#include "fish.h"
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using pi=pair<int,int>;
using vi=vector<int>;
#define mp make_pair
#define eb emplace_back
#define x first
#define y second
#define sz(x)int((x).size())
#define all(x)(x).begin(),(x).end()
#define rep(i,a,b)for(int i=(a);i<(b);i++)
#define per(i,a,b)for(int i=(b)-1;i>=(a);i--)
bool ckmin(auto&a,auto b){return b<a?a=b,1:0;}
bool ckmax(auto&a,auto b){return b>a?a=b,1:0;}
#ifdef LOCAL
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.x<<", "<<p.y<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto&e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X);
#else
#define debug(...){}
#endif
struct Container {
ll shift=0,best=0;
void add(ll delta) {
shift += delta;
best += delta;
}
void ins(ll v) {
ckmax(best, v);
}
ll get() {
return best;
}
};
long long max_weights(int N, int M, vector<int> X, vector<int> Y,
vector<int> W) {
vector<vector<pi>> sweep(N + 2);
rep(i,0,M) {
sweep[X[i]+1].eb(Y[i],W[i]);
}
rep(i,0,N+2) {
sweep[i].eb(N,0);
sort(all(sweep[i]));
}
vector<vector<ll>> dp(N+2);
vector<ll> best_dp(N+2);
rep(i,0,N+2) {
dp[i].resize(sz(sweep[i]));
}
ll ans = 0;
rep(i,1,N+1) {
debug(i);
int ptr_l=0,ptr_r=0;
ll sum_l=0,sum_cur=0,sum_r=0;
Container best_l;
rep(j,0,sz(sweep[i])) {
auto [y,w] = sweep[i][j];
while (ptr_l < sz(sweep[i-1]) && sweep[i-1][ptr_l].x < y) {
sum_l+=sweep[i-1][ptr_l].y;
best_l.ins(dp[i-1][ptr_l]);
best_l.add(sweep[i-1][ptr_l].y);
ptr_l++;
}
while (ptr_r < sz(sweep[i+1]) && sweep[i+1][ptr_r].x < y) {
sum_r+=sweep[i+1][ptr_r].y;
ptr_r++;
}
ckmax(dp[i][j], best_l.get());
ckmax(dp[i+1][ptr_r], best_l.get() + sum_r); // cur takes from left and right
ckmax(dp[i+1][ptr_r], best_dp[i-1] + sum_r); // prev does not take any from column i
ckmax(dp[i+1][ptr_r], best_dp[i] + sum_r - sum_cur); // prev takes unlimited amount from column i
sum_cur+=w;
}
rep(s,0,2) {
rep(j,0,sz(sweep[i+s])) {
ckmax(best_dp[i+s], dp[i+s][j]);
}
}
debug(dp);
}
rep(i,0,N+2) {
rep(j,0,sz(dp[i])) {
ckmax(ans, dp[i][j]);
}
}
return ans;
}
