#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
#define OPTM ios_base::sync_with_stdio(0); cin.tie(0);
#define INF int(1e9+7)
#define ln '\n'
#define ll long long
#define ull unsigned long long
#define ui unsigned int
#define us unsigned short
#define FOR(i,s,n) for (int i = s; i < n; i++)
#define FORR(i,n,s) for (int i = n; i > s; i--)
#define FORX(u, arr) for (auto u : arr)
#define PB push_back
#define in(v,x) (v.find(x) != v.end())
#define F first
#define S second
#define PII pair<int, int>
#define PLL pair<ll, ll>
#define UM unordered_map
#define US unordered_set
#define PQ priority_queue
#define ALL(v) v.begin(), v.end()
const ll LLINF = 1e18+1;
#define int long long
const int MAXN = 3e5+10;
int n,m;
vector<PII> p[MAXN];
vector<int> v1[MAXN];
vector<PII> v[MAXN], v2[MAXN];
vector<PII> dp[MAXN], dp1[MAXN], dp2[MAXN], dp3[MAXN];
int dp4, dp5;
US<int> vis1[MAXN];
void precalc() {
FOR(i,1,n+1) {
US<int> vis, vis2;
FORX(u,v[i]) {
if (!vis.count(u.F)) {
vis.insert(u.F);
v2[i].PB(u);
}
}
FORX(u,v[i+1]) {
if (!vis2.count(u.F)) {
vis2.insert(u.F);
v1[i].PB(u.F);
}
}
FORX(u,v[i-1]) {
if (!vis2.count(u.F)) {
vis2.insert(u.F);
v1[i].PB(u.F);
}
}
}
FOR(i,1,n+1) {
sort(ALL(v[i]));
sort(ALL(v1[i]));
sort(ALL(v2[i]));
}
FOR(i,1,n+1) {
int cur = 0LL;
FORX(u,v2[i]) {
p[i].PB({u.F,cur+u.S});
cur += u.S;
}
}
}
int locate(vector<PII> vec, int x, int t) {
if (t == 0) {
int ans = lower_bound(ALL(vec), make_pair(x,-LLINF))-vec.begin();
return ans == vec.size() ? -1 : ans;
}
else {
return upper_bound(ALL(vec), make_pair(x,LLINF))-vec.begin()-1;
}
}
void pr(vector<PII> vec) {
FORX(u,vec) cout << "(" << u.F << "," << u.S << ")" << " ";
cout << ln;
}
long long max_weights(int32_t N, int32_t M, std::vector<int32_t> X, std::vector<int32_t> Y, std::vector<int32_t> W) {
OPTM;
n = N; m = M;
FOR(i,0,m) {
if (!vis1[i+1].count(Y[i]+1)) {
vis1[i+1].insert(Y[i]+1);
v[X[i]+1].PB({Y[i]+1,W[i]});
}
}
FOR(i,0,n+2) {
v[i].PB({0LL,0LL});
if (!vis1[i].count(n)) {
vis1[i].insert(n);
v[i].PB({n,0LL});
}
}
precalc();
dp[1].PB({0LL,0LL});
dp1[1].PB({0LL,0LL});
dp2[1].PB({0LL,0LL});
int ma3 = 0LL;
int vn = v1[1].size();
FORR(pos,vn-1,-1) {
int j = v1[1][pos];
int idx = locate(p[2],j,1);
ma3 = max(ma3, p[2][idx].S);
dp3[1].PB({j,ma3});
}
reverse(ALL(dp3[1]));
// FOR(i,1,n+1) {
// // pr(v2[i]);
// // FORX(u,v1[i]) cout << u << " ";
// // cout << ln;
// }
// pr(dp3[1]);
// FOR(i,1,n+1) {
// pr(p[i]);
// }
FOR(i,2,n+1) {
int vn = v1[i].size();
int idx = 0, idx1 = 0, idx2 = 0, idx3 = dp3[i-1].size()-1;
int pn = p[i].size(), p1n = p[i-1].size(), dp2n = dp2[i-1].size();
FORX(j,v1[i]) {
while (idx < pn-1 && p[i][idx+1].F <= j) idx++;
while (idx1 < p1n-1 && p[i-1][idx1+1].F <= j) idx1++;
while (idx2 < dp2n-1 && dp2[i-1][idx2+1].F <= j) idx2++;
while (idx3 > 0 && dp3[i-1][idx3-1].F >= j) idx3--;
int zero = max(dp4, dp5+p[i-1][idx1].S);
dp[i].PB({j, max(zero, dp2[i-1][idx2].S + p[i-1][idx1].S)});
dp1[i].PB({j, max(zero, dp3[i-1][idx3].S - p[i][idx].S)});
}
// cout << i << ": \n";
// pr(dp[i]); pr(dp1[i]);
if (i == n) break;
int ma2 = 0LL;
dp4 = 0LL, dp5 = 0LL;
idx = 0, idx1 = 0, idx2 = 0, idx3 = dp3[i-1].size()-1;
int dpn = dp[i].size(), dpi1n = dp[i-1].size();
FORX(j,v1[i]) {
while (idx < dpn-1 && dp[i][idx+1].F <= j) idx++;
while (idx1 < pn-1 && p[i][idx1+1].F <= j) idx1++;
while (idx2 < dpi1n-1 && dp1[i-1][idx2+1].F <= j) idx2++;
ma2 = max(ma2, dp[i][idx].S - p[i][idx1].S);
dp2[i].PB({j,ma2});
dp4 = max(dp4, max(dp[i-1][idx2].S, dp1[i-1][idx2].S) + p[i][idx1].S);
dp5 = max(dp5, max(dp[i-1][idx2].S, dp1[i-1][idx2].S));
}
int ma3 = 0LL;
int p2n = p[i+1].size();
idx = p2n-1;
FORR(pos,vn-1,-1) {
int j = v1[i][pos];
while (idx > 0 && p[i+1][idx].F > j) idx--;
ma3 = max(ma3, max(dp[i][pos].S, dp1[i][pos].S) + p[i+1][idx].S);
dp3[i].PB({j,ma3});
}
reverse(ALL(dp3[i]));
}
int res = -LLINF;
FORX(u,dp[n]) res = max(res, u.S);
FORX(u,dp1[n]) res = max(res, u.S);
return res;
}
