/* cerberus97 - Hanit Banga */
// #pragma comment(linker, "stack:200000000")
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include "squad.h"
#include <iostream>
#include <iomanip>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
using namespace std;
#define pb push_back
#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL)
typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
const int N = 3e5 + 10;
// Attribution - t3nsor codebook
struct ConvexHullTrick {
typedef long long LL;
vector<int> M;
vector<int> B;
vector<int> ids;
vector<double> left;
ConvexHullTrick() {}
bool bad(LL m1, LL b1, LL m2, LL b2, LL m3, LL b3) {
// Careful, this may overflow
return (b3-b1)*(m1-m2) < (b2-b1)*(m1-m3);
}
// Add a new line to the structure, y = mx + b.
// Lines must be added in decreasing order of slope.
void add(LL m, LL b, int id) {
while (M.size() >= 2 && bad(M[M.size()-2], B[B.size()-2], M.back(), B.back(), m, b)) {
M.pop_back(); B.pop_back(); ids.pop_back(); left.pop_back();
}
if (M.size() && M.back() == m) {
if (B.back() > b) {
M.pop_back(); B.pop_back(); ids.pop_back(); left.pop_back();
} else {
return;
}
}
if (M.size() == 0) {
left.push_back(-numeric_limits<double>::infinity());
} else {
left.push_back((double)(b - B.back())/(M.back() - m));
}
M.push_back(m);
B.push_back(b);
ids.push_back(id);
}
// Get the minimum value of mx + b among all lines in the structure.
// There must be at least one line.
pll query(LL x, LL y) {
int i = upper_bound(left.begin(), left.end(), double(y) / x) - left.begin();
return {-(M[i-1]*y + B[i-1]*x), ids[i - 1]};
}
};
struct player_t {
int a, d, p;
bool operator<(const player_t &o) const {
return p < o.p;
}
};
int n;
player_t player[N];
ConvexHullTrick cht_atk[3], cht_def[3];
void build(int n, vector<pii> vals, ConvexHullTrick cht[3]);
ll BestSquad(int x, int y);
void Init(std::vector<int> A, std::vector<int> D, std::vector<int> P){
n = A.size();
for (int i = 1; i <= n; ++i) {
player[i] = {A[i - 1], D[i - 1], P[i - 1]};
}
sort(player + 1, player + n + 1);
vector<pii> def_vals, atk_vals;
for (int i = 1; i <= n; ++i) {
def_vals.pb({player[i].d, player[i].p});
atk_vals.pb({player[i].a, player[i].p});
}
build(n, def_vals, cht_def);
build(n, atk_vals, cht_atk);
}
void build(int n, vector<pii> vals, ConvexHullTrick cht[3]) {
for (int i = 0; i < n; ++i) {
cht[2].add(-vals[i].second, -vals[i].first, i);
}
vector<vector<bool>> at(2, vector<bool>(n, false));
int sz = cht[2].ids.size();
for (int j = 0; j < sz; ++j) {
at[j % 2][cht[2].ids[j]] = true;
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < 2; ++j) {
if (!at[j][i]) {
cht[j].add(-vals[i].second, -vals[i].first, i);
}
}
}
}
ll BestSquad(int x, int y) {
// auto ba = cht_atk.query(x, y);
// auto bd = cht_def.query(x, y);
// if (ba.second != bd.second) {
// return ba.first + bd.first;
// }
// auto sa =
// auto sd =
// return max(ba.first + td.first, bd.first + ta.first);
ll best = 0;
for (int ja = 0; ja < 2; ++ja) {
auto qa = cht_atk[ja].query(x, y);
for (int jd = 0; jd < 2; ++jd) {
auto qd = cht_def[jd].query(x, y);
if (qa.second != qd.second) {
best = max(best, qa.first + qd.first);
}
}
}
return best;
}
