#include <bits/stdc++.h>
#include "fish.h"
using namespace std;
using ll = long long;
ll max_weights(
int n, int m, vector<int> x, vector<int> y, vector<int> w) {
vector arr(n+1, vector<pair<int,ll>>());
for (int i = 0; i < m; i++) {
arr[x[i]+1].emplace_back(y[i], w[i]);
}
for (int i = 0; i < n; i++)
sort(arr[i].begin(), arr[i].end());
auto pref = arr;
for (int i = 0; i <= n; i++) {
for (int j = 1; j < (int)pref[i].size(); j++) {
pref[i][j].second += pref[i][j-1].second;
}
}
auto sum_right = [&](int c, int right)->ll{
int l = -1, r = pref[c].size();
while (l < r-1) {
int mid = (l+r) / 2;
if (pref[c][mid].first <= right) l = mid;
else r= mid;
}
return l==-1 ? 0 : pref[c][l].second;
};
auto sum = [&](int c, int l, int r) { // [l, r]
if (l <= r) return sum_right(c, r) - sum_right(c, l-1);
else return 0ll;
};
vector<vector<int>> byx(n+2), used(n+1);
for (int i = 0; i < m; i++)
byx[x[i]+1].push_back(y[i]);
for (int i = 0; i <= n; i++) {
if (i) for (int j : byx[i-1])
used[i].push_back(j+1);
if (n-i) for (int j : byx[i+1])
used[i].push_back(j+1);
used[i].push_back(0);
sort(used[i].begin(), used[i].end());
}
vector memo(2, vector(n+1, vector<ll>()));
for (int i = 1; i <= n; i++) {
memo[0][i].assign(used[i-1].size(), -1);
memo[1][i].assign(used[i-1].size(), -1);
}
vector memp(2, vector(n+1, vector<ll>{}));
auto dp = [&](auto& dp, bool inc, int c, int h2_key)->ll{
if (c == n+1) return 0;
int h2 = used[c-1][h2_key];
ll& res = memo[inc][c][h2_key];
if (res!=-1) return res;
res = 0;
if (inc) {
if (memp[inc][c].empty()) {
for (int j = 0; j < (int)used[c].size(); j++) {
int h3 = used[c][j];
ll val = sum(c-1, 0, h3-1);
memp[inc][c].push_back(val + max(
dp(dp, true, c+1, j),
dp(dp, false, c+1, j)));
}
}
for (int j = 0; j < (int)used[c].size(); j++) {
int h3 = used[c][j];
if (h3 < h2) continue;
res = max(res, memp[inc][c][j]);
}
res -= sum(c-1, 0, h2-1);
} else {
if (memp[inc][c].empty()) {
for (int j = 0; j < (int)used[c].size(); j++) {
int h3 = used[c][j];
ll val = -sum(c, 0, h3-1);
memp[inc][c].push_back(val + dp(dp, false, c+1, j));
}
}
for (int j = 0; j < (int)used[c].size(); j++) {
int h3 = used[c][j];
if (h3 > h2) break;
res = max(res, memp[inc][c][j]);
}
res += sum(c, 0, h2-1);
}
res = max(res, dp(dp, true, c+1, 0));
res = max(res, 0ll);
return res;
};
ll res = dp(dp, true, 1, 0);
return res;
}
