#include <bits/stdc++.h>
#include "aliens.h"
#define DIMN 100010
#define DIMM 1000010
#define INF 2000000000000000000LL
using namespace std;
int n,k,m,i,j,x,y;
vector <int> r,c;
long long dp[DIMN],cnt[DIMN];
pair <int, int> v[DIMN];
int d[DIMM];
struct dreapta{
long long a,b,cnt;
};
dreapta w[DIMM];
long long f (long long a, long long b, int x){
if (a == INF && b == INF)
return INF;
return a*x + b;
}
bool intersectie (pair<long long,long long> c, pair<long long,long long> b, pair<long long,long long> a){
return (a.second-c.second)*(b.first-a.first) < (a.second-b.second)*(c.first-a.first);
}
long long patrat (long long x){
return x*x;
}
long long modul (long long x){
return max (x,-x);
}
inline int cmp (pair<int,int> a, pair<int,int> b){
if (a.first == b.first)
return a.second > b.second;
return a.first < b.first;
}
void solve (long long lambda){
/// dp[i] - costul mimim daca am primele i puncte
/// cnt[i] - de cate subsecvente am nevoie
int p = 1, u = 0;
for (int i=1;i<=n;++i){
w[i-1].a = -2*v[i].first, w[i-1].b = dp[i-1] + patrat(v[i].first) - patrat(max(0,v[i-1].second - v[i].first + 1));
// add (,, cnt[i-1]);
while (u > 1 && intersectie (make_pair(w[i-1].a,w[i-1].b), make_pair(w[d[u]].a,w[d[u]].b), make_pair(w[d[u-1]].a,w[d[u-1]].b) ) )
u--;
d[++u] = i-1;
while (p < u && f(w[d[p]].a,w[d[p]].b,v[i].second+1) > f(w[d[p+1]].a,w[d[p+1]].b,v[i].second+1))
p++;
dp[i] = f(w[d[p]].a,w[d[p]].b,v[i].second+1) + patrat (v[i].second+1) + lambda;
cnt[i] = cnt[d[p]] + 1;
}
}
long long take_photos (int N, int M, int K, std::vector <int> r, std::vector <int> c){
n = N, m = M, k = K;
for (i=0;i<n;++i)
v[i+1] = make_pair(min(r[i],c[i])+1,max(r[i],c[i])+1);
sort (v+1,v+n+1,cmp);
/// elimin intervalele care sunt incluse in altele
int St = -1, Dr = -1, el = 0;
for (i=1;i<=n;++i){
if (!(v[i].first >= St && v[i].second <= Dr)){
v[++el] = v[i];
St = v[i].first, Dr = v[i].second;
}}
n = el;
k = min (k,n);
long long st = 0, dr = INF;
while (st <= dr){
long long lambda = (st + dr)>>1;
solve (lambda);
if (cnt[n] > k)
st = lambda + 1;
else dr = lambda - 1;
}
solve (st);
return dp[n] - k * st;
}
