// Why am I so dumb? :c
// chrono::system_clock::now().time_since_epoch().count()
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include "aliens.h"
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#define debug(x) cerr << #x << " = " << x << '\n';
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int, int> pii;
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int MAXN = (int)5e4 + 5;
const ll INF = (ll)1e18;
struct Line {
ll k, b;
Line() {
k = b = 0ll;
}
Line(ll k, ll b) : k(k), b(b) {}
ll get(ll x) {
return k * x + b;
}
};
double inter(Line a, Line b) {
return (double)(a.b - b.b) / (double)(b.k - a.k);
}
struct CHT {
pair<Line, int> H[MAXN];
int sz, ptr;
CHT() {
sz = ptr = 0;
}
bool good(Line a, Line b, Line c) {
return inter(a, b) < inter(b, c);
}
void addLine(Line l, int x) {
//while (sz >= 2 && !good(H[sz - 2].fi, H[sz - 1].fi, l)) {
//--sz;
//}
H[sz++] = mp(l, x);
ptr = min(ptr, sz - 1);
}
pair<ll, int> query(ll x) {
while (ptr + 1 < sz && inter(H[ptr].fi, H[ptr + 1].fi) < x) {
++ptr;
}
pair<ll, int> ret = mp(INF, INF);
for (int i = 0; i < sz; ++i) {
ret = min(ret, mp(H[i].fi.get(x), H[i].se));
}
return ret;
}
} T;
pair<ll, int> dp[MAXN];
pii arr[MAXN];
int n, m, k;
bool cmp(pii a, pii b) {
if (a.fi == b.fi) {
return a.se > b.se;
}
return a.fi < b.fi;
}
void resolveOverlaps() {
sort(arr + 1, arr + n + 1, cmp);
int lim = 0, nn = 0;
for (int i = 1; i <= n; ++i) {
if (arr[i].se > lim) {
arr[++nn] = arr[i];
lim = arr[i].se;
}
}
n = nn;
}
ll f(int a, int b) {
int len = max(0, b - a);
return len * 1ll * len;
}
pair<ll, int> calc(ll pen) {
//T.sz = 0;
for (int i = 1; i <= n; ++i) {
dp[i] = mp(INF, -1);
for (int j = 1; j <= i; ++j) {
pair<ll, int> cur = dp[j - 1];
++cur.se;
cur.fi += f(arr[j].fi, arr[i].se);
cur.fi -= f(arr[j].fi, arr[j - 1].se);
dp[i] = min(dp[i], cur);
}
dp[i].fi += pen;
}
// dp[i] = min(dp[i], dp[j] + (r[i] - l[j])^2 - (r[j + 1] - l[j])^2)
//for (int i = 1; i <= n; ++i) {
//Line l(-2 * arr[i].fi, dp[i - 1].fi);
//l.b += arr[i].fi * 1ll * arr[i].fi;
//l.b -= f(arr[i].fi, arr[i - 1].se);
//T.addLine(l, dp[i - 1].se);
//pair<ll, int> tmp = T.query(arr[i].se);
//dp[i].fi = tmp.fi + arr[i].se * 1ll * arr[i].se + pen;
//dp[i].se = tmp.se + 1;
//}
return dp[n];
}
ll solve() {
for (int i = 1; i <= n; ++i) {
if (arr[i].fi > arr[i].se) {
swap(arr[i].fi, arr[i].se);
}
++arr[i].se;
}
resolveOverlaps();
k = min(k, n);
ll l = 1, r = INF + 12324432, opt;
while (l <= r) {
ll mid = (l + r) >> 1;
pair<ll, int> tmp = calc(mid);
if (tmp.se < k) {
r = mid - 1;
}
else {
opt = mid;
l = mid + 1;
}
}
pair<ll, int> tmp = calc(opt);
return tmp.fi - k * opt;
}
ll take_photos(int _n, int _m, int _k, vector<int> r, vector<int> c) {
n = _n;
m = _m;
k = _k;
for (int i = 1; i <= n; ++i) {
arr[i] = mp(r[i - 1] + 1, c[i - 1] + 1);
}
return solve();
}
