#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
long long max_weights(int n, int m, std::vector<int> fx, std::vector<int> fy,
std::vector<int> fw)
{
n += 2;
vector < map < int, ll > > a (n);
for (int i = 0; i < m; ++i) a[fx[i] + 1][fy[i]] += fw[i];
ll mxdp = 0;
vector < vector < pair < int, ll > > > p (3), q (2), dp (3);
map < int, int > is;
for (auto &x : a[1]) ++is[x.first];
for (int i = 2; i < n; ++i)
{
for (auto &x : a[i]) ++is[x.first];
if (i - 3 >= 1)
for (auto &x : a[i - 3])
{
--is[x.first];
if (!is[x.first]) is.erase (is.find (x.first));
}
ll ls = 0, rs = 0, ms = 0;
ll mxp = -1e18, mxq = -1e18;
ll id = -1;
stack < int > st;
auto itp = p[2].begin ();
auto itq = q[1].begin ();
for (auto &[x, tmp] : is)
{
st.push (x);
ls += a[i - 2].count (x) ? a[i - 2][x] : 0ll;
ms += a[i - 1].count (x) ? a[i - 1][x] : 0ll;
rs += a[i].count (x) ? a[i][x] : 0ll;
if (a[i].count (x) + a[i - 2].count (x) == 0) continue;
dp[0].push_back ({ x, 0 });
p[0].push_back ({ x, 0 });
q[0].push_back ({ x, 0 });
++id;
dp[0][id].second = ls + rs + mxdp;
while (itp != p[2].end () && itp->first <= x)
mxp = max (mxp, itp->second), ++itp;
while (itq != q[1].end () && itq->first <= x)
mxq = max (mxq, itq->second), ++itq;
dp[0][id].second = max (dp[0][id].second, ls + rs + mxp);
dp[0][id].second = max (dp[0][id].second, ls + rs + mxq);
}
mxp = -1e18, mxq = -1e18;
auto ritp = dp[2].rbegin (), ritq = dp[1].rbegin ();
while (st.size ())
{
int x = st.top ();
st.pop ();
if (a[i].count (x) + a[i - 2].count (x) == 0) goto cont;
while (ritp != dp[2].rend () && ritp->first >= x)
mxp = max (mxp, ritp->second), ++ritp;
while (ritq != dp[1].rend () && ritq->first >= x)
mxq = max (mxq, ritq->second), ++ritq;
dp[0][id].second = max (dp[0][id].second, rs + mxp);
q[0][id].second = dp[0][id].second - ms - rs;
dp[0][id].second = max (dp[0][id].second, rs + mxq - ms);
p[0][id].second = dp[0][id].second - rs;
--id;
cont:
ls -= a[i - 2].count (x) ? a[i - 2][x] : 0ll;
ms -= a[i - 1].count (x) ? a[i - 1][x] : 0ll;
rs -= a[i].count (x) ? a[i][x] : 0ll;
}
swap (p[2], p[1]);
swap (p[1], p[0]);
p[0].clear ();
swap (q[1], q[0]);
q[0].clear ();
swap (dp[2], dp[1]);
swap (dp[1], dp[0]);
for (auto &x : dp[0]) mxdp = max (mxdp, x.second);
dp[0].clear ();
}
for (int i = 1; i <= 2; ++i) for (auto &x : dp[i]) mxdp = max (mxdp, x.second);
return mxdp;
}
