#include <bits/stdc++.h>
using namespace std;
#define forsn(i, s, n) for (int i = int(s); i < int(n); i++)
#define forn(i, n) forsn(i, 0, n)
#define dforsn(i, s, n) for (int i = int(n) - 1; i >= int(s); i--)
#define dforn(i, n) dforsn(i, 0, n)
#define sz(x) int(x.size())
#define all(x) begin(x), end(x)
using ii = pair<int, int>;
using vi = vector<int>;
using ll = long long;
using vll = vector<ll>;
#define fst first
#define snd second
#define pb push_back
#define eb emplace_back
void chmax(ll &x, ll v) {
if (x < v) x = v;
}
ll max_weights(int N, int M, vi X, vi Y, vi W) {
vector<vi> pos(N, vi(1, 0));
vector<vector<ii>> byCol(N);
forn(i, M) {
byCol[X[i]].eb(Y[i] + 1, W[i]);
if (X[i] > 0) {
pos[X[i] - 1].pb(Y[i] + 1);
}
if (X[i] < N - 1) {
pos[X[i] + 1].pb(Y[i] + 1);
}
pos[X[i]].pb(Y[i] + 1);
}
vector<vll> cant(N);
forn(i, N) {
sort(all(byCol[i]));
sort(all(pos[i]));
pos[i].erase(unique(all(pos[i])), end(pos[i]));
cant[i].resize(sz(pos[i]));
int k = 0;
ll sum = 0;
forn(j, sz(pos[i])) {
while (k < sz(byCol[i]) && byCol[i][k].fst <= pos[i][j]) {
sum += byCol[i][k++].snd;
}
cant[i][j] = sum;
}
}
vector<vector<vll>> dp(N);
forn(i, N) {
dp[i] = vector<vll>(sz(pos[i]), vll(2, 0));
if (i == 0) continue;
const int m = sz(pos[i - 1]);
forn(j, m) chmax(dp[i][0][0], dp[i - 1][j][1]);
forn(j, sz(pos[i])) chmax(dp[i][j][0], dp[i - 1][0][1]);
int j = 0;
ll maxPref = dp[i - 1][0][0] - cant[i - 1][0];
forn(k, sz(pos[i])) {
while (j + 1 < m && pos[i - 1][j + 1] <= pos[i][k]) {
j++;
chmax(maxPref, dp[i - 1][j][0] - cant[i - 1][j]);
}
chmax(dp[i][k][0], maxPref + cant[i - 1][j]);
}
j = m;
ll maxSuff = 0;
int jPrime = sz(pos[i]) - 1;
dforn(k, sz(pos[i])) {
while (j > 0 && pos[i - 1][j - 1] >= pos[i][k]) {
j--;
while (pos[i][jPrime] > pos[i - 1][j]) jPrime--;
chmax(maxSuff, max(dp[i - 1][j][0], dp[i - 1][j][1]) + cant[i][jPrime]);
}
chmax(dp[i][k][1], maxSuff - cant[i][k]);
}
}
ll ret = 0;
forn(i, N) forn(j, sz(pos[i])) forn(k, 2) chmax(ret, dp[i][j][k]);
return ret;
}
