#include "fish.h"
#include <bits/stdc++.h>
using namespace std;
constexpr size_t N = 100001;
struct state
{
vector<int64_t> s, l, z;
};
state f[N];
vector<int64_t> p[N];
vector<uint32_t> coords[N];
size_t ind(size_t x, int y)
{
return lower_bound(coords[x].begin(), coords[x].end(), y) - coords[x].begin();
}
long long max_weights(int n, int m, vector<int> x, vector<int> y, vector<int> w)
{
for (size_t i = 0; i < m; ++i)
{
coords[x[i]].push_back(y[i] + 1);
if (x[i])
coords[x[i] - 1].push_back(y[i] + 1);
if (x[i] + 1 < n)
coords[x[i] + 1].push_back(y[i] + 1);
}
for (size_t i = 0; i < n; ++i)
{
coords[i].push_back(0);
sort(coords[i].begin(), coords[i].end());
coords[i].resize(unique(coords[i].begin(), coords[i].end()) - coords[i].begin());
f[i].s.resize(coords[i].size());
f[i].l.resize(coords[i].size());
f[i].z.resize(i ? coords[i - 1].size() : 1);
p[i].resize(coords[i].size());
}
for (size_t i = 1; i < n; ++i)
{
fill(f[i].s.begin(), f[i].s.end(), INT64_MIN / 2);
fill(f[i].l.begin(), f[i].l.end(), INT64_MIN / 2);
fill(f[i].z.begin(), f[i].z.end(), INT64_MIN / 2);
}
for (size_t i = 0; i < m; ++i)
p[x[i]][ind(x[i], y[i] + 1)] = w[i];
for (size_t i = 0; i < n; ++i)
for (size_t j = 1; j < p[i].size(); ++j)
p[i][j] += p[i][j - 1];
for (size_t i = 1; i < n; ++i)
{
// Update s
int64_t h = f[i - 1].s[0];
size_t k = 0, l = i == 1 ? SIZE_MAX : 0;
for (size_t j = 1; j < coords[i].size(); ++j)
{
while (k < coords[i - 1].size() && coords[i - 1][k] < coords[i][j])
{
h = max(h, f[i - 1].s[k] - p[i - 1][k]);
++k;
}
while (l < f[i - 1].z.size() && coords[i - 2][l] < coords[i][j])
{
size_t v = ind(i - 1, coords[i - 2][l]);
if (v == coords[i - 1].size() || coords[i - 1][v] > coords[i - 2][l])
--v;
h = max(h, f[i - 1].z[l] - p[i - 1][v]);
++l;
}
size_t u = ind(i - 1, coords[i][j]);
if (u == coords[i - 1].size() || coords[i - 1][u] > coords[i][j])
--u;
f[i].s[j] = max(f[i].s[j], h + p[i - 1][u]);
}
h = INT64_MIN;
l = f[i - 1].z.size() - 1;
for (size_t j = coords[i].size() - 1; j < coords[i].size(); --j)
{
while (l != SIZE_MAX && (i == 1 || coords[i - 2][l] > coords[i][j]))
{
h = max(h, f[i - 1].z[l]);
f[i].s[j] = max(f[i].s[j], h);
--l;
}
if (l != SIZE_MAX)
{
h = max(h, f[i - 1].z[l]);
f[i].s[j] = max(f[i].s[j], h);
--l;
}
}
// Update l
int64_t g = 0; // max f_i-1,k,s f_i-1,k-l + p_ik over all k >= j
k = coords[i - 1].size() - 1;
for (size_t j = coords[i].size() - 1; j < coords[i].size(); --j)
{
while (k != SIZE_MAX && coords[i - 1][k] > coords[i][j])
{
size_t u = ind(i, coords[i - 1][k]);
if (u == coords[i].size() || coords[i][u] > coords[i - 1][k])
--u;
g = max(g, max(f[i - 1].l[k], f[i - 1].s[k]) + p[i][u]);
--k;
}
if (k != SIZE_MAX)
{
size_t u = ind(i, coords[i - 1][k]);
if (u == coords[i].size() || coords[i][u] > coords[i - 1][k])
--u;
g = max(g, max(f[i - 1].l[k], f[i - 1].s[k]) + p[i][u]);
--k;
}
f[i].l[j] = max(f[i].l[j], g - p[i][j]);
}
// Update z
k = 0;
for (size_t j = 0; j < f[i].z.size(); ++j)
{
while (k + 1 < coords[i].size() && coords[i][k + 1] <= coords[i - 1][j])
++k;
f[i].z[j] = max(f[i].z[j], max(f[i - 1].s[j], f[i - 1].l[j]) + p[i][k]);
if (!j)
{
for (size_t k = 0; k < f[i - 1].z.size(); ++k)
f[i].z[j] = max(f[i].z[j], f[i - 1].z[k]);
}
}
}
int64_t ans = 0;
for (size_t j = 0; j < f[n - 1].s.size(); ++j)
ans = max(ans, max(f[n - 1].s[j], f[n - 1].l[j]));
for (size_t j = 0; j < f[n - 1].z.size(); ++j)
ans = max(ans, f[n - 1].z[j]);
return ans;
}
