#include <bits/stdc++.h>
#include "fish.h"
using namespace std;
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define sz(v) ((int)((v).size()))
template<typename T>
void chmax(T &x, const T &v) { if (x < v) x = v; }
template<typename T>
void chmin(T &x, const T &v) { if (x > v) x = v; }
using ll = long long;
using v64 = vector<ll>;
using a2v64 = array<v64, 2>;
using p64 = pair<ll, ll>;
string to_string(string s) { return s; }
template <typename T> string to_string(T v) {
bool first = true;
string res = "[";
for (const auto &x : v) {
if (!first)
res += ", ";
first = false;
res += to_string(x);
}
res += "]";
return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
cout << ' ' << to_string(H);
dbg_out(T...);
}
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
const ll INF = 3e18;
const int INCR = 0, DECR = 1;
ll max_weights(int szCarre, int totFish, std::vector<int> X, std::vector<int> Y, std::vector<int> W) {
++szCarre;
vector<vector<p64>> fish(szCarre);
vector<vector<int>> niceTake(szCarre);
rep(i, 0, totFish) {
++X[i];
fish[X[i]].emplace_back(Y[i], W[i]);
// Y+1 pour couvrir Y
niceTake[X[i]-1].push_back(Y[i] + 1);
if (X[i]+1 < szCarre) {
niceTake[X[i]+1].push_back(Y[i] + 1);
}
}
v64 nbNice(szCarre), nbFish(szCarre);
vector<v64> prefSum(szCarre);
rep(col, 0, szCarre) {
auto &nice = niceTake[col];
nice.push_back(0);
sort(all(nice));
nice.resize(unique(all(nice)) - begin(nice));
nbNice[col] = sz(nice);
sort(all(fish[col]));
nbFish[col] = sz(fish[col]);
auto &ss = prefSum[col];
ss.push_back(0);
for (auto [_, w] : fish[col]) {
ss.push_back(ss.back() + w);
}
}
a2v64 dpOld;
dpOld[0] = dpOld[1] = v64(nbNice[0], -INF);
dpOld[INCR][0] = dpOld[DECR][0] = 0;
rep(col, 1, szCarre) {
a2v64 dpNew;
dpNew[0] = dpNew[1] = v64(nbNice[col], -INF);
dpNew[INCR][0] = *max_element(all(dpOld[DECR]));
if (true) {
ll maxTr = -INF;
int ptrOld = 0, ptrOldFish = 0, ptrNewFish = 0;
/// retourne la somme des poissons < upTo dans col-1
auto sfIncr = [&] (int &ptr, int upTo) {
while (ptr < nbFish[col-1] && fish[col-1][ptr].first < upTo) {
++ptr;
}
return prefSum[col-1][ptr];
};
rep(ptrNew, 0, nbNice[col]) {
int newTake = niceTake[col][ptrNew];
while (ptrOld < nbNice[col-1] && niceTake[col-1][ptrOld] <= newTake) {
int oldTake = niceTake[col-1][ptrOld];
chmax(maxTr, dpOld[INCR][ptrOld] - sfIncr(ptrOldFish, oldTake));
++ptrOld;
}
chmax(dpNew[INCR][ptrNew], maxTr + sfIncr(ptrNewFish, newTake));
}
}
if (true) {
ll maxTr = -INF;
int ptrOld = nbNice[col-1]-1, ptrOldFish = nbFish[col], ptrNewFish = nbFish[col];
/// retourne la somme des poissons < upTo dans col
auto sfDecr = [&] (int &ptr, int upTo) {
while (ptr > 0 && fish[col][ptr-1].first >= upTo) {
--ptr;
}
return prefSum[col][ptr];
};
for (int ptrNew = nbNice[col]-1; ptrNew >= 0; --ptrNew) {
int newTake = niceTake[col][ptrNew];
while (ptrOld >= 0 && niceTake[col-1][ptrOld] >= newTake) {
int oldTake = niceTake[col-1][ptrOld];
chmax(maxTr, dpOld[DECR][ptrOld] + sfDecr(ptrOldFish, oldTake));
--ptrOld;
}
chmax(dpNew[DECR][ptrNew], maxTr - sfDecr(ptrNewFish, newTake));
}
}
rep(take, 0, nbNice[col]) {
chmax(dpNew[DECR][take], dpNew[INCR][take]);
}
dpOld = dpNew;
}
return *max_element(all(dpOld[DECR]));
}
