#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
#define sz(a) (int)(a.size())
typedef long long int ll;
typedef pair<int,int> pii;
vector<ll>dp[100001];
const ll INF = 1e18;
vector<int>b,h;
struct line{
ll m = 0,c = 0;
line(){}
line(ll _m,ll _c):m(_m),c(_c){}
ll eval(ll x){return m*x+c;}
};
deque<line>hull;
//increasing slope
//incresing query
void add(line t){
while(sz(hull)>1){
line a = hull[sz(hull)-2];
line b = hull[sz(hull)-1];
//inter(t,a) >= inter(t,b)
if((t.c - a.c) * (b.m - t.m) >= (a.m - t.m) * (t.c - b.c))hull.pop_back();
else break;
}
hull.push_back(t);
}
ll query(ll x){
while(sz(hull)>1 && hull[1].eval(x) >= hull[0].eval(x))hull.pop_front();
return hull[0].eval(x);
}
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
h.assign(m,m);
for(int i=0;i<n;i++){
int a = max(r[i],c[i]);
int b = min(r[i],c[i]);
h[a] = min(h[a],b);
}
int L = m;
for(int i=m-1;i>=0;i--){
if(h[i]==m)continue;
if(h[i]<L)b.push_back(i);
L = min(L,h[i]);
}
b.push_back(-1);
reverse(b.begin(),b.end());
n = b.size()-1;
for(int i=0;i<=n;i++){
dp[i].assign(k+1,INF);
}
dp[0][0] = 0;
for(int i=1;i<=k;i++){
hull.clear();
for(int j=1;j<=n;j++){
ll m = 2*h[b[j]]-2;
ll c = -dp[j-1][i-1] - (h[b[j]]-1)*(h[b[j]]-1);
if(j!=1){
ll a = b[j-1] - h[b[j]]+1;
a = max(a,0LL);
c+=a*a;
}
add(line(m,c));
/*
cout<<i<<" "<<j<<'\n';
cout<<"lines :"<<'\n';
cout<<"add "<<m<<" "<<c<<'\n';
for(line x:hull)cout<<x.m<<" "<<x.c<<'\n';
cout<<'\n';
* */
dp[j][i] = b[j] * 1LL * b[j] - query(b[j]);
}
/*
cout<<"dpval"<<'\n';
for(int j=1;j<=n;j++)cout<<dp[j][i]<<" ";
cout<<'\n';
* */
}
ll ans = INF;
for(int i=1;i<=k;i++)ans = min(ans,dp[n][i]);
return ans;
}
