#include "bits/stdc++.h"
using namespace std;
#define int int64_t
#define all(x) begin(x), end(x)
#define sz(x) (int) (x).size()
const int MXN=1e5+5, INF=1e9;
int N,M,K;
array<int,2> arr[MXN];
int dp[MXN], amt[MXN];
bool cc1(const array<int,2> &a, const array<int,2> &b) {
if (a[0]==b[0]) {
return a[1]>b[1];
}
return a[0]<b[0];
}
bool cc2(const array<int,2> &a, const array<int,2> &b) {
return a[1]<b[1];
}
namespace monoline {
const int lo = -10, hi = 1e6+5;
deque<array<int,5>> lines;
void reset() {while (sz(lines)) lines.pop_back();}
int eval(array<int,5> a, int x) {
return a[0]*x+a[1];
}
int first_lower(array<int,5> a, array<int,5> b) {
if (eval(a,lo)<=eval(b,lo) && eval(a,hi)<=eval(b,hi)) {return -69420;}
if (eval(a,lo)>=eval(b,lo) && eval(a,hi)>=eval(b,hi)) {return 0;}
int fp = (a[1]-b[1])/(b[0]-a[0]);
fp--;
while (eval(a,fp) <= eval(b,fp)) {
fp++;
}
return fp;
}
void insert_line(int m, int b, int v=0) {
array<int,5> ln = {m,b,v,-69,-69};
while (1) {
if (!sz(lines)) {
ln[3] = lo, ln[4] = hi;
lines.push_back(ln);
return;
}
array<int,5>& pv = lines.back();
pv[4] = hi;
int fp = first_lower(pv,ln);
if (fp==-69420) return;
if (fp <= pv[3]) {
lines.pop_back();
continue;
}
pv[4] = fp-1;
ln[3] = fp, ln[4] = hi;
lines.push_back(ln);
return;
}
}
array<int,2> get_value(int x) {
while (lines.front()[4] < x) {
lines.pop_front();
}
int vv = eval(lines.front(),x);
if (sz(lines)>1) {
auto temp = lines.front(); lines.pop_front();
if (eval(lines.front(),x) >= vv) {
lines.push_front(temp);
}
}
return {eval(lines.front(),x),lines.front()[2]};
}
}
int check(int w) {
memset(dp,0x3f,sizeof(dp));
memset(amt,0,sizeof(amt));
dp[0] = 0;
monoline::reset();
monoline::insert_line(-2*(arr[0+1][0]-1), dp[0] + (arr[0+1][0]-1)*(arr[0+1][0]-1) - (max(0ll,arr[0][1]-arr[0+1][0]+1ll))*(max(0ll,arr[0][1]-arr[0+1][0]+1ll)),0);
for (int i=1; i<=N; i++) {
auto [v,a] = monoline::get_value(arr[i][1]);
dp[i] = v+w+arr[i][1]*arr[i][1];
amt[i] = a+1;
monoline::insert_line(-2*(arr[i+1][0]-1), dp[i] + (arr[i+1][0]-1)*(arr[i+1][0]-1) - (max(0ll,arr[i][1]-arr[i+1][0]+1ll))*(max(0ll,arr[i][1]-arr[i+1][0]+1ll)),amt[i]);
}
return amt[N];
}
int search(int lo, int hi) {
if (lo==hi) return lo;
if (lo+1==hi) {
if (check(hi)==K) return hi;
return lo;
}
int mid = (lo+hi)/2;
if (check(mid) <= K) {
return search(lo,mid);
}
return search(mid,hi);
}
int take_photos(int32_t n, int32_t m, int32_t k, vector<int32_t> r, vector<int32_t> c) {
N = n, M = m, K = k;
for (int i=1; i<=N; i++) {
arr[i] = {min(r[i-1],c[i-1]),max(r[i-1],c[i-1])};
}
arr[0] = {-INF,-INF};
sort(arr,arr+N+1,cc1);
int pv = 0,sub = 0;
for (int i=1; i<=N; i++) {
if (arr[pv][1] >= arr[i][1]) {
sub++; arr[i] = {INF,INF};
} else pv = i;
}
sort(arr,arr+1+N,cc2);
N -= sub; K = min(K,N);
int w = search(-1e12,1e12);
check(w);
while (amt[N] > K) {
w++; check(w);
}
return dp[N]-w*(K);
}
/*
signed main() {
ios::sync_with_stdio(false); cin.tie(nullptr);
int32_t a,b,c; cin>>a>>b>>c;
vector<int32_t> x(a),y(a);
for (int i=0; i<a; i++) {
cin>>x[i]>>y[i];
}
cout<<take_photos(a,b,c,x,y);
return 0;
}
*/
