#include "fish.h"
#include <algorithm>
#include <cassert>
#include <deque>
#include <iostream>
#include <vector>
#define ll long long
#define ff first
#define ss second
#define ln "\n"
using namespace std;
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y,
std::vector<int> W) {
ll n=N, m=M;
vector a(N, vector<pair<ll, ll>>());
vector dp(N, vector<pair<ll, ll>>());
for (ll i=0; i<m; i++){
a[X[i]].push_back({W[i], Y[i]});
dp[X[i]].push_back({0, 0});
}
for (ll i=0; i<n; i++){
sort(a[i].begin(), a[i].end(), [](auto op1, auto op2)->bool{ return op1.ss<op2.ss;});
dp[i].push_back({0, 0});
}
for (ll i=1; i<N; i++){
// cout << i << ": " << endl;
deque<pair<ll, ll>> bestU;
pair<ll, ll> mx = {-1, -1};
ll sum=0, rsum=0;
for (ll j=0; j<(ll)a[i].size(); j++) rsum+=a[i][j].ff;
sum=rsum;
ll pi=a[i].size()-1;
for (ll j=a[i-1].size(); j>=0; j--){
while (j<(ll)a[i-1].size() and pi>=0 and a[i-1][j].ss-1<a[i][pi].ss) sum-=a[i][pi--].ff;
if (max(dp[i-1][j].ff, dp[i-1][j].ss)+sum>mx.ff){
mx = {max(dp[i-1][j].ff, dp[i-1][j].ss)+sum, (j==(ll)a[i-1].size())?n:a[i-1][j].ss-1};
bestU.push_back(mx);
// cout << "Add: " << mx.ff << " " << mx.ss << " at " << j << endl;
}
}
sum=0;
for (ll j=0; j<=(ll)a[i].size(); j++){
while (!bestU.empty() and bestU.back().ss<(j==(ll)a[i].size()?n:a[i][j].ss-1)) {
// cout << "Remove: " << bestU.back().ff << " " << bestU.back().ss << " at " << j << endl;
bestU.pop_back();
}
// cout << i << "-" << j << endl;
dp[i][j].ss=(bestU.empty()?0:bestU.back().ff)-sum;
if (j<(ll)a[i].size()) sum+=a[i][j].ff;
// cout << i << "-" << j << endl;
}
if (i>1){ //-Change-
// cout << i << ": ";
pair<ll, ll> best = {-1, -1};
for (ll j=0; j<=(ll)a[i-2].size(); j++){
best=max(best, {max(dp[i-2][j].ff, dp[i-2][j].ss), (j==(ll)(a[i-2].size())?n:a[i-2][j].ss-1)});
}
ll osum=0;
for (ll j=0; j<(ll)a[i-1].size() and a[i-1][j].ss<=best.ss; j++){
osum+=a[i-1][j].ff;
}
// cout << osum << " -> ";
sum=0;
pi=0;
for (ll j=0; j<=(ll)a[i].size(); j++){
while (pi<(ll)a[i-1].size() and a[i-1][pi].ss<=(j==(ll)(a[i].size())?n:a[i][j].ss-1)) sum+=a[i-1][pi++].ff;
dp[i][j].ff=best.ff+max(sum, osum);
}
}
assert(bestU.size()<=1);
while (!bestU.empty()) bestU.pop_back();
mx = {-1, -1};
sum=rsum=0;
for (ll j=0; j<(ll)a[i-1].size(); j++) rsum+=a[i-1][j].ff;
for (ll j=0; j<=(ll)a[i-1].size(); j++){
if (rsum-sum+dp[i-1][j].ff>mx.ff){
mx = {rsum-sum+dp[i-1][j].ff, (j==(ll)a[i-1].size()?n:a[i-1][j].ss-1)};
bestU.push_back(mx);
// cout << "Add: " << mx.ff << " " << mx.ss << " at " << j << endl;
}
if (j<(ll)a[i-1].size()) sum+=a[i-1][j].ff;
}
sum=0;
pi=(ll)a[i-1].size()-1;
for (ll j=(ll)(a[i].size()); j>=0; j--){
// cout << "Spec: " << a[i-1][pi].ss << " w " << (j==(ll)(a[i].size())?n+1:a[i][j].ss-1) << endl;
while (pi>=0 and a[i-1][pi].ss>(j==(ll)(a[i].size())?n+1:a[i][j].ss-1)) {sum+=a[i-1][pi--].ff;}
while (!bestU.empty() and bestU.back().ss>(j==(ll)(a[i].size())?n+1:a[i][j].ss-1)) {
// cout << "Remove: " << bestU.back().ff << " " << bestU.back().ss << " at " << j << endl;
bestU.pop_back();
}
// cout << i << "-" << j << "-" << sum << endl;
dp[i][j].ff=max(dp[i][j].ff, (bestU.empty()?0:bestU.back().ff)-sum);
}
}
// for (ll i=0; i<n; i++){
// for (ll j=0; j<(ll)dp[i].size(); j++) cout << dp[i][j].ff << " ";
// cout << ln;
// }
// for (ll i=0; i<n; i++){
// for (ll j=0; j<(ll)dp[i].size(); j++) cout << dp[i][j].ss << " ";
// cout << ln;
// }
// Thing to lookup -> the fact that dp[i][j] is column up to height[i][j]-1;
ll res=0;
for (ll i=0; i<=(ll)a[n-1].size(); i++){
res=max(res, max(dp[n-1][i].ff,dp[n-1][i].ss));
}
return res;
}
