#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef pair<int,int> pi;
typedef vector<pi> pii;
typedef tuple<int,int,int> ti;
typedef vector<ll> li;
typedef vector<li> lii;
#define REP(i,a,b) for(int i=a;i<b;i++)
#define F first
#define S second
#define PB push_back
#define LSOne(s) ((s)&(-s))
#define all(x) (x).begin(),(x).end()
ll INF=1000000000000000010;
int inf=1e9+10;
ll M=1e9+7;
vector<pair<ll,ll>> a;
vector<vector<ll>> dp;
ll dist(int p,int q){
ll x=a[p].F,y=a[q].S;
ll val=(y-x+1)*(y-x+1);
if(p!=0){
ll z=a[p-1].S-a[p].F+1;
if(z>0)val-=z*z;
}
return val;
}
ll cnst(int x,int y){
ll ans=(a[x+1].F)*(a[x+1].F)+dp[x][y-1],z=a[x].S-a[x+1].F+1;
if(z>0)ans-=(z*z);
return ans;
}
ll grad(int x){
return ((-2)*a[x+1].F);
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
REP(i,0,n)a.PB({max((ll)r[i],(ll)c[i]),min((ll)r[i],(ll)c[i])});
sort(all(a));reverse(all(a));
int pos=0;
while(pos+1<a.size()){
if(a[pos].S<=a[pos+1].S)a.erase(a.begin()+pos+1);
else pos++;
}
pos=0;
REP(i,0,n)swap(a[i].F,a[i].S);
reverse(all(a));
while(pos+1<a.size()){
if(a[pos].S==a[pos+1].S&&a[pos].F<=a[pos+1].S)a.erase(a.begin()+pos+1);
else pos++;
}
n=a.size();
dp.resize(n,vector<ll>(k+1,INF));
REP(i,0,n)dp[i][1]=dist(0,i);
REP(j,2,k+1){
deque<int> q;
int pos=0;
while(pos<n&&dp[pos][j-1]==INF)pos++;
q.PB(pos);
REP(i,pos+1,n){
while(q.size()>1&&dp[q[0]][j-1]+dist(q[0]+1,i)>=dp[q[1]][j-1]+dist(q[1]+1,i))q.pop_front();
dp[i][j]=dp[q[0]][j-1]+dist(q[0]+1,i);
if(i==n-1)break;
while(q.size()>1&&(cnst(i,j)-cnst(q[q.size()-1],j))*(grad(q[q.size()-2])-grad(q[q.size()-1]))<=(cnst(q[q.size()-1],j)-cnst(q[q.size()-2],j))*(grad(q[q.size()-1])-grad(i)))q.pop_back();
q.push_back(i);
}
}
ll ans=INF;
REP(i,1,k+1)ans=min(ans,dp[n-1][i]);
return ans;
}
