#include <bits/stdc++.h>
#include "fish.h"
using namespace std;
typedef long long int lli;
typedef vector<lli> vi;
typedef pair<int,int> ii;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define ROF(i,a,b) for(int i=(b)-1;i>=(a);--i)
#define pb push_back
#define fi first
#define se second
#define all(v) begin(v),end(v)
const int INF = 2e9;
long long max_weights(int N, int M, std::vector<int> X, std::vector<int> Y, std::vector<int> W) {
map<ii,lli> inc, dec;
inc[{-1,-INF}] = inc[{-1,INF}] = 0;
vector<pair<ii,lli>> ptw;
FOR(i,0,M) ptw.pb({{X[i],Y[i]},W[i]});
FOR(i,0,N) ptw.pb({{i,INF},0});
sort(all(ptw));
vector<ii> pts;
vector<lli> wts{0};
FOR(i,0,M+N) {
pts.pb(ptw[i].fi);
wts.pb(wts.back()+ptw[i].se);
}
//counts fish in [{x,y1},{x,y2}], inclusive of endpoints
//uses two pointers for const op
function<lli(lli,lli,lli,int&,int&)> countFish = [&] (lli x, lli y1, lli y2, int &l, int &r) {
if(x<0||x>=N||y1>y2) return 0LL;
else {
while(l<int(pts.size())&&pts[l] < ii{x,y1}) l++;
while(l>0 && pts[l-1] >= ii{x,y1}) l--;
while(r<int(pts.size())&&pts[r] <= ii{x,y2}) r++;
while(r>0 && pts[r-1] > ii{x,y2}) r--;
return wts[r]-wts[l];
}
};
int lPtr, rPtr;
FOR(i,0,N) {
map<ii,lli> colInc[3];
map<ii,lli> colDec;
int l = lower_bound(all(pts), ii{i,0}) - begin(pts);
int r = lower_bound(all(pts), ii{i+1,0}) - begin(pts);
int p = lower_bound(all(pts), ii{i-2,0}) - begin(pts);
lPtr = rPtr = lower_bound(all(pts), ii{i-1,0}) - begin(pts);
FOR(j,l,r) {
if(j>l) colInc[0][pts[j]]=max(colInc[0][pts[j]],colInc[0][pts[j-1]]);
while(p<int(pts.size())&&pts[p].fi==i-2&&pts[p].se<=pts[j].se) {
colInc[0][pts[j]]=max(colInc[0][pts[j]],dec[pts[p]]);
p++;
}
}
FOR(j,l,r) colInc[0][pts[j]] += countFish(i-1,0,pts[j].se-1,lPtr,rPtr);
p = lower_bound(all(pts), ii{i-2,0}) - begin(pts);
while(p<int(pts.size())&&pts[p].fi==i-2) {
colInc[1][pts[l]] = max(colInc[1][pts[l]],dec[pts[p]]+countFish(i-1,0,pts[p].se-1,lPtr,rPtr)),p++;
}
FOR(j,l+1,r) colInc[1][pts[j]] = max(colInc[1][pts[j]],colInc[1][pts[j-1]]);
p = lower_bound(all(pts), ii{i-1,0}) - begin(pts);
FOR(j,l,r) {
if(j>l) colInc[2][pts[j]]=max(colInc[2][pts[j]],colInc[2][pts[j-1]]+countFish(i-1,pts[j-1].se,pts[j].se-1,lPtr,rPtr));
while(p<int(pts.size())&&pts[p].fi==i-1&&pts[p].se<=pts[j].se) {
colInc[2][pts[j]]=max(colInc[2][pts[j]],inc[pts[p]]+countFish(i-1,pts[p].se,pts[j].se-1,lPtr,rPtr));
p++;
}
}
p = lower_bound(all(pts), ii{i-1,INF}) - begin(pts);
ROF(j,l,r) {
if(i>0&&j<r-1) colDec[pts[j]]=max(colDec[pts[j]],colDec[pts[j+1]]+ptw[j].se);
while(p>=0&&pts[p].fi==i-1&&pts[p].se>=pts[j].se) {
colDec[pts[j]]=max(colDec[pts[j]],dec[pts[p]]+countFish(i,pts[j].se,pts[p].se-1,lPtr,rPtr));
p--;
}
}
FOR(j,l,r) {
FOR(k,0,3) {
inc[pts[j]] = max(inc[pts[j]],colInc[k][pts[j]]);
}
dec[pts[j]] = max(dec[pts[j]],colDec[pts[j]]);
}
dec[ii{i,INF}] = max(inc[ii{i,INF}],dec[ii{i,INF}]);
while(!inc.empty() && inc.begin()->fi.fi < i-1) inc.erase(inc.begin());
while(!dec.empty() && dec.begin()->fi.fi < i-1) dec.erase(dec.begin());
}
lli ans = max(inc[{N-1,INF}],dec.lower_bound({N-1,0})->second);
return ans;
}
