#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int INF = 1e9 + 5;
long long max_weights(int n, int m, vector<int> x, vector<int> y,
vector<int> w) {
vector<vector<pair<int,int>>> g(n + 2, vector<pair<int,int>>(1, {0,0}));
vector<vector<int>> pts(n + 2, vector<int>(1, 0));
for(int i = 0; i < m; i++){
g[x[i] + 1].emplace_back(y[i] + 1, w[i]);
if(x[i] != 0) pts[x[i]].push_back(y[i] + 1);
pts[x[i] + 2].push_back(y[i] + 1);
}
for(int i = 0; i <= n + 1; i++){
sort(g[i].begin(), g[i].end());
sort(pts[i].begin(), pts[i].end());
pts[i].resize(unique(pts[i].begin(), pts[i].end()) - pts[i].begin());
}
for(int i = 1; i <= n; i++){
if(pts[i].back() != n){
pts[i].push_back(n);
}
}
vector<vector<ll>> sums(n + 2);
for(int i = 0; i <= n + 1; i++){
for(auto [j, x]: g[i]){
sums[i].push_back(x + (sums[i].empty() ? 0 : sums[i].back()));
}
}
vector<vector<ll>> dpl(n + 1);
vector<vector<ll>> dpr(n + 1);
vector<vector<ll>> dpr2(n + 1);
vector<vector<ll>> ans(n + 1);
dpl[0].push_back(0);
dpr[0].push_back(0);
dpr2[0].push_back(0);
ll fans = 0;
ll pre = 0;
for(int col = 1; col <= n; col++){
for(int row: pts[col]){
if(col >= 3){
pre = max(dpr[col - 3].front(), pre);
pre = max(dpl[col - 3].back(), pre);
}
auto it = prev(upper_bound(g[col].begin(), g[col].end(), make_pair(row, INF)));
ll sumUp = sums[col].back() - sums[col][it - g[col].begin()];
it = prev(upper_bound(g[col - 1].begin(), g[col - 1].end(), make_pair(row, INF)));
ll removeLeft = sums[col - 1].back() - sums[col - 1][it - g[col - 1].begin()];
auto it2 = prev(upper_bound(pts[col - 1].begin(), pts[col - 1].end(), row));
// left to left
if(row == 0){
dpl[col].push_back(dpl[col - 1][it2 - pts[col - 1].begin()] + sumUp - removeLeft);
}else{
dpl[col].push_back(max(dpl[col].back(), dpl[col - 1][it2 - pts[col - 1].begin()] + sumUp - removeLeft));
}
//left to right
it = prev(upper_bound(g[col + 1].begin(), g[col + 1].end(), make_pair(row, INF)));
ll rsum = sums[col + 1][it - g[col + 1].begin()];
dpr[col].push_back(dpl[col - 1][it2 - pts[col - 1].begin()] - removeLeft + rsum);
// right to right
it = prev(upper_bound(g[col].begin(), g[col].end(), make_pair(row, INF)));
it2 = lower_bound(pts[col - 1].begin(), pts[col - 1].end(), row);
ll ss = 0;
if(it2 != pts[col - 1].end()){
ss = dpr[col - 1][it2 - pts[col - 1].begin()] - sums[col][it - g[col].begin()];
dpr[col].back() = max(dpr[col].back(), dpr[col - 1][it2 - pts[col - 1].begin()] + rsum - sums[col][it - g[col].begin()]);
}
if(row == 0) dpr2[col].push_back(dpr[col].back() - rsum);
else dpr2[col].push_back(max(dpr2[col].back(), ss));
if(col >= 2){
// lower prev higher now
it2 = prev(upper_bound(pts[col - 2].begin(), pts[col - 2].end(), row));
dpl[col].back() = max(dpl[col].back(), dpr2[col - 2][it2 - pts[col - 2].begin()] + sumUp + sums[col - 1].back() - removeLeft);
it2 = lower_bound(pts[col - 2].begin(), pts[col - 2].end(), row);
if(it2 != pts[col - 2].end()){
dpr[col].back() = max(dpr[col].back(), dpr[col - 2][it2 - pts[col - 2].begin()] + rsum);
}
}
dpl[col].back() = max(dpl[col].back(), pre + sumUp + sums[col - 1].back() - removeLeft);
dpr[col].back() = max(dpr[col].back(), pre + sums[col - 1].back() - removeLeft + rsum);
fans = max(fans, dpr[col].back());
}
for(int i = (int) dpr[col].size() - 2; i >= 0; i--){
dpr[col][i] = max(dpr[col][i], dpr[col][i + 1]);
}
}
return fans;
}
