#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
void maxup(ll &a, ll b) {
a = max(a, b);
}
long long max_weights(int n, int cnt_fish, std::vector<int> XX, std::vector<int> YY, std::vector<int> WW) {
const ll inf = (ll) 1e18 + 7;
n += 7;
vector<set<int>> interestingSet(n);
vector<vector<int>> interesting(n);
vector<vector<vector<ll>>> dp(2, vector<vector<ll>> (n));
vector<vector<ll>> both(n);
vector<ll> dp_zero(n, 0LL);
vector<vector<pair<int, ll>>> pe(n);
assert((int) XX.size() == cnt_fish);
assert((int) YY.size() == cnt_fish);
assert((int) WW.size() == cnt_fish);
for (int i = 0; i < cnt_fish; i++) {
int x = XX[i] + 5, y = YY[i] + 1, w = WW[i];
pe[x].push_back({y, w});
vector<int> xs = {x - 1, x + 1};
for (auto &i : xs) {
interestingSet[i].insert(y);
}
}
for (int x = 0; x < n; x++) {
interestingSet[x].insert(0);
for (auto &y : interestingSet[x]) {
interesting[x].push_back(y);
}
dp[0][x].resize((int) interesting[x].size(), 0LL);
dp[1][x].resize((int) interesting[x].size(), 0LL);
both[x].resize((int) interesting[x].size(), 0LL);
sort(pe[x].begin(), pe[x].end());
ll sum = 0;
for (auto &it : pe[x]) {
sum += it.second;
it.second = sum;
}
}
function<ll(int, int)> get = [&] (int x, int y) {
if (x == n) {
return 0LL;
}
assert(0 <= x && x < n);
assert(0 <= y && y < n);
ll sol = 0;
int low = 0, high = (int) pe[x].size() - 1;
while (low <= high) {
int mid = (low + high) / 2;
if (pe[x][mid].first <= y) {
sol = pe[x][mid].second;
low = mid + 1;
} else {
high = mid - 1;
}
}
return sol;
};
for (int i = 5; i < n - 2; i++) {
{
maxup(dp_zero[i], dp_zero[i - 1]);
for (int ant_j = 0; ant_j < (int) interesting[i - 1].size(); ant_j++) {
int h2 = interesting[i - 1][ant_j];
maxup(dp_zero[i], both[i - 1][ant_j]);
}
}
{
vector<ll> dp_ant0((int) interesting[i].size());
{
int q = 0, w = 0;
ll Fpref = -inf, Spref = -inf;
for (int j = 0; j < (int) interesting[i].size(); j++) {
int h = interesting[i][j];
while (q < (int) interesting[i - 2].size() && interesting[i - 2][q] < h) {
maxup(Fpref, both[i - 2][q]);
q++;
}
while (w < (int) interesting[i - 1].size() && interesting[i - 1][w] < h) {
int h2 = interesting[i - 1][w];
maxup(Spref, dp[1][i - 1][w] - get(i, h2) - get(i - 1, h2));
w++;
}
maxup(dp_ant0[j], Fpref + get(i + 1, h));
maxup(dp_ant0[j], dp_zero[i - 2] + get(i - 1, h) + get(i + 1, h));
maxup(dp[1][i][j], Spref + get(i - 1, h) + get(i + 1, h));
}
}
{
int q = (int) interesting[i - 2].size(), w = (int) interesting[i - 1].size();
ll Fsuf = -inf, Ssuf = -inf;
for (int j = (int) interesting[i].size() - 1; j >= 0; j--) {
int h = interesting[i][j];
while (q - 1 >= 0 && interesting[i - 2][q - 1] >= h) {
q--;
maxup(Fsuf, both[i - 2][q] + - get(i - 1, interesting[i - 2][q]));
}
while (w - 1 >= 0 && interesting[i - 1][w - 1] >= h) {
w--;
maxup(Ssuf, both[i - 1][w]);
}
maxup(dp_ant0[j], Fsuf + get(i - 1, h) + get(i + 1, h));
maxup(dp[0][i][j], Ssuf - get(i, h) + get(i + 1, h));
}
}
for (int j = 0; j < (int) interesting[i].size(); j++) {
maxup(dp[0][i][j], dp_ant0[j]);
maxup(dp[1][i][j], dp_ant0[j]);
both[i][j] = max(dp[0][i][j], dp[1][i][j]);
}
}
}
ll sol = 0;
for (int i = 0; i < n; i++) {
maxup(sol, dp_zero[i]);
for (int j = 0; j < (int) interesting[i].size(); j++) {
maxup(sol, both[i][j]);
}
}
return sol;
}
