#include "aliens.h"
#include <bits/stdc++.h>
#define x first
#define y second
#define all(v) v.begin(), v.end()
#define chkmin(a, b) a = min(a, b)
#define chkmax(a, b) a = max(a, b)
//#define int ll
using namespace std;
//typedef __int128_t ll;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pii;
typedef vector<pii> vii;
const int MAX_N = 1e5 + 5;
const ll infinity = 1e18;
struct Rmq {
vi loga;
vvi rmq_min, rmq_max;
Rmq() {}
Rmq(vi &v_min, vi &v_max) {
int n = v_min.size();
loga.resize(n + 1);
for (int i = 2; i <= n; i++) loga[i] = loga[i >> 1] + 1;
rmq_min.resize(loga[n] + 1, vi(n));
rmq_max.resize(loga[n] + 1, vi(n));
rmq_min[0] = v_min, rmq_max[0] = v_max;
for (int i = 1; i <= loga[n]; i++) {
for (int j = 0; j < n; j++) {
rmq_min[i][j] = min(rmq_min[i - 1][j], rmq_min[i - 1][min(j + (1 << (i - 1)), n - 1)]);
rmq_max[i][j] = max(rmq_max[i - 1][j], rmq_max[i - 1][min(j + (1 << (i - 1)), n - 1)]);
}
}
}
inline pii query(int l, int r) {
if (r <= l) return {-1, -1};
int x = min(rmq_min[loga[r - l]][l], rmq_min[loga[r - l]][r - (1 << loga[r - l])]);
int y = max(rmq_max[loga[r - l]][l], rmq_max[loga[r - l]][r - (1 << loga[r - l])]);
return {x, y};
}
};
pii dp[MAX_N];
int ind[MAX_N];
int r[MAX_N], c[MAX_N];
Rmq rmq;
bitset<MAX_N> inside;
int n, m;
ll Cost(int j, int i) {
auto [left, right] = rmq.query(j, i + 1);
ll x = ll(right - left) * (right - left);
int pre = rmq.query(0, j).y;
if (pre > left) {
x -= ll(pre - left) * (pre - left);
}
return x;
}
pii Solve(ll lambda) {
for (int i = 0; i < n; i++) {
dp[i] = {infinity, infinity};
int begin = 0, end = i;
while (begin < end) {
int mid1 = (begin + end) >> 1;
int mid2 = mid1 + 1;
ll x1 = (mid1 ? dp[mid1 - 1].x : 0) + Cost(mid1, i) + lambda;
ll cnt1 = mid1 ? dp[mid1 - 1].y : 0;
ll x2 = (mid2 ? dp[mid2 - 1].x : 0) + Cost(mid2, i) + lambda;
ll cnt2 = mid2 ? dp[mid2 - 1].y : 0;
if (pii(x1, cnt1) < pii(x2, cnt2)) end = mid1;
else begin = mid2;
}
int l = end;
ll x = (l ? dp[l - 1].x : 0) + Cost(l, i) + lambda;
ll cnt = l ? dp[l - 1].y : 0;
chkmin(dp[i], pii(x, cnt + 1));
// for (int l = i; l >= 0; l--) {
// ll x = (l ? dp[l - 1].x : 0) + Cost(l, i) + lambda;
// ll cnt = l ? dp[l - 1].y : 0;
// chkmin(dp[i], pii(x, cnt + 1));
// }
}
return dp[n - 1];
}
long long take_photos(int32_t N, int32_t M, int32_t k, std::vector<int32_t> R, std::vector<int32_t> C) {
n = N, m = M;
for (int i = 0; i < n; i++) {
r[i] = R[i], c[i] = C[i];
if (r[i] > c[i]) swap(r[i], c[i]);
}
iota(ind, ind + n, 0);
sort(ind, ind + n, [&] (int i, int j) {
return r[i] == r[j] ? c[i] < c[j] : r[i] < r[j];
});
int max_c = 0;
for (int i = 0; i < n; i++) {
chkmax(max_c, c[ind[i]]);
if (max_c > c[ind[i]]) {
inside[ind[i]] = true;
r[ind[i]] = m + 1, c[ind[i]] = m + 1;
}
}
sort(ind, ind + n, [&] (int i, int j) {
return r[i] + c[i] < r[j] + c[j];
});
n -= inside.count();
vi v_min(n), v_max(n);
for (int i = 0; i < n; i++) v_min[i] = r[ind[i]], v_max[i] = c[ind[i]] + 1;
rmq = Rmq(v_min, v_max);
// for (int i = 0; i < n; i++) {
// prefix_max[i + 1] = max(prefix_max[i], c[ind[i]] + 1);
// }
pii p = Solve(0);
if (p.y <= k) return p.x;
ll begin = 0, end = ll(m) * m + 5, mid;
while (begin < end) {
mid = (begin + end) >> 1;
p = Solve(mid);
if (p.y <= k) end = mid;
else begin = mid + 1;
}
return Solve(end).x - k * (end);
}
//6 7 2
//0 3
//4 4
//4 6
//4 5
//4 6
//0 5
