#include "aliens.h"
#include <vector>
#include <iostream>
#include <utility>
#include <algorithm>
#include <set>
#include <limits.h>
using namespace std;
#define v vector
#define pii pair<int,int>
#define fi first
#define se second
#define ll long long
int N,K;
v<pii> pos;
v<v<long long>> memo;
long long diagSolve(int cur, int k){//cover first cur with k photos
if(memo[cur][k]!=-1) return memo[cur][k];
if(cur==0) return memo[cur][k] = 0;
if(k==0) return LLONG_MAX/2;
long long ret=LLONG_MAX/2;
for(int i=0;i<cur;i++){
long long curArea=(pos[cur-1].se-pos[i].fi+1) * (pos[cur-1].se-pos[i].fi+1);
//check for intersection with prev:
if(i!=0){
long long length = max(0, pos[i-1].se-pos[i].fi+1);
curArea-=length*length;
}
long long take = diagSolve(i,k-1);
if(take+curArea<ret) ret=take+curArea;
}
return memo[cur][k] = ret;
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
set<pii> tmp;
for(int i=0;i<n;i++){
tmp.insert({min(r[i],c[i]),-max(c[i],r[i])});
}
for(pii it:tmp){
if(pos.size()==0) {
pos.push_back({it.fi,-it.se});
continue;
}
if(it.fi<=pos.back().se && -it.se<=pos.back().se) continue;
pos.push_back({it.fi,-it.se});
}
N=pos.size();
K=k;
//top down:
//memo=v<v<ll>>(N+1,v<long long>(k+1,-1));
//return diagSolve(N,k);
//bottom up: for convex hull soon:
memo=v<v<ll>>(K+1,v<ll>(N+1,-1));
for(int i=0;i<=K;i++) memo[i][0]=0;
for(int i=1;i<=N;i++) memo[0][i]=LLONG_MAX/2;
for(k=1;k<=K;k++){
for(int i=1;i<=N;i++){
long long val=LLONG_MAX/2;
for(int j=0;j<i;j++){
long long curArea=(pos[i-1].se-pos[j].fi+1) * (pos[i-1].se-pos[j].fi+1);
//check for intersection with prev:
if(j!=0){
long long length = max(0, pos[j-1].se-pos[j].fi+1);
curArea-=length*length;
}
long long take = memo[k-1][j];
if(take+curArea<val) val=take+curArea;
}
memo[k][i]=val;
}
}
return memo[K][N];
}
