//#pragma GCC optimize("O3")
#include <bits/stdc++.h>
#include "aliens.h"
using namespace std;
#define ve vector
typedef long long ll;
typedef pair<int, int> pii;
const int INF = 1e9 + 10;
const ll LLINF = (ll)1e18 + 10;
struct segment {
ll m, b, l, r;
};
double intersect(ll m1, ll m2, ll b1, ll b2) {
return (double) (b1 - b2) / (double) (m2 - m1);
}
ll sq(int x) { return (ll)x*x; }
ll take_photos(int n, int m, int k, ve<int> R, ve<int> C) {
map<int, int> M;
ve<pii> P;
for (int i = 0; i < n; i++) {
int r = R[i];
int c = C[i];
if (c < r) swap(r, c);
if (M.find(r) == M.end()) M[r] = c;
else M[r] = max(M[r], c);
}
int cOld = -1;
n = 0;
for (pii p : M) {
int r, c;
tie(r, c) = p;
if (c > cOld) {
cOld = c;
P.push_back({r, c});
n++;
}
}
ve<ll> L(n);
for (int i = 1; i < n; i++) {
if (P[i - 1].second >= P[i].first) {
L[i] = sq(P[i - 1].second - P[i].first + 1);
}
}
ve<ve<ll>> DP(k + 1, ve<ll>(n));
for (int i = 0; i < n; i++) {
DP[1][i] = sq(P[i].second - P[0].first + 1);
}
for (int i = 2; i <= k; i++) {
list<segment> H;
for (int j = i - 1; j < n; j++) {
ll x = -P[j].first + 1;
ll b = DP[i - 1][j - 1] - L[j] + x * x;
ll m = 2 * x;
if (H.size() == 0) H.push_back({m, b, -LLINF, LLINF});
else {
while (intersect(H.back().m, m, H.back().b, b) < (double)H.back().l) {
H.pop_back();
}
double z = intersect(H.back().m, m, H.back().b, b);
ll l = (ll)ceil(z);
H.back().r = (ll)floor(z);
H.push_back({m, b, l, LLINF});
}
while (H.begin()->r < P[j].second) {
H.pop_front();
}
H.begin()->l = -LLINF;
ll q = H.begin()->m * P[j].second + H.begin()->b;
DP[i][j] = q + sq(P[j].second);
}
}
return DP[min(k, n)][n - 1];
}
