#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 nbFish, std::vector<int> X, std::vector<int> Y, std::vector<int> W) {
++szCarre;
vector<v64> carre(szCarre, v64(szCarre));
vector<vector<bool>> nice(szCarre, vector<bool>(szCarre+1, false));
rep(i, 0, nbFish) {
++X[i];
carre[X[i]][Y[i]] = W[i];
nice[X[i]-1][Y[i]] = true;
if (X[i]+1 < szCarre) {
nice[X[i]+1][Y[i]] = true;
}
}
vector<v64> prefSum(szCarre, v64(szCarre+1, 0));
rep(col, 0, szCarre) {
nice[col][0] = nice[col][szCarre] = true;
auto &ss = prefSum[col];
rep(lig, 0, szCarre) {
ss[lig+1] = ss[lig] + carre[col][lig];
}
}
a2v64 minInf;
minInf[0] = minInf[1] = v64(szCarre+1, -INF);
a2v64 dpOld = minInf;
dpOld[INCR][0] = dpOld[DECR][0] = 0;
rep(col, 1, szCarre) {
a2v64 dpNew = minInf;
dpNew[INCR][0] = *max_element(all(dpOld[DECR]));
if (true) {
auto &sumPrev = prefSum[col-1];
ll maxTr = -INF;
rep(take, 0, szCarre+1) {
int ptrNice = take;
while (!nice[col-1][ptrNice]) --ptrNice;
chmax(maxTr, dpOld[INCR][ptrNice] - sumPrev[take]);
chmax(dpNew[INCR][take], maxTr + sumPrev[take]);
}
}
if (true) {
auto &sumCur = prefSum[col];
ll maxTr = -INF;
for (int take = szCarre; take >= 0; --take) {
int ptrNice = take;
while (!nice[col-1][ptrNice]) ++ptrNice;
chmax(maxTr, dpOld[DECR][ptrNice] + sumCur[take]);
chmax(dpNew[DECR][take], maxTr - sumCur[take]);
}
}
rep(take, 0, szCarre+1) {
if (nice[col][take])
chmax(dpNew[DECR][take], dpNew[INCR][take]);
else
dpNew[INCR][take] = dpNew[DECR][take] = -INF;
}
dpOld = dpNew;
}
return *max_element(all(dpOld[DECR]));
}
