#include <bits/stdc++.h>
#include "fish.h"
#define ll long long
#define ar array
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
using namespace std;
const ll INF = 1e18;
template<typename T> bool ckmin(T &a, const T &b ) { return a > b ? a = b, 1 : 0; }
template<typename T> bool ckmax(T &a, const T &b ) { return a < b ? a = b, 1 : 0; }
long long max_weights(int n, int m, std::vector<int> x, std::vector<int> y, std::vector<int> w) {
vector<vector<ar<ll, 2>>> each(n);
for (int i = 0; i < m; i++) {
each[x[i]].push_back({y[i], w[i]});
each[x[i]].push_back({y[i]-1, 0});
}
for (int i = 0; i < n; i++) each[i].push_back({n-1, 0}), each[i].push_back({-1, 0});
for (int i = 0; i < n; i++) {
sort(all(each[i]));
vector<ar<ll, 2>> nw;
ll s = 0;
for (int j = 0; j < sz(each[i]); j++) {
int r = j;
while (r+1 < sz(each[i]) && each[i][r+1][0] == each[i][r][0]) r++;
for (int k = j; k <= r; k++) s += each[i][k][1];
nw.push_back({each[i][j][0], s});
j = r;
}
swap(each[i], nw);
}
vector<vector<ll>> dp;
auto query = [&](int pos, int x) {
return prev(upper_bound(all(each[pos]), ar<ll, 2>{x, LLONG_MAX})) - each[pos].begin();
};
vector<vector<ar<int, 3>>> val(n);
for (int i = 0; i < n; i++) {
val[i].resize(sz(each[i]));
for (int k = 0; k < sz(each[i]); k++) {
for (int j = -1; j <= 1; j++) {
if (i + j >= 0 && i + j < n) {
val[i][k][j+1] = query(i + j, each[i][k][0]);
}
}
}
}
for (int i = 0; i < n; i++) {
vector<vector<ll>> dp2;
const int N = sz(each[i]);
dp2.resize(i ? sz(each[i-1]) : 1, vector<ll>(N, -INF));
if (!i) {
for (int j = 0; j < N; j++) {
dp2[0][j] = 0;
}
swap(dp, dp2);
}
else {
for (int k = 0; k < sz(dp[0]); k++) {
for (int l = 0; l < N; l++) {
// val[i-2][j][2] <= val[i][l][0]
int ans = 0;
{
int l = 0, r = i-2 >= 0 ? sz(each[i-2]) - 1 : -1;
while (l <= r) {
int mid = (l+r)/2;
if (val[i-2][mid][2] <= val[i][l][0]) ans = mid, l = mid+1;
else r = mid-1;
}
}
for (int j = 0; j <= ans; j++) {
int L = k, R = val[i][l][0];
ckmax(dp2[k][l], dp[j][k] + (L <= R ? each[i-1][R][1] - each[i-1][L][1] : 0));
}
for (int j = ans+1; j < sz(dp); j++) {
int L = k, R = val[i-2][j][2];
ckmax(dp2[k][l], dp[j][k] + (L <= R ? each[i-1][R][1] - each[i-1][L][1] : 0));
}
}
}
swap(dp, dp2);
}
}
ll ans = -INF;
for (int i = 0; i < sz(dp); i++) {
for (int j = 0; j < sz(dp[i]); j++) {
int L = j, R = val[n-2][i][2];
ckmax(ans, dp[i][j] + (L <= R ? each[n-1][R][1] - each[n-1][L][1] : 0));
}
}
return ans;
}
