#include "aliens.h"
#include <vector>
#include <stdio.h>
#include <algorithm>
#include <math.h>
using namespace std;
struct interval {
int l, r;
bool operator < (interval a) {
if (l == a.l)
return r > a.r;
return l < a.l;
}
};
const int MAX_N = 1e5;
const long long INF = 1e18;
int cnt[MAX_N + 1];
long long dp[MAX_N + 1];
interval v[MAX_N + 1];
struct line {
int ind;
long long a, b;
long long operator ()(int x) {
return a * x + b;
}
};
long long overtake(line l, line m) {
long long t = ceil((double)(m.b - l.b) / (l.a - m.a));
return t;
}
struct CHT {
vector<pair<long long, line>> lines;
void clear() {
lines.clear();
}
void addLine(line l) {
while (!lines.empty() && overtake(l, lines.back().second) < lines.back().first)
lines.pop_back();
long long t = (lines.empty() ? 0 : overtake(l, lines.back().second));
lines.push_back({t, l});
}
int getMin(int x) {
int l = 0, r = lines.size();
while (r - l > 1) {
int mid = (l + r) / 2;
if (lines[mid].first > x)
r = mid;
else
l = mid;
}
return lines[l].second.ind;
}
};
const int BASE = 1e5 + 1;
void computeDp(int n, long long coef) {
CHT cht;
for (int i = 1; i <= n; i++) {
long long overI = max(0, (v[i - 1].r - v[i].l));
line a;
a.ind = i;
a.a = -2LL * v[i].l * BASE;
a.b = (long long)dp[i - 1] + (long long)v[i].l * v[i].l - overI * overI;
a.b = a.b * BASE + cnt[i - 1];
cht.addLine(a);
int j = cht.getMin(v[i].r);
long long len = (v[i].r - v[j].l);
long long over = max(0, (v[j - 1].r - v[j].l));
long long cost = dp[j - 1] + len * len - over * over + coef;
dp[i] = cost;
cnt[i] = cnt[j - 1] + 1;
// printf("%d %d\n", v[i].l, v[i].r);
// printf("%d\n", j);
}
// printf("%lld %lld %d\n", coef, dp[n], cnt[n]);
}
long long take_photos(int n, int m, int k, vector<int> R, vector<int> C) {
vector<interval> rc(n);
for (int i = 0; i < n; i++) {
if (R[i] > C[i])
swap(R[i], C[i]);
C[i]++;
rc[i] = {R[i], C[i]};
}
sort(rc.begin(), rc.end());
n = 0;
int maxR = -1;
for (interval a: rc) {
if (a.r > maxR) {
v[++n] = a;
maxR = a.r;
}
}
k = min(k, n);
long long lb = 0, rb = 1e12;
while (rb - lb > 1) {
long long coef = (lb + rb) / 2;
computeDp(n, coef);
if (cnt[n] > k)
lb = coef;
else
rb = coef;
}
computeDp(n, rb);
return dp[n] - rb * k;
}
