#include <cstdio>
#include <stdio.h>
#include <iostream>
#include <math.h>
#include <vector>
#include <queue>
#include <stack>
#include <deque>
#include <algorithm>
#include <utility>
#include <set>
#include <map>
#include <stdlib.h>
#include <cstring>
#include <string.h>
#include <string>
#include <sstream>
#include <assert.h>
#include <climits>
#include <sstream>
#include <numeric>
#include <time.h>
#include <limits.h>
#include <list>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <iomanip>
#include <complex>
#include <chrono>
#include <fstream>
#include <functional>
#include <unistd.h>
// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx,avx2,bmi,bmi2,lzcnt,popcnt")
#define lowbit(x) ((x) & -(x))
#define ml(a, b) ((1ll * (a) * (b)) % M)
#define tml(a, b) (a) = ((1ll * (a) * (b)) % M)
#define ad(a, b) ((0ll + (a) + (b)) % M)
#define tad(a, b) (a) = ((0ll + (a) + (b)) % M)
#define mi(a, b) ((0ll + M + (a) - (b)) % M)
#define tmi(a, b) (a) = ((0ll + M + (a) - (b)) % M)
#define tmin(a, b) (a) = min((a), (b))
#define tmax(a, b) (a) = max((a), (b))
#define iter(a) (a).begin(), (a).end()
#define riter(a) (a).rbegin(), (a).rend()
#define init(a, b) memset((a), (b), sizeof(a))
#define cpy(a, b) memcpy((a), (b), sizeof(a))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define pb emplace_back
#define mpr make_pair
#define ls(i) ((i) << 1)
#define rs(i) ((i) << 1 | 1)
#define INF 0x3f3f3f3f
#define NIF 0xc0c0c0c0
#define eps 1e-9
#define F first
#define S second
#define AC cin.tie(0)->sync_with_stdio(0)
using namespace std;
typedef long long llt;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef pair<llt, llt> pll;
typedef complex<double> cd;
// const int M = 998244353;
// random_device rm;
// mt19937 rg(rm());
// default_random_engine rg(rm());
// uniform_int_distribution<int> rd(INT_MIN, INT_MAX);
// uniform_real_distribution<double> rd(0, M_PI);
void db() { cerr << "\n"; }
template <class T, class... U>
void db(T a, U... b) { cerr << a << " ", db(b...); }
inline char gc()
{
const static int SZ = 1 << 16;
static char buf[SZ], *p1, *p2;
if (p1 == p2 && (p2 = buf + fread(p1 = buf, 1, SZ, stdin), p1 == p2))
return -1;
return *p1++;
}
void rd() {}
template <typename T, typename... U>
void rd(T &x, U &...y)
{
x = 0;
bool f = 0;
char c = gc();
while (!isdigit(c))
f ^= !(c ^ 45), c = gc();
while (isdigit(c))
x = (x << 1) + (x << 3) + (c ^ 48), c = gc();
f && (x = -x), rd(y...);
}
template <typename T>
void prt(T x)
{
if (x < 0)
putchar('-'), x = -x;
if (x > 9)
prt(x / 10);
putchar((x % 10) ^ 48);
}
struct L
{
llt a, b;
inline llt operator()(llt x) { return a * x + b; }
};
inline llt itp(const L &l1, const L &l2)
{
return (l1.b - l2.b) / (l2.a - l1.a);
}
inline bool ck(const L &l1, const L &l2, const L &l3)
{
return itp(l2, l3) <= itp(l1, l2);
}
const int N = 1e5 + 5;
pll pt[N];
vector<pll> ar(1, mpr(-1, -1));
llt dp[N], vv;
int fr[N];
void slv(int n)
{
deque<pair<L, int>> q;
q.pb(mpr(L{-2 * ar[1].F, ar[1].F * ar[1].F}, 0));
for (int i = 1; i <= n; i++)
{
while (q.size() > 1 && q[1].F(ar[i].S) <= q[0].F(ar[i].S))
q.pop_front();
fr[i] = q[0].S + 1, dp[i] = q[0].F(ar[i].S) + ar[i].S * ar[i].S + vv;
if (i == n)
return;
L tp = {-2 * ar[i + 1].F, dp[i] + ar[i + 1].F * ar[i + 1].F};
if (ar[i].S > ar[i + 1].F)
tp.b -= (ar[i].S - ar[i + 1].F) * (ar[i].S - ar[i + 1].F);
while (q.size() > 1 && ck(q[q.size() - 2].F, q.back().F, tp))
q.pop_back();
q.pb(mpr(tp, fr[i]));
}
}
llt take_photos(int n, int m, int k, vector<int> xr, vector<int> yr)
{
for (int i = 0; i < n; i++)
{
pt[i].F = xr[i], pt[i].S = yr[i];
if (pt[i].F > pt[i].S)
swap(pt[i].F, pt[i].S);
pt[i].S++;
}
sort(pt, pt + n);
for (int i = 0; i < n; i++)
{
if (pt[i].F == ar.back().F)
tmax(ar.back().S, pt[i].S);
else if (pt[i].S > ar.back().S)
ar.pb(pt[i]);
}
n = ar.size() - 1, tmin(k, n);
llt l = -1000000000000ll, r = 1000000000000ll;
while (l < r - 1)
{
vv = (l + r) >> 1, slv(n);
if (fr[n] == k)
return dp[n] - vv * k;
if (fr[n] > k)
l = vv;
else
r = vv;
}
vv = l, slv(n);
llt a1 = dp[n] - vv * fr[n], p1 = fr[n];
vv = r, slv(n);
llt a2 = dp[n] - vv * fr[n], p2 = fr[n];
assert(p1 > p2 + 1);
assert(!((a1 - a2) % (p1 - p2)));
vv = l, slv(n);
return dp[n] - vv * k;
}
// signed main()
// {
// int n, m, k;
// rd(n, m, k);
// vector<int> xr(n), yr(n);
// for (int i = 0; i < n; i++)
// rd(xr[i], yr[i]);
// cerr << take_photos(n, m, k, xr, yr) << ' ';
// }
