#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;
pii dp[MAX_N];
int ind[MAX_N];
int prefix_max[MAX_N];
int r[MAX_N], c[MAX_N];
bitset<MAX_N> inside;
int n, m;
pii Solve(ll lambda) {
for (int i = 0; i < n; i++) {
dp[i] = {infinity, infinity};
int left = m, right = 0;
for (int l = i; l >= 0; l--) {
chkmin(left, int(r[ind[l]]));
chkmax(right, int(c[ind[l]] + 1));
ll x = (l ? dp[l - 1].x : 0) + ll(right - left) * (right - left) + lambda;
if (prefix_max[l] > left) {
x -= ll(prefix_max[l] - left) * (prefix_max[l] - left);
}
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++) {
if (max_c > c[ind[i]]) {
inside[ind[i]] = true;
r[ind[i]] = m + 1, c[ind[i]] = m + 1;
}
chkmax(max_c, c[ind[i]]);
}
sort(ind, ind + n, [&] (int i, int j) {
return r[i] + c[i] < r[j] + c[j];
});
n -= inside.count();
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
