// 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 int INF = (int)1e9;
const ll LINF = (ll)1e15;
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 {
Line 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) {
while (sz >= 2 && !good(H[sz - 2], H[sz - 1], l)) {
--sz;
}
H[sz++] = l;
ptr = min(ptr, sz - 1);
}
ll query(ll x) {
while (ptr + 1 < sz && inter(H[ptr], H[ptr + 1]) < x) {
++ptr;
}
return H[ptr].get(x);
}
};
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;
}
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();
vector<vector<ll> > dp(k + 5, vector<ll>(n + 5, 0));
for (int i = 0; i <= k; ++i) {
for (int j = 1; j <= n; ++j) {
dp[i][j] = LINF;
}
}
CHT T;
for (int lvl = 1; lvl <= k; ++lvl) {
T.sz = 0;
for (int i = 1; i <= n; ++i) {
Line l(-2 * arr[i].fi, dp[lvl - 1][i - 1]);
l.b += arr[i].fi * 1ll * arr[i].fi;
l.b -= f(arr[i].fi, arr[i - 1].se);
T.addLine(l);
dp[lvl][i] = T.query(arr[i].se) + arr[i].se * 1ll * arr[i].se;
}
}
return dp[k][n];
}
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();
}
