#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll MOD = 998244353;
const ll INF = 1e18;
const ld EPS = 1e-12;
#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);
ll max_weights(int n, int m, vector<int> x, vector<int> y, vector<int> w) {
// this will contain at most O(n? + m)
// time complexity O(n + m log m)
vector<vector<pair<ll, ll>>> fish(n);
map<ll, ll> total;
REP(i, 0, m) {
fish[x[i]].push_back({y[i], w[i]});
total[x[i]] += w[i];
}
REP(i, 0, n) {
sort(all(fish[i]));
}
vector<pair<ll, ll>> prev1, prev2, curr;
prev1.push_back({-1, 0}), prev2.push_back({-1, 0});
REP(i, 0, n) {
cerr << "i:" sp i sp "here" << endl;
// gap
ll mx = 0;
for (auto &v : prev1) {
mx = max(mx, v.second);
}
// adjacent
vector<ll> pref;
if (prev2.size()) pref.push_back(prev2[0].second);
REP(j, 1, prev2.size()) {
pref.push_back(pref.back() + prev2[j].second);
}
// self
ll cnt = 0;
for (auto &v : fish[i]) {
cnt += v.second;
ll cand = 0;
auto it = lower_bound(curr.begin(), curr.end(), make_pair(v.first, -1LL));
if (it != curr.end() and it->first == v.first) {
cand = max(cand, it->second);
curr.erase(it);
}
// gap
cand = max(cand, mx + cnt);
// adj
int amt = i > 0 ? lower_bound(fish[i-1].begin(), fish[i-1].end(), make_pair(v.first, INF)) - fish[i-1].begin() : -1;
ll add = (pref.size() and amt > 0) ? pref[amt-1] : 0;
cand = max(cand, add + total[i] - cnt);
curr.push_back({v.first, cand});
}
if (i > 0) {
curr.push_back({n, total[i-1]});
}
prev1.swap(prev2);
prev2.swap(curr);
curr.clear();
}
ll ans = -1;
for (auto &v : prev2) {
ans = max(ans, v.second);
}
return ans;
}
// signed main() {
// int n, m; cin >> n >> m;
// vector<int> x(m), y(m), w(m);
// REP(i, 0, m) {
// cin >> x[i] >> y[i] >> w[i];
// }
// cout << max_weights(n, m, x, y, w) << endl;
// }
