#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
#define X first
#define Y second
ll INF = 1e18;
ld EPS = 1e-10;
inline ll sq(ll x) {
return 2LL * x * x;
}
struct Parabolas {
int ind = 0;
vector<ll> A, B, C;
ld intersection(ll a, ll b, ll c, ll d) {
return (ld(sq(c) + d - sq(a) - b) / ld(2LL * c - 2LL * a));
}
bool ok(ll a, ll b, ll c, ll d) {
if(a == c)
return false;
//~ cout << "ok" << (ld(sq(c) + d - sq(a) - b) / ld(2LL * c - 2LL * a)) + EPS << endl;
return intersection(a, b, c, d) + EPS > max(a, c);
}
void clear() {
ind = 0;
A.clear();
B.clear();
C.clear();
}
void insert(ll a, ll b, ll c) {
//~ cout << "ins"<<a << " "<< b << endl;
while((!A.empty() && !ok(A.back(), B.back(), a, b))
|| (A.size() >= 2 && intersection(A[A.size()-2], B[B.size()-2], A.back(), B.back()) > intersection(a, b, A.back(), B.back())) ){
A.pop_back();
B.pop_back();
C.pop_back();
if(ind == A.size()) ind--;
}
ind = max(ind, 0);
A.push_back(a);
B.push_back(b);
C.push_back(c);
}
//~ ll query(ll x) {
//~ ll res = INF;
//~ for(int i = 0 ; i < A.size() ; i++)
//~ res= min(res, sq(x-A[i]) + B[i]);
//~ return res;
//~ }
pll query(ll x) {
if(A.size() == 0)
return {INF, INF};
while(ind + 1 < A.size() && sq(x - A[ind + 1]) + B[ind + 1] <= sq(x - A[ind]) + B[ind])
ind++;
//~ for(int i = 0 ; i < A.size() ; i++)
//~ cout << "(" << A[i] << ", " << B[i] << ": " << sq(x - A[i]) + B[i] << ") ";
//~ cout << endl << "x=" << x << " ind=" << ind << endl;
return {sq(x - A[ind]) + B[ind], C[ind] + 1};
}
};
int l, k;
int d[100007], x[100007];
int maxx[1000007];
Parabolas P;
pll dp[100007]; // n => {res, parts}
pll calc_dp(ll alfa) {
for(int i = 0 ; i < 100007 ; i++)
dp[i] = {INF, INF};
dp[0] = {0, 0};
P.clear();
for(int i = 0 ; i <= l ; i++) {
if(i > 0)
dp[i] = P.query(x[i]);
//~ cout << i << " " << j << " " << dp[j][i] << endl;
if(i < l && dp[i].X != INF)
P.insert(d[i + 1] - 1, dp[i].X - sq(max(0, x[i] - d[i + 1] + 1)) + alfa, dp[i].Y);
}
if(alfa <= 0) {
dp[l].X += alfa * (k - dp[l].Y);
dp[l].Y = k;
}
return dp[l];
}
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
::k = k;
for(int i = 0 ; i < n ; i++) {
if(c[i] >= r[i]) maxx[r[i] + 1] = max(maxx[r[i] + 1], c[i] + 1);
else maxx[c[i] + 1] = max(maxx[c[i] + 1], r[i] + 1);
}
for(int i = 1 ; i <= m ; i++) {
if(maxx[i] && (l == 0 || x[l] < maxx[i])) {
l++;
d[l] = i;
x[l] = maxx[i];
//~ cout << d[l] << " " << x[l] << endl;
}
}
ll pocz = 0, kon = ll(2e12), mid;
while(pocz < kon) {
mid = (pocz + kon) / 2;
pll p = calc_dp(2LL * mid - 1);
if(p.Y <= k)
kon = mid;
else
pocz = mid + 1;
}
pll p = calc_dp(2LL * pocz - 1);
ll res = (p.X - p.Y * (2LL * pocz - 1)) / 2LL;
if(p.Y < k) {
pll p2 = calc_dp(2LL * pocz - 3);
ll res2 = (p2.X - p2.Y * (2LL * pocz - 3)) / 2LL;
//~ cout << 2LL * pocz - 1 << " "<< p.X << " " << p.Y << " " << res<<endl;
//~ cout << 2LL * pocz - 3 << " "<< p2.X << " " << p2.Y << " " << res2<<endl;
return res - (res - res2) / (p2.Y - p.Y) * (k - p.Y);
}
//~ cout << p.X << " " << p.Y << endl;
return res;
}
