This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
const int N = 1 << 12;
using ll = int64_t;
struct S {
ll pref, suff, ans, sum;
S(ll x = 0) : sum{x} { ans = pref = suff = x > 0 ? x : 0; }
S(const S &l, const S &r) : ans{max(l.ans, r.ans)} {
pref = max(l.pref, l.sum + r.pref);
suff = max(l.suff + r.sum, r.suff);
ans = max(ans, l.suff + r.pref);
sum = l.sum + r.sum;
}
} t[N << 1];
int sz = 1;
void update(int p, ll x) { for (t[p += sz] = x; p >>= 1; ) t[p] = {t[p << 1], t[p << 1|1]}; }
#define rep(i, a, b) for (auto i = (a); i < (b); ++i)
#define all(x...) begin(x), end(x)
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
using point = complex<ll>;
ll cross(const point &a, const point &b) { return imag(conj(a) * b); }
int w[N], ord[N], pos[N];
point p[N];
vector<int> g[N], line;
bool vis[N];
void dfs(int u) {
vis[u] = 1; line.push_back(u);
for (int v : g[u]) if (!vis[v]) dfs(v);
}
pair<point, pair<int, int>> m[N * N];
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n; cin >> n; while (sz < n) sz <<= 1;
rep(i, 0, n) { int x, y; cin >> x >> y >> w[i]; p[i] = {x, y}; ord[i] = i; }
sort(ord, ord + n, [&](int a, int b) {
return pair(imag(p[a]), -real(p[a])) < pair(imag(p[b]), -real(p[b]));
});
rep(i, 0, n) pos[ord[i]] = i;
rep(i, 0, n) update(pos[i], w[i]);
int c = 0;
rep(i, 0, n) {
rep(j, i + 1, n) {
point z = p[i] - p[j];
ll g = gcd(real(z), imag(z));
assert(g != 0);
z = {real(z) / g, imag(z) / g};
if (imag(z) <= 0) z = -z;
m[c++] = {z, {i, j}};
m[c++] = {z, {j, i}};
}
}
sort(m, m + c, [&](auto a, auto b) { return cross(a.first, b.first) > 0; });
ll ans = t[1].ans;
for (int i = 0, j = 0; i < c; i = j) {
while (j < c && m[i].first == m[j].first) ++j;
rep(k, i, j) g[m[k].second.first].push_back(m[k].second.second);
rep(k, i, j) {
if (vis[m[k].second.first]) continue;
line.clear(); dfs(m[k].second.first);
sort(all(line), [&](int x, int y) { return pos[x] < pos[y];});
int s = line.size();
for (int i = 0; i < s - i - 1; ++i)
swap(pos[line[i]], pos[line[s - i - 1]]);
for (int i : line) update(pos[i], w[i]);
}
ans = max(ans, t[1].ans);
rep(k, i, j) g[m[k].second.first].clear(), vis[m[k].second.first] = 0;
}
cout << ans << '\n';
}
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