens.h"
#define MAX_N 100005
#define fi first
#define se second
#define sq(x) ((x)*(x))
using namespace std;
typedef long long LL;
typedef pair<LL,LL> pil;
struct node{
LL s,e;
}V[MAX_N];
LL s,e;
LL dp[MAX_N];
pil L[MAX_N];
bool is_ok(pil a,pil b,pil c){
return (b.se-a.se)*(b.fi-c.fi)<(a.fi-b.fi)*(c.se-b.se);
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
LL i;
for(i=1;i<=n;i++){
V[i].s=min(r[i-1],c[i-1]);
V[i].e=max(r[i-1],c[i-1]);
}
sort(V+1,V+n+1,[&](const node x,const node y){return (x.s==y.s)?(x.e>y.e):(x.s<y.s);});
m=0;
LL x=-1;
for(i=1;i<=n;i++){
if(x<V[i].e) V[++m]=V[i];
x=max(x,V[i].e);
}
n=m;
sort(V+1,V+n+1,[&](const node x,const node y){return x.e<y.e;});
s=e=0;
L[e++]={-2*V[1].s,sq(V[1].s)-2*V[1].s};
for(i=1;i<=n;i++){
while(e-s>1 && L[s].fi*V[i].e+L[s].se>=L[s+1].fi*V[i].e+L[s+1].se) s++;
dp[i]=L[s].fi*V[i].e+L[s].se+sq(V[i].e+1);
pil p={-2*V[i+1].s,sq(V[i+1].s)-2*V[i+1].s+dp[i]};
if(V[i].e-V[i+1].s+1>0) p.se+=sq(V[i].e-V[i+1].s+1);
while(e-s>1 && !is_ok(L[e-2],L[e-1],p)) e--;
L[e++]=p;
}
return dp[n];
}
