#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
// ============
#ifdef DEBUGF
#else
#define DBG(...) (void)0
#endif
// ============
#include <cassert>
#include <utility>
#include <functional>
template <typename F, typename I, typename Comp = std::less<>>
auto golden_search(const F &f, I mn, I mx, Comp comp = Comp()) -> std::pair<I, decltype(f(mn))> {
using V = decltype(f(mn));
assert(mn <= mx);
I x0, x1, x2;
{
x0 = mn - 1;
I s = 1, t = 1;
while (x0 + s + t <= mx) {
I u = s + t;
s = t;
t = u;
}
x1 = x0 + s + t;
x2 = x0 + s;
}
V fx2 = f(x2);
V fx3 = 0;
while (2 * x2 != x0 + x1) {
I x3 = x0 + x1 - x2;
if (x3 > mx) {
x1 = x0;
x0 = x3;
} else {
fx3 = f(x3);
if (comp(fx2, fx3)) {
x1 = x0;
x0 = x3;
} else {
x0 = x2;
x2 = x3;
fx2 = fx3;
}
}
}
return std::pair<I, V>(x2, fx2);
}
// ============
class CHT {
deque<pl> lines;
static i64 fdiv(i64 x, i64 y) { return x / y - ((x ^ y) < 0 && x % y); }
static i64 inter(pl l0, pl l1) {
// ax + b = cx + d
// (a - c) x = d - b
// x = (d - b) / (a - c)
return (l1.second - l0.second) / (l0.first - l1.first);
}
static bool is_needed(pl l0, pl l1, pl l2) {
return inter(l0, l1) < inter(l1, l2);
}
public:
CHT() : lines() {}
void add(i64 a, i64 b) {
while (LEN(lines) >= 2 &&
!is_needed(lines[LEN(lines) - 2], lines.back(), pl(a, b))) {
lines.pop_back();
}
lines.emplace_back(a, b);
}
i64 get(i64 x) {
while (LEN(lines) >= 2 && lines[0].first * x + lines[0].second >
lines[1].first * x + lines[1].second) {
lines.pop_front();
}
return lines[0].first * x + lines[0].second;
}
};
i64 take_photos(i32 n, i32 m, i32 k, V<i32> r, V<i32> c) {
V<pi> pts(n);
REP(i, n) {
pts[i] = pi(r[i], c[i]);
if (pts[i].first > pts[i].second) {
swap(pts[i].first, pts[i].second);
}
}
DBG(pts);
sort(ALL(pts), [&](const pi &p, const pi &q) -> bool {
if (p.first != q.first) {
return p.first < q.first;
} else {
return p.second > q.second;
}
});
DBG(pts);
r.clear();
c.clear();
i32 ym = -1;
for (auto [x, y] : pts) {
if (chmax(ym, y)) {
r.push_back(x);
c.push_back(y);
}
}
DBG(r, c);
n = LEN(r);
chmin(k, n);
auto relaxed = [&](i64 lambda) -> i64 {
CHT cht;
cht.add(-2LL * r[0], (i64)r[0] * r[0] + lambda);
i64 mem = 0;
REP(i, n) {
mem = cht.get(c[i] + 1) + (i64)(c[i] + 1) * (c[i] + 1);
if (i != n - 1) {
i64 a = -2LL * r[i + 1];
i64 b = mem + (i64)r[i + 1] * r[i + 1] + lambda;
if (r[i + 1] <= c[i]) {
b -= (i64)(c[i] - r[i + 1] + 1) * (c[i] - r[i + 1] + 1);
}
cht.add(a, b);
}
}
return mem - k * lambda;
};
i64 ans = golden_search(relaxed, 0LL, (i64)m * m, greater()).second;
return ans;
}
