#include "fish.h"
#include "bits/stdc++.h";
using namespace std;
#define forR(i, x) for(int i = 0; i < (x); ++i)
#define REP(i, a, b) for(int i = (a); i < (b); ++i)
#define all(x) x.begin(), x.end()
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<int> vi;
typedef vector<vi> vvi;
struct pii{int a, b;};
ll INF = 1e16;
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
std::vector<int> W) {
int MH = Y[0] + 1;
for(int i : Y) MH = max(MH, i + 1);
vvll wp(N, vll(MH));
vvll wpsa(N, vll(MH));
forR(i, M) wp[X[i]][Y[i]] = W[i];
forR(x, N) {
wpsa[x][0] = wp[x][0];
REP(y, 1, MH) wpsa[x][y] = wpsa[x][y-1] + wp[x][y];
}
vector<set<int>> sCare(N);
forR(i, M) {
if(X[i] > 0) sCare[X[i]-1].insert(Y[i] + 1);
if(X[i] + 1 < N) sCare[X[i] + 1].insert(Y[i] + 1);
if(X[i] > 1) sCare[X[i]-2].insert(Y[i] + 1);
if(X[i] + 2 < N) sCare[X[i] + 2].insert(Y[i] + 1);
sCare[X[i]].insert(Y[i]+1);
}
forR(i, N) sCare[i].insert(0);
vector<vi> care(N);
forR(i, N) for(int j : sCare[i]) care[i].push_back(j);
vvll I(N), D(N), E(N);
forR(i, N) I[i].resize(care[i].size()), D[i].resize(care[i].size()), E[i].resize(care[i].size());
// h = HEIGHT, not the index of last element!
forR(i, N) {
ll besIE = -INF, besII = -INF;
if(i > 0) {
forR(ki, care[i-1].size()) {
int k = care[i-1][ki];
besIE = max(besIE, E[i-1][ki] - (k > 0 ? wpsa[i-1][k-1] : 0));
}
}
int api = 0;
forR(hi, care[i].size()) {
int h = care[i][hi];
if(h > 0) {
if(i == 0) I[i][hi] = 0;
else {
I[i][hi] = max(I[i][hi], besIE + wpsa[i-1][h-1]);
while(api < care[i-1].size() && care[i-1][api] <= h) {
int k = care[i-1][api];
besII = max(besII, I[i-1][api] - (k > 0 ? wpsa[i-1][k-1] : 0));
++api;
}
I[i][hi] = max(I[i][hi], besII + wpsa[i-1][h-1]);
}
}
}
api = (int) care[i-1].size() - 1;
ll besD = -INF;
for(int hi = (int) care[i].size() - 1; hi >= 0; --hi){
int h = care[i][hi];
if(h > 0) {
if(i == 0) D[i][hi] = 0;
else {
while(api >= 0 && care[i-1][api] >= h + 1) {
int k = care[i-1][api];
if(k <= MH) {
besD = max(besD, max(I[i-1][api], D[i-1][api]) + wpsa[i][k - 1]);
}
--api;
}
D[i][hi] = max(D[i][hi], besD - (h > 0 ? wpsa[i][h-1] : 0));
}
}
}
ll besE = -INF;
if(i > 0) {
forR(yi, care[i-1].size()) besE = max(besE, E[i-1][yi]);
}
forR(hi, care[i].size()){
int h = care[i][hi];
if(i == 0) E[i][hi] = 0;
else {
int pInd = lower_bound(all(care[i-1]), h) - care[i-1].begin();
if(care[i-1][pInd] == h) {
ll tot = max(I[i-1][pInd], D[i-1][pInd]) + (h > 0 ? wpsa[i][h-1] : 0);
E[i][hi] = max(E[i][hi], max(tot, besE));
}
}
}
}
ll mx = 0;
forR(hi, care[N-1].size()) if(care[N-1][hi] > 0) mx = max(mx, max(I[N-1][hi], D[N-1][hi]));
forR(hi, care[N-1].size()) mx = max(mx, E[N-1][hi]);
return mx;
}
