#include "fish.h"
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
#define all(x) x.begin(),x.end()
bool deb_inf_col=false;
bool deb_inf_state=false;
void pri(string s, vector<ll> v){
printf("%s: ",s.c_str());
for(ll i: v) printf("%lld ",i);
printf("\n");
}
void pri(string s, vector<ll> a, vector<ll> b){
printf("%s: ",s.c_str());
for(ll i: a) printf("%lld ",b[i]);
printf("\n");
}
void fill(vector<ll> &pier, vector<ll> &fish, vector<ll> &v){
for(int i=0,j=0;i<(int)pier.size();)
if(j==(int)fish.size()-1 || (pier[i]>=fish[j] && pier[i]<fish[j+1])){
v[i]=j;
i++;
}
else j++;
}
ll max_weights(int n, int m, vector<int> x, vector<int> y, vector<int> w){
vector<ll> sum[n],fish[n],temp_pier[n],pier[n];
vector<pair<ll,ll>> inf_fish[n];
for(int i=0;i<m;i++) inf_fish[x[i]].push_back({y[i]+1,w[i]});
for(int i=0;i<n;i++){
sum[i].push_back(0); fish[i].push_back(0); temp_pier[i].push_back(0);
sort(all(inf_fish[i]));
for(int j=0;j<(int)inf_fish[i].size();j++){
fish[i].push_back(inf_fish[i][j].first);
sum[i].push_back(inf_fish[i][j].second);
if(i) temp_pier[i-1].push_back(inf_fish[i][j].first);
if(i!=n-1) temp_pier[i+1].push_back(inf_fish[i][j].first);
}
}
for(int i=0;i<n;i++){
sort(all(temp_pier[i]));
pier[i].push_back(temp_pier[i][0]);
for(int j=1;j<(int)temp_pier[i].size();j++)
if(temp_pier[i][j]!=temp_pier[i][j-1])
pier[i].push_back(temp_pier[i][j]);
for(int j=1;j<(int)fish[i].size();j++)
sum[i][j]+=sum[i][j-1];
}
vector<ll> left[n],me[n],right[n];
for(int i=0;i<n;i++){
left[i].assign(pier[i].size(),0);
me[i].assign(pier[i].size(),0);
right[i].assign(pier[i].size(),0);
if(i) fill(pier[i],fish[i-1],left[i]);
fill(pier[i],fish[i],me[i]);
if(i!=n-1) fill(pier[i],fish[i+1],right[i]);
}
if(deb_inf_col){
for(int i=0;i<n;i++){
printf("%d:\n",i);
pri("fish:",fish[i]);
pri("sum:",sum[i]);
pri("pier:",pier[i]);
if(i) pri("left:",left[i],fish[i-1]);
pri("me:",me[i],fish[i]);
if(i!=n-1) pri("right:",right[i],fish[i+1]);
printf("\n");
}
}
vector<vector<vector<ll>>> dp[n];
for(int i=0;i<n;i++){
int j=(i>=2) ? pier[i-2].size() : 1;
int k=(i) ? pier[i-1].size() : 1;
int l=pier[i].size();
dp[i].assign(j,vector<vector<ll>>(k,vector<ll>(l,0)));
}
for(int i=1;i<n;i++){
int size_j=(i>=2) ? pier[i-2].size() : 1;
for(int j=0;j<size_j;j++){
for(int k=0;k<(int)pier[i-1].size();k++){
ll prev=0;
int size_l=(i>=3) ? pier[i-3].size() : 1;
int pos=0;
for(int l=0;l<size_l;l++){
ll aux=dp[i-1][l][j][k];
if(aux>=prev){
prev=aux;
pos=l;
}
}
for(int l=0;l<(int)pier[i].size();l++){
dp[i][j][k][l]+=prev;
if(deb_inf_state){
if(i>=2) printf("%d: %lld\n",i-2,pier[i-2][j]);
printf("%d: %lld\n",i-1,pier[i-1][k]);
printf("%d: %lld\n",i,pier[i][l]);
printf("prev: %lld at %d %d %d\n",prev,pos,j,k);
}
if(pier[i-1][k]>=pier[i][l]){
ll up=sum[i][right[i-1][k]];
ll down=sum[i][me[i][l]];
if(deb_inf_state){
printf("sum in %d\n",i);
printf("up: %lld\n",fish[i][right[i-1][k]]);
printf("down: %lld\n",fish[i][me[i][l]]);
printf("-> %lld - %lld = %lld\n",up,down,up-down);
}
dp[i][j][k][l]+=sum[i][right[i-1][k]]-sum[i][me[i][l]];
}
else{
if(deb_inf_state) printf("sum in %d\n",i-1);
if(i>=2 && pier[i-2][j]>=pier[i-1][k]){
ll up=sum[i-1][left[i][l]];
ll down=sum[i-1][right[i-2][j]];
if(deb_inf_state){
printf("tallest in middle: %d\n",i-2);
printf("up: %lld\n",fish[i-1][left[i][l]]);
printf("down: %lld\n",fish[i-1][right[i-2][j]]);
printf("-> %lld - %lld = %lld\n",up,down,up-down);
}
dp[i][j][k][l]+=sum[i-1][left[i][l]]-sum[i-1][right[i-2][j]];
}
else{
ll up=sum[i-1][left[i][l]];
ll down=sum[i-1][me[i-1][k]];
if(deb_inf_state){
printf("tallest in back: %d\n",i-1);
printf("up: %lld\n",fish[i-1][left[i][l]]);
printf("down: %lld\n",fish[i-1][me[i-1][k]]);
printf("-> %lld - %lld = %lld\n",up,down,up-down);
}
dp[i][j][k][l]+=sum[i-1][left[i][l]]-sum[i-1][me[i-1][k]];
}
}
if(deb_inf_state){
printf("----> %lld\n",dp[i][j][k][l]);
printf("\n");
}
}
}
}
}
ll res=0;
int size_i=(n>=3) ? pier[n-3].size() : 1;
for(int i=0;i<size_i;i++)
for(int j=0;j<(int)pier[n-2].size();j++)
for(int k=0;k<(int)pier[n-1].size();k++)
res=max(res,dp[n-1][i][j][k]);
return res;
}
