#include "fish.h"
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define mp make_pair
#define fr first
#define sc second
#define all(x) x.begin(),x.end()
const int maxn = 1e5+10;
const int maxqh = 12;
const int inf = 1e18+10;
int n, m;
vector<vector<int>> dp[maxn];
map<int,int> pf[maxn], pfmx0[maxn], pfmx1[maxn];
vector<pair<int,int>> fish[maxn]; // fishs from column i
vector<int> hr[maxn]; // important heights from column i, the ones that can be chosen
long long max_weights(int32_t N, int32_t M, vector<int32_t> X, vector<int32_t> Y, vector<int32_t> W) {
n = N;
m = M;
for(int i = 0; i < m; i++) {
fish[X[i]+1].pb(mp(Y[i]+1,W[i]));
hr[X[i]+1].pb(Y[i]);
}
for(int i = 0; i <= n; i++) {
hr[i].pb(0);
hr[i].pb(n);
sort(all(hr[i]));
sort(all(fish[i]));
hr[i].erase(unique(all(hr[i])),hr[i].end());
// Store only the relevant heights
for(int j = 0; j < hr[i].size(); j++) {
dp[i].pb({0,0});
}
}
for(int i = 1; i <= n; i++) {
for(auto j : hr[i-1]) pf[i][j] = 0;
for(auto j : hr[i]) pf[i][j] = 0;
for(auto j : hr[i+1]) pf[i][j] = 0;
for(auto aux : fish[i]) {
int y = aux.fr;
int w = aux.sc;
pf[i][y]+= w;
}
// Do a prefix sum on the weight of the fishs
pf[i][0] = 0;
for(auto it = next(pf[i].begin()); it != pf[i].end(); it++) {
it->sc+= prev(it)->sc;
}
}
// dp[i][h0][0/1] = until i, with h[i] = hr[i][h0]
// and it's greater/smaller tha the previous
// dp[1][h0][0/1] = 0
for(int h0 = 0; h0 < hr[1].size(); h0++) {
dp[1][h0][0] = 0;
dp[1][h0][1] = 0;
pfmx0[1][hr[1][h0]] = max(pfmx0[1][hr[1][h0]],dp[1][h0][0]-pf[1][hr[1][h0]]);
}
for(auto j : hr[2]) {
pfmx0[1][j] = max(pfmx0[1][j],0LL);
}
for(auto it = next(pfmx0[1].begin()); it != pfmx0[1].end(); it++) {
it->sc = max(it->sc,prev(it)->sc);
}
for(int i = 2; i <= n; i++) {
for(int h0 = 0; h0 < hr[i].size(); h0++) {
// It's greater than the previous
dp[i][h0][0] = 0;
dp[i][h0][0] = max(dp[i][h0][0], pfmx0[i-1][hr[i][h0]] + pf[i-1][hr[i][h0]]);
if(i != 2) {
// for(int h2 = 0; h2 < hr[i-2].size(); h2++) {
// if(hr[i-2][h2] > hr[i][h0]) continue;
// dp[i][h0][0] = max(dp[i][h0][0], dp[i-2][h2][1] + pf[i-1][hr[i][h0]]);
// dp[i][h0][0] = max(dp[i][h0][0], dp[i-2][h2][0] + pf[i-1][hr[i][h0]]);
// }
dp[i][h0][0] = max(dp[i][h0][0],pfmx1[i-2][hr[i][h0]] + pf[i-1][hr[i][h0]]);
}
// It's smaller than the previous
dp[i][h0][1] = 0;
for(int h1 = 0; h1 < hr[i-1].size(); h1++) {
if(hr[i-1][h1] < hr[i][h0]) continue;
dp[i][h0][1] = max(dp[i][h0][1], dp[i-1][h1][0]-pf[i][hr[i][h0]] + pf[i][hr[i-1][h1]]);
dp[i][h0][1] = max(dp[i][h0][1], dp[i-1][h1][1]-pf[i][hr[i][h0]] + pf[i][hr[i-1][h1]]);
}
pfmx0[i][hr[i][h0]] = max(pfmx0[i][hr[i][h0]],dp[i][h0][0]-pf[i][hr[i][h0]]);
pfmx1[i][hr[i][h0]] = max(pfmx1[i][hr[i][h0]],dp[i][h0][1]);
pfmx1[i][hr[i][h0]] = max(pfmx1[i][hr[i][h0]],dp[i][h0][0]);
}
for(auto j : hr[i+1]) {
pfmx0[i][j] = max(pfmx0[i][j],0LL);
}
for(auto it = next(pfmx0[i].begin()); it != pfmx0[i].end(); it++) {
it->sc = max(it->sc,prev(it)->sc);
}
for(auto j : hr[i+2]) {
pfmx1[i][j] = max(pfmx1[i][j],0LL);
}
for(auto it = next(pfmx1[i].begin()); it != pfmx1[i].end(); it++) {
it->sc = max(it->sc,prev(it)->sc);
}
}
int ans = 0;
for(int h0 = 0; h0 < hr[n].size(); h0++) {
ans = max(ans, dp[n][h0][0]);
ans = max(ans, dp[n][h0][1]);
}
return ans;
}
