#include <bits/stdc++.h>
using namespace std;
const long long oo = 1LL << 60;
using ll = long long;
struct Line {
mutable ll k, m, p; // y = kx + m
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) { x->p = inf; return false; }
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
long long take_photos(int n, int m, int k, vector<int> r, vector<int> c)
{
vector<pair<int, int>> a = {{-1, -1}};
for (int i = 0; i < n; i++)
a.push_back({min(r[i], c[i]), max(r[i], c[i]) + 1});
sort(begin(a), end(a));
int cur = 0;
for (int i = 1; i <= n; i++)
if (a[i].first == a[cur].first) a[cur].second = a[i].second;
else if (a[i].second > a[cur].second) a[++cur] = a[i];
n = cur;
auto sqr = [&](int x)
{
return 1LL * x * x;
};
long long ans = oo;
vector<long long> f(n + 1, oo);
f[0] = 0;
for (int i = 1; i <= k; i++)
{
LineContainer lc;
vector<long long> newF(n + 1, oo);
for (int j = 1; j <= n; j++)
{
long long value = f[j - 1] + sqr(a[j].first) - sqr(max(0, a[j - 1].second - a[j].first));
if (f[j - 1] != oo)
lc.add(- a[j].first * 2, value);
if (!lc.empty())
newF[j] = lc.query(a[j].second) + sqr(a[j].second);
}
swap(f, newF);
ans = min(ans, f[n]);
}
return ans;
}
