#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
#define sp " "
#define endl "\n"
#define pii pair<int, int>
#define st first
#define nd second
#define fileio() freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout)
#define fastio() cin.tie(0), ios_base::sync_with_stdio(0)
#define pb push_back
#define ll long long
#define LL node * 2
#define RR node * 2 + 1
#define MAXN 600005
const int modulo = 1e9 + 7;
const ll INF = 2e18 + 7;
ll start[MAXN], dp[2][MAXN];
ll pref[MAXN], suff[MAXN];
vector<pii> fish[MAXN];
long long max_weights(int N, int M, vector<int> X, vector<int> Y, vector<int> W) {
int n = N, m = M;
vector<array<int, 3>> v;
map<pii, int> done;
for (int i = 0; i < m; i++) done[{X[i], Y[i]}] = 1;
for (int i = 0; i < n; i++){
if (done.count({i, 0}) == 0){
X.pb(i), Y.pb(0), W.pb(0);
}
}
m = X.size();
for (int i = 0; i < m; i++) v.pb({X[i] + 1, Y[i], W[i]});
sort(v.begin(), v.end());
vector<int> x(m + 5), y(m + 5), w(m + 5);
for (int i = 1; i <= m; i++) x[i] = v[i - 1][0], y[i] = v[i - 1][1], w[i] = v[i - 1][2];
for (int i = 1; i <= m; i++) fish[x[i]].pb({y[i], i});
vector<ll> pre(m + 5, 0);
for (int i = 1; i <= m; i++) pre[i] = pre[i - 1] + w[i];
for (int i = n; i >= 1; i--){
start[i] = max(start[i + 1], start[i + 2] + pre[fish[i].back().nd] - pre[fish[i].front().nd - 1]);
if (i == n) {
for (auto j : fish[i]){
int k = j.nd, b = j.st;
pref[k] = -pre[k - 1];
int tmp = lower_bound(fish[i - 1].begin(), fish[i - 1].end(), make_pair(b, 0)) - fish[i - 1].begin();
tmp--;
if (tmp >= 0){
int to2 = fish[i - 1][tmp].nd;
suff[k] = dp[1][k] + pre[to2];
}
for (int j = fish[i].front().nd + 1; j <= fish[i].back().nd; j++) pref[j] = max(pref[j - 1], pref[j]);
for (int j = fish[i].back().nd - 1; j >= fish[i].front().nd; j--) suff[j] = max(suff[j], suff[j + 1]);
}
continue;
}
for (auto J = 0; J < fish[i].size(); J++){
pii j = fish[i][J];
int k = j.nd;
int a = x[k], b = y[k];
//todo : continue decreasing
int to = lower_bound(fish[i + 1].begin(), fish[i + 1].end(), make_pair(b, 0)) - fish[i + 1].begin();
to--;
if (to >= 0){
int to2 = fish[i + 1][to].nd;
int gh = lower_bound(fish[i + 1].begin(), fish[i + 1].end(), make_pair(b + 1, 0)) - fish[i + 1].begin();
gh--;
if (gh >= 0){
dp[0][k] = max(dp[0][k], pref[fish[i + 1][gh].nd] + pre[to2]);
}
}
//todo : switch to increasing
if (b == 0){
dp[0][k] = max(dp[0][k], dp[1][fish[i + 1].front().nd]);
}
//////////////////////////////////////////
//todo : continue increasing
int gh = lower_bound(fish[i + 1].begin(), fish[i + 1].end(), make_pair(b, 0)) - fish[i + 1].begin();
if (gh != fish[i + 1].size()){
dp[1][k] = max(dp[1][k], suff[fish[i + 1][gh].nd] - pre[k - 1]);
}
//todo : connect to full column
dp[1][k] = max(dp[1][k], start[i + 2] + pre[fish[i].back().nd] - pre[k - 1]);
/////////////////////////////////////////
pref[k] = dp[0][k] - pre[k - 1];
int tmp = lower_bound(fish[i - 1].begin(), fish[i - 1].end(), make_pair(b, 0)) - fish[i - 1].begin();
tmp--;
if (tmp >= 0){
int to2 = fish[i - 1][tmp].nd;
suff[k] = dp[1][k] + pre[to2];
}
}
for (int j = 0; j < fish[i].size(); j++){
int curr = fish[i][j].nd;
start[i] = max(start[i], dp[0][curr] + pre[fish[i].back().nd] - pre[curr - 1]);
}
for (int j = fish[i].front().nd + 1; j <= fish[i].back().nd; j++) pref[j] = max(pref[j - 1], pref[j]);
for (int j = fish[i].back().nd - 1; j >= fish[i].front().nd; j--) suff[j] = max(suff[j], suff[j + 1]);
}
ll ans = start[2];
for (int i = 1; i <= m; i++) {
//cout<<i<<sp<<x[i]<<sp<<y[i]<<sp<<w[i]<<" : "<<dp[0][i]<<sp<<dp[1][i]<<endl;
ans = max(ans, max(dp[0][i], dp[1][i]));
}
return ans;
}
/*
int main() {
fileio();
int N, M;
assert(2 == scanf("%d %d", &N, &M));
std::vector<int> X(M), Y(M), W(M);
for (int i = 0; i < M; ++i) {
assert(3 == scanf("%d %d %d", &X[i], &Y[i], &W[i]));
}
long long result = max_weights(N, M, X, Y, W);
printf("%lld\n", result);
return 0;
}*/
