#include <bits/stdc++.h>
using namespace std;
using ll = long long;
ll dp[3005][3005][2];
ll pref[3005][3005];
ll max_weights(int N, int M, vector<int> X, vector<int> Y, vector<int> W){
bool evn=true;
bool lwr=true;
bool sb3=true;
ll sm1=0;
ll sm2=0;
int sub_2[N][2];
for (int i=0; i<N; i++){
for (int j=0; j<2; j++){
sub_2[i][j]=0;
}
}
for (int i=0; i<M; i++){
if (Y[i]!=0){sb3=false;}
if (X[i]%2){evn=false;sm1+=W[i];sub_2[Y[i]][X[i]%2]=W[i];}
else{sm2+=W[i];sub_2[Y[i]][X[i]%2]=W[i];}
if (X[i]>1){lwr=false;}
}
if (evn){return (sm1+sm2);}
if (lwr && N==2){return max(sm1,sm2);}
if (lwr){
vector<ll> A(N+1,0), B(N+1,0);
for (int i=0; i<N; i++){
A[i+1]=A[i]+sub_2[i][0];
B[i+1]=B[i]+sub_2[i][1];
}
ll ans=0;
for (int i=0; i<=N; i++) {
ans=max(ans, B[N]-B[i]+A[i]);
}
return ans;
}
if (sb3){
vector <int> w(N,0);
for (int i=0; i<M; i++){w[X[i]]=W[i];}
ll dp[N][2];
dp[0][0]=0;
dp[0][1]=0;
dp[1][0]=w[1];
dp[1][1]=w[0];
for (int i=2; i<N; i++){
dp[i][0]=max(dp[i-1][0],dp[i-1][1]+w[i]);
dp[i][1]=max({dp[i-1][0],dp[i-1][1],dp[i-2][0]+w[i-1]});
}
return max(dp[N-1][0],dp[N-1][1]);
}
//actual o(n^2 solution);
for (int i=0; i<M; i++){pref[X[i]+1][Y[i]+1]+=W[i];}
for (int i=0; i<N+1; i++){
for (int j=1; j<N+1; j++){
pref[i][j]+=pref[i][j-1];
}
}
for (int i=0; i<N+2; i++){
for (int j=0; j<N+2; j++){
for (int z=0; z<2; z++){
dp[i][j][z]=LLONG_MIN;
}
}
}
ll ans=0;
dp[0][0][1]=0;
for (int i=1; i<N+1; i++){
ll ndp=LLONG_MIN;
vector<ll>prefMax(N+2,LLONG_MIN),sufMax(N+2, LLONG_MIN);
for(int x=0; x<N+1; x++){
ndp=max({ndp,dp[i-1][x][0],dp[i-1][x][1]});
if (x>0)prefMax[x]=max(prefMax[x-1], dp[i-1][x][1]-pref[i-1][x]);
else prefMax[x]=dp[i-1][x][1]-pref[i-1][x];
}
for(int x=N; x>=0; x--){
sufMax[x]=max(sufMax[x+1],max(dp[i-1][x][0],dp[i-1][x][1])+pref[i][x]);
}
for(int x=0; x<N+1; x++){
if(x==0){
dp[i][x][0]=dp[i][x][1]=ndp;
}
dp[i][x][1]=max(dp[i][x][1],pref[i-1][x]+prefMax[x]);
dp[i][x][0]=max(dp[i][x][0],sufMax[x]-pref[i][x]);
ans=max({ans,dp[i][x][1],dp[i][x][0]});
}
}
return ans;
}
