#include <bits/stdc++.h>
#define ll long long
#define rep(i,m,n) for(int i=(m); i<=(n); i++)
#define reb(i,m,n) for(int i=(m); i>=(n); i--)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define MP make_pair
#define fs first
#define se second
#define bit(msk, i) ((msk >> i) & 1)
#define iter(id, v) for(auto id : v)
#define pb push_back
#define SZ(v) (int)v.size()
#define ALL(v) v.begin(),v.end()
using namespace std;
mt19937_64 rd(chrono :: steady_clock :: now ().time_since_epoch().count());
ll Rand (ll l, ll r) { return uniform_int_distribution<ll> (l, r) (rd); }
const int N = 1e5 + 7;
const int Mod = 1e9 + 7;
const ll INF = 2e9 + 7;
const ll BASE = 137;
const int szBL = 320;
void inline maximize (ll &A, ll B) { if (A < B) A = B; }
struct Fish {
int fs, se;
ll W;
};
int n, m;
vector<ll> pcur[N], dp[N], fsuf[N], f[N], fpre[N], dppre[N], Left[N], Right[N];
vector<int> high[N];
Fish a[(int)3e5 + 7];
vector<pll> vec[N];
ll premx[N], sufmx[N];
void init (int j, int m) {
pcur[j].resize(m + 2, 0);
Left[j].resize(m + 2, 0);
Right[j].resize(m + 2, 0);
fpre[j].resize(m + 2, 0);
dppre[j].resize(m + 2, 0);
f[j].resize(m + 2, 0);
fsuf[j].resize(m + 2, 0);
dp[j].resize(m + 2, 0); ///sửa ik
}
//void solution () {
ll max_weights(int _n, int _m, vector<int> X, vector<int> Y, vector<int> W) {
// cin >> n >> m;
// n = 1e5;
// m = Rand(1, (n - 1) / 2);
// m = min(1LL * n * n - Rand(1, n * n), (ll)3e5);
n = _n;
m = _m;
// vector<ll> val;
// rep (i, 0, (n - 1) / 2) val.pb(i * 2);
// random_shuffle(ALL(val));
rep (j, 0, n) high[j] = {0};
rep (i, 1, m) {
// cin >> a[i].fs >> a[i].se >> a[i].W;
// a[i].fs = val[i - 1].fs;
// a[i].se = val[i - 1].se;
// a[i].W = Rand(1, 100000);
// a[i].fs = val[i];
// a[i].se = Rand(0, n - 1);
// a[i].W = 1e9;
a[i].fs = X[i - 1];
a[i].se = Y[i - 1];
a[i].W = W[i - 1];
++a[i].fs;
++a[i].se;
// cout << a[i].fs<<","<<a[i].se<<"\n";
vec[a[i].fs].pb(MP(a[i].se, a[i].W));
high[a[i].fs].pb(a[i].se);
}
init(0, 5);
rep (j, 1, n) {
iter (&id, vec[j + 1])
high[j].pb(id.fs);
iter (&id, vec[j - 1])
high[j].pb(id.fs);
sort (ALL(high[j]));
high[j].resize(unique(ALL(high[j])) - high[j].begin());
int m = SZ(high[j]);
init(j, m);
iter (&id, vec[j]) pcur[j][lower_bound(ALL(high[j]), id.fs) - high[j].begin()] = id.se;
rep (i, 1, m){
pcur[j][i] += pcur[j][i - 1];
}
rep (i, 1, m - 1) {
int pos = lower_bound(ALL(high[j - 1]), high[j][i]) - high[j - 1].begin();
Left[j][i] = pcur[j - 1][pos];
// if (j == 2) cout << i<<" "<<<pcur[j][i] <<".\n";
}
}
rep (j, 1, n - 1) {
int m = SZ(high[j]);
rep (i, 1, m - 1) {
int pos = lower_bound(ALL(high[j + 1]), high[j][i]) - high[j + 1].begin();
Right[j][i] = pcur[j + 1][pos];
}
}
// return;
rep (j, 1, n) {
int m = SZ(high[j]);
vector<int> &ch = high[j];
if (j >= 2) {
ll prem = *max_element(ALL(dp[j - 2]));
rep (i, 0, m - 1) {
int pos = upper_bound(ALL(high[j - 1]), ch[i]) - high[j - 1].begin();
// if (j == 3 && high[j][i] == 4) {
// cout << dp[j][i] <<" "<<Left[j][i]<<"hihih\n";
// }
maximize(f[j][i], fpre[j - 1][pos - 1] + Left[j][i]);
maximize(dp[j][i], prem + Left[j][i]);
maximize(dp[j][i], fsuf[j - 1][pos] - pcur[j][i]);
maximize(dp[j][i], f[j][i]);
}
rep (i, 0, m - 1) {
int pos = upper_bound(ALL(high[j - 2]), ch[i]) - high[j - 2].begin();
// if (j == 3 && high[j][i] == 4) {
// cout << dp[j][i] <<" "<<Left[j][i]<<"hihih\n";
// }
maximize(f[j][i], dppre[j - 2][pos - 1] + Left[j][i]);
maximize(f[j][i], fsuf[j - 2][pos]);
maximize(dp[j][i], f[j][i]);
}
}
if (j > 3) {
ll prem = 0;
rep (i, 0, SZ(high[j - 3]) - 1) {
prem = max(prem, dp[j - 3][i] + Right[j - 3][i]);
}
rep (i, 0, m - 1) {
maximize(dp[j][i], Left[j][i] + prem);
maximize(f[j][i], Left[j][i] + prem);
}
}
fpre[j][0] = f[j][0];
dppre[j][0] = dp[j][0];
rep (i, 1, m - 1) {
fpre[j][i] = max(fpre[j][i - 1], f[j][i] - pcur[j][i]);
dppre[j][i] = max(dppre[j][i - 1], dp[j][i]);
}
reb (i, m - 1, 0) {
fsuf[j][i] = max(fsuf[j][i + 1], dp[j][i] + Right[j][i]);
}
rep (i, 0, m - 1) {
// cout << j << " "<<high[j][i] <<" "<< dp[j][i] <<"\n";
}
}
// cout << *max_element(ALL(dp[n])) <<"\n";
return *max_element(ALL(dp[n]));
}
//
//#define file(name) freopen(name".inp","r",stdin); \
//freopen(name".out","w",stdout);
//int main () {
//// file("c");
//// ios_base :: sync_with_stdio(false); cin.tie(0); cout.tie(0);
// int num_Test = 1;
//// cin >> num_Test;
// while (num_Test--)
//// solution();
// cout << max_weights(5, 4, {0, 1, 4, 3}, {2, 1, 4, 3}, {5, 2, 1, 3});
//}
/*
no bug challenge +2
2 + 8 * 2 - 9
7 7
0 2 5
0 1 1
2 1 2
2 2 1
4 4 1
4 6 2
6 3 3
*/
