#include "aliens.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
#define endl "\n"
#define ll long long
#define IOS ios_base::sync_with_stdio(false); cin.tie(nullptr);
const int N = 1e5 + 5;
const int R = 3e6;
const int MAX = 1e6;
const long long INF = 1e18;
pair<long long, int> dp[N];
struct Line {
long long k, b; int j;
pair<long long, int> f(long long x) {
return make_pair(k * x + b, j);
}
Line(long long k, long long b, int j) : k(k), b(b), j(j) {}
};
struct Node {
Line line;
int left;
int right;
Node(Line line) : line(line), left(-1), right(-1) {}
Node() : line(0, INF, 0), left(-1), right(-1) {}
};
Node nodes[MAX];
int idx = 0;
void add(int l, int r, int node, Line cur) {
if (l > r) {
return;
}
int mid = (l + r) / 2;
if (r - l == 1 && mid == r) {
mid--;
}
bool lf = cur.f(l) < nodes[node].line.f(l);
bool md = cur.f(mid) < nodes[node].line.f(mid);
if (md) {
swap(nodes[node].line, cur);
}
if (l == r) {
return;
}
if (lf != md) {
if (nodes[node].left == -1) {
nodes[node].left = idx;
nodes[idx++] = Node(cur);
} else {
add(l, mid, nodes[node].left, cur);
}
} else {
if (nodes[node].right == -1) {
nodes[node].right = idx;
nodes[idx++] = Node(cur);
} else {
add(mid + 1, r, nodes[node].right, cur);
}
}
return;
}
pair<long long, int> query(int l, int r, int node, int x) {
if (l > r) {
return make_pair(INF, 0);
}
int mid = (l + r) / 2;
if (r - l == 1 && mid == r) {
mid--;
}
pair<long long, int> ans = nodes[node].line.f(x);
if (l == r) {
return ans;
}
if (x <= mid && nodes[node].left != -1) {
ans = min(ans, query(l, mid, nodes[node].left, x));
}
if (x > mid && nodes[node].right != -1) {
ans = min(ans, query(mid + 1, r, nodes[node].right, x));
}
return ans;
}
pair<long long, int> calc(int n, long long cost, vector<pair<int, int>> &a) {
/*for (int i = 0; i < n; i++) {
dp[i] = make_pair(INF, 0);
for (int j = i - 1; j >= 0; j--) {
long long cur = dp[j].first + (long long)(a[i].second - a[j + 1].first + 1) * (a[i].second - a[j + 1].first + 1) + cost;
if (a[j].second >= a[j + 1].first) {
cur -= (long long)(a[j].second - a[j + 1].first + 1) * (a[j].second - a[j + 1].first + 1);
}
dp[i] = min(dp[i], make_pair(cur, dp[j].second - 1));
}
dp[i] = min(dp[i], make_pair((long long)(a[i].second - a[0].first + 1) * (a[i].second - a[0].first + 1) + cost, -1));
}*/
idx = 0;
nodes[idx++] = Node();
for (int i = 0; i < n; i++) {
dp[i] = make_pair((long long)(a[i].second - a[0].first + 1) * (a[i].second - a[0].first + 1) + cost, -1);
if (i != 0) {
pair<long long, int> qr = query(0, R, 0, 2 * (a[i].second + 1));
qr.first += cost + (long long)(a[i].second + 1) * (a[i].second + 1);
qr.second += -1;
dp[i] = min(dp[i], qr);
}
if (i != n - 1) {
long long overlap = (a[i].second >= a[i + 1].first ? (long long)(a[i].second - a[i + 1].first + 1) * (a[i].second - a[i + 1].first + 1) : 0);
Line line(-a[i + 1].first, dp[i].first - overlap + (long long)a[i + 1].first * a[i + 1].first, dp[i].second);
add(0, R, 0, line);
}
}
return dp[n - 1];
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
map<int, int> mp;
for (int i = 0; i < n; i++) {
int x, y;
x = r[i], y = c[i];
if (x > y) {
swap(x, y);
}
auto it = mp.find(y);
if (it == mp.end()) {
mp[y] = x;
} else {
it->second = min(it->second, x);
}
}
stack<pair<int, int>> st;
for (auto it = mp.begin(); it != mp.end(); ++it) {
int y = it->first, x = it->second;
while (st.size() && st.top().first >= x) {
st.pop();
}
st.push(make_pair(x, y));
}
vector<pair<int, int>> a;
while (st.size()) {
a.push_back(st.top());
st.pop();
}
reverse(a.begin(), a.end());
n = a.size();
/*vector<long long> dp(n);
dp[0] = (long long)(a[0].second - a[0].first + 1) * (a[0].second - a[0].first + 1);
for (int i = 1; i < n; i++) {
dp[i] = dp[i - 1] + (a[i].second - a[i].first + 1) * (a[i].second - a[i].first + 1);
if (a[i - 1].second >= a[i].first) {
dp[i] -= (long long)(a[i - 1].second - a[i].first + 1) * (a[i - 1].second - a[i].first + 1);
}
}
cout << dp[n - 1];*/
long long L = 0, R = 1e12, opt = 0;
while (L <= R) {
long long mid = (L + R) / 2;
if (-calc(n, mid, a).second >= k) {
opt = mid;
L = mid + 1;
} else {
R = mid - 1;
}
}
long long ans = calc(n, opt, a).first - opt * k;
return ans;
}
