#include <iostream>
#include <vector>
#include <tuple>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <cmath>
#include <random>
#include <string>
#include <cassert>
#include <climits>
#include <algorithm>
#include <unordered_set>
#include <unordered_map>
using namespace std;
#define ll long long
#define f first
#define s second
void __print (int x) { cerr << x; }
void __print (long x) { cerr << x; }
void __print (long long x) { cerr << x; }
void __print (unsigned x) { cerr << x; }
void __print (unsigned long x) { cerr << x; }
void __print (unsigned long long x) { cerr << x; }
void __print (float x) { cerr << x; }
void __print (double x) { cerr << x; }
void __print (long double x) { cerr << x; }
void __print (char x) { cerr << '\'' << x << '\''; }
void __print (const char *x) { cerr << '\"' << x << '\"'; }
void __print (const string &x) { cerr << '\"' << x << '\"'; }
void __print (bool x) { cerr << (x ? "true" : "false"); }
template<typename A> void __print (const A &x);
template<typename A, typename B> void __print (const pair<A, B> &p);
template<typename... A> void __print (const tuple<A...> &t);
template<typename T> void __print (stack<T> s);
template<typename T> void __print (queue<T> q);
template<typename T, typename... U> void __print (priority_queue<T, U...> q);
template<typename A> void __print (const A &x) {
bool first = true;
cerr << '{';
for (const auto &i : x) {
cerr << (first ? "" : ","), __print(i);
first = false;
}
cerr << '}';
}
template<typename A, typename B> void __print (const pair<A, B> &p) {
cerr << '(';
__print(p.f);
cerr << ',';
__print(p.s);
cerr << ')';
}
template<typename... A> void __print (const tuple<A...> &t) {
bool first = true;
cerr << '(';
apply([&first] (const auto &...args) { ((cerr << (first ? "" : ","), __print(args), first = false), ...); }, t);
cerr << ')';
}
template<typename T> void __print (stack<T> s) {
vector<T> debugVector;
while (!s.empty()) {
T t = s.top();
debugVector.push_back(t);
s.pop();
}
reverse(debugVector.begin(), debugVector.end());
__print(debugVector);
}
template<typename T> void __print (queue<T> q) {
vector<T> debugVector;
while (!q.empty()) {
T t = q.front();
debugVector.push_back(t);
q.pop();
}
__print(debugVector);
}
template<typename T, typename... U> void __print (priority_queue<T, U...> q) {
vector<T> debugVector;
while (!q.empty()) {
T t = q.top();
debugVector.push_back(t);
q.pop();
}
__print(debugVector);
}
void _print() { cerr << "]\n"; }
template <typename Head, typename... Tail> void _print (const Head &H, const Tail &...T) {
__print(H);
if (sizeof...(T)) cerr << ", ";
_print(T...);
}
#ifdef DEBUG
#define D(...) cerr << "Line:" << __LINE__ << " [" << #__VA_ARGS__ << "] = ["; _print(__VA_ARGS__)
#else
#define D(...)
#endif
const double EPS = numeric_limits<double>::epsilon();
struct Line {
ll m;
ll c;
ll k;
double p;
};
struct CHT {
vector<Line> lines;
double getX(ll m1, ll c1, ll m2, ll c2) {
return (double) (c1 - c2) / (double) (m2 - m1 + EPS);
}
void addLine(ll m, ll c, ll k) {
double p = LLONG_MIN;
while (!lines.empty()) {
p = getX(m, c, lines.back().m, lines.back().c);
if (p < lines.back().p - EPS) lines.pop_back();
else break;
}
lines.push_back({m, c, k, p});
}
pair<ll, int> getY(ll x) {
int l = 0, r = lines.size() - 1, ret = 0;
while (l <= r) {
int m = (l + r) / 2;
if (lines[m].p <= x + EPS) {
ret = m;
l = m + 1;
} else {
r = m - 1;
}
}
assert(ret < lines.size());
return {lines[ret].m * x + lines[ret].c, lines[ret].k};
}
void reset() { lines.clear(); }
CHT() {}
CHT(Line l) { addLine(l.m, l.c, l.k); }
} ch;
int sz;
vector<ll> lf, rh;
vector<pair<int, int>> temp;
ll sm, lg, md, idx;
pair<ll, int> calc(ll bonus) {
vector<pair<ll, int>> dp(sz + 1);
dp[0] = {0, 0};
ch.reset();
ch.addLine(-2 * lf[1], lf[1] * lf[1], 0);
for (int i = 1; i <= sz; i++) {
ll curr = rh[i] + 1;
pair<ll, int> bst = ch.getY(curr);
dp[i].f = bst.f + curr * curr + bonus;
dp[i].s = bst.s + 1;
if (i < sz) {
ch.addLine(-2 * lf[i + 1], dp[i].f + lf[i + 1] * lf[i + 1] - max(0ll, rh[i] - lf[i + 1] + 1) * max(0ll, rh[i] - lf[i + 1] + 1), dp[i].s);
}
}
return dp[sz];
}
ll take_photos(int n, int m, int k, vector<int> r, vector<int> c) {
lf.push_back(-1);
rh.push_back(-1);
for (int i = 0; i < n; i++) {
if (c[i] < r[i]) swap(r[i], c[i]);
temp.push_back({c[i], r[i]});
}
sort(temp.begin(), temp.end());
temp.erase(unique(temp.begin(), temp.end()), temp.end());
D(temp);
for (pair<int, int> curr : temp) {
if (curr.f == rh.back()) continue;
while (lf.size() && curr.s <= lf.back() && rh.back() <= curr.f) {
lf.pop_back();
rh.pop_back();
}
lf.push_back(curr.s);
rh.push_back(curr.f);
}
D(lf);
D(rh);
sm = 0, lg = (ll) (m + 1) * (ll) (m + 1), idx = 200, sz = lf.size() - 1;
while (idx--) {
md = (sm + lg) / 2;
pair<ll, int> curr = calc(md);
if (curr.s == k) {
return curr.f - md * (ll) k;
}
if (curr.s < k) lg = md;
else sm = md;
}
return calc(lg).f - lg * (ll) k;
}
