#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
#include<bits/stdc++.h>
#include "aliens.h"
#define rc(x) return cout<<x<<endl,0
#define pb push_back
#define mkp make_pair
#define in insert
#define er erase
#define fd find
#define fr first
#define sc second
typedef long long ll;
typedef long double ld;
const ll INF=0x3f3f3f3f3f3f3f3f;
const ll llinf=(1LL<<62);
const int inf=(1<<30);
const int nmax=1e5+50;
const int mod=1e9+7;
using namespace std;
int n,m,k,i,j,t,id,x,y;
ll f[2][nmax];
pair<int,int>pr[nmax],v[nmax];
ll cst(int l,int r)
{
ll x=v[r].sc-v[l].fr;
ll y=max(0,v[l-1].sc-v[l].fr);
return x*x-y*y;
}
void rec(int l,int r,int opl,int opr)
{
if(l>r)return;
int mid=(l+r)/2,bst;
for(int i=opl;i<=min(mid,opr);i++)
{
if(f[0][i-1]+cst(i,mid)<=f[1][mid])
{
f[1][mid]=f[0][i-1]+cst(i,mid);
bst=i;
}
}
rec(l,mid-1,opl,bst);
rec(mid+1,r,bst,opr);
}
ll take_photos(int N,int M,int K,vector<int>r,vector<int>c)
{
n=N,m=M,k=K;
for(i=1;i<=n;i++)
{
pr[i].fr=min(r[i-1],c[i-1]);
pr[i].sc=max(r[i-1],c[i-1])+1;
}
for(j=1;j<=n;j++)f[0][j]=f[1][j]=llinf;
sort(pr+1,pr+n+1);
int mx=-1;
for(i=1;i<=n;i++)
{
if(pr[i].sc>mx)v[++id]=mkp(pr[i].fr,mx=pr[i].sc);
}
n=id;
k=min(k,n);
for(i=1;i<=k;i++)
{
rec(1,n,1,n);
for(j=1;j<=n;j++)
{
f[0][j]=f[1][j];
f[1][j]=llinf;
}
}
return f[0][n];
}
