//#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
//#include "grader.cpp"
const ll inf = 1e16;
typedef long double ld;
const ld eps = 1e-9;
inline ll sq (ll x) {
return x * x;
}
struct CHT {
deque <pair <ll, ll>> dd;
void init () {
}
ld inter (pair <ll, ll> x, pair <ll, ll> y) {
return 1.0 * (x.second - y.second) / (y.first - x.first);
}
ll query (ll x) {
while (dd.size() >= 2) {
if (inter(dd[dd.size() - 1], dd[dd.size() - 2]) <= x) {
break;
}
dd.pop_back();
}
return dd.back().first * x + dd.back().second;
}
void insert (ll x, ll y) {
pair <ll, ll> g = {x, y};
while (dd.size() >= 2 && inter(g, dd[0]) > inter(dd[0], dd[1]) + eps) {
dd.pop_front();
}
dd.push_front(g);
}
};
int n;
array <ll, 2> a[200002];
pair <ll, ll> eval (ll mid) {
ll g[n + 2] = {}, h[n + 2] = {};
for (int i = n; i >= 1; i--) {
ll mn = inf, pos = -1;
for (int j = i + 1; j <= n + 1; j++) {
ll z = sq(a[j - 1][1] - a[i][0] + 1) - sq(max(0ll, a[j - 1][1] - a[j][0] + 1)) + g[j] + mid;
if (z < mn) {
mn = z; pos = j;
}
}
g[i] = mn; h[i] = h[pos] + 1;
}
return {g[1], h[1]};
}
ll take_photos (int N, int m, int k, vector <int> r, vector <int> c) {
n = N;
for (int i = 0; i < n; i++) {
if (r[i] < c[i]) {
swap(r[i], c[i]);
}
c[i]++; r[i]++;
a[i + 1] = {c[i], r[i]};
}
sort(a + 1, a + n + 1, [&] (array <ll, 2> &x, array <ll, 2> &y) {
return x[0] == y[0] ? x[1] > y[1] : x[0] < y[0];
});
ll mx = 0;
array <ll, 2> b[n + 2];
int d = 0;
for (int i = 1; i <= n; i++) {
if (mx >= a[i][1]) {
continue;
}
b[++d] = a[i];
mx = a[i][1];
}
n = d;
for (int i = 1; i <= n; i++) {
a[i] = b[i];
}
a[n + 1] = {m + 1, m + 1};
ll L = 0, R = m * m, p1 = -1;
while (L <= R) {
ll mid = (L + R) / 2;
pair <ll, ll> x = eval(mid);
if (x.second <= k) {
R = mid - 1; p1 = mid;
} else {
L = mid + 1;
}
}
return eval(p1).first - p1 * k;
/*
ll dp[n + 2][k + 2] = {};
for (int i = 1; i <= n; i++) {
dp[i][0] = inf;
}
for (int j = 1; j <= k; j++) {
CHT cur;
cur.init();
for (int i = n; i >= 1; i--) {
cur.insert(-2 * a[i][1], sq(a[i][1]) + 2 * a[i][1] - sq(max(0ll, a[i][1] - a[i + 1][0] + 1)) + dp[i + 1][j - 1]);
dp[i][j] = cur.query(a[i][0]) + sq(a[i][0]) - 2 * a[i][0] + 1;
}
}
for (int i = 0; i <= n; i++) {
for (int j = 1; j < k; j++) {
assert(dp[i][j - 1] - dp[i][j] >= dp[i][j] - dp[i][j + 1]);
}
}
return dp[1][k];*/
}
