#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
typedef long long ll;
typedef pair<ll,ll> ii;
const int N = 1e5;
const ll INF = 1e18;
int sz;
ll dp[N+2], bt[N+2];
vector<int> r, c;
struct line {
ll m, c;
line(ll x, ll y): m(x), c(y) {}
bool operator == (line v) {
return m == v.m && c == v.c;
}
ll operator () (ll x) {
return m*x+c;
}
};
struct convexHull {
vector<line> v;
vector<int> id;
convexHull() {
v.clear(); id.clear();
}
bool greater(ll a, ll b, ll c, ll d) {
if (a/b != c/d) return a/b > c/d;
return (a%b)*d >= (c%d)*b;
}
bool bad(line a, line b, line c, int x, int y) {
if (b == c) return bt[x] > bt[y];
return greater(b.c-a.c,a.m-b.m,c.c-b.c,b.m-c.m);
}
void insert(line x, int y) {
int sz = v.size();
while (sz >= 2 && bad(v[sz-2],v[sz-1],x,id[sz-1],y)) {
v.pop_back(); sz--;
id.pop_back();
}
v.push_back(x);
id.push_back(y);
}
ii query(ll x) {
ii ret = ii(INF,INF);
for (int l = 0, r = v.size()-1; l <= r; ) {
int mid = (l+r)/2;
if (v[mid](x) < ret.fi || v[mid](x) == ret.fi && bt[id[mid]] < ret.se) ret = ii(v[mid](x),bt[id[mid]]);
if (mid+1 <= r && v[mid+1](x) < v[mid](x)) l = mid+1;
else r = mid-1;
}
return ret;
}
};
ll sqr(ll a) {
return a*a;
}
int monge(ll mid) {
convexHull ch;
for (int i = 1; i <= sz; i++) {
ch.insert(line(-2*(r[i]-1),dp[i-1]+sqr(r[i]-1)),i-1);
ii opt = ch.query(c[i]);
dp[i] = opt.fi+sqr(c[i])+mid;
bt[i] = opt.se+1;
// cout << dp[i] << ' ';
}
// cout << '\n';
return bt[sz];
}
ll take_photos(int n, int m, int k, vector<int> R, vector<int> C) {
vector<ii> tmp;
for (int i = 0; i < n; i++) {
if (R[i] > C[i]) swap(R[i],C[i]);
tmp.push_back(ii(R[i],C[i]));
}
sort(tmp.begin(),tmp.end());
r.push_back(-1); c.push_back(-1);
for (auto i : tmp) {
while (r.back() == i.fi) {
r.pop_back(); c.pop_back();
}
r.push_back(i.fi); c.push_back(i.se);
}
sz = r.size()-1;
ll cost = -1, ans = -1;
for (ll l = 0, r = (ll)m*m; l <= r; ) {
ll mid = (l+r)/2;
if (monge(mid) <= k) {
ans = dp[sz], cost = mid;
r = mid-1;
}
else l = mid+1;
}
assert(ans >= 0);
return ans-cost*k;
}
/*
5 7 2
0 3
4 4
4 6
4 5
4 6
2 6 2
1 4
4 1
*/
