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>
#define endl '\n'
using namespace std;
typedef long long ll;
struct Point
{
ll x, y;
Point(ll _x = 0, ll _y = 0)
{
x = _x;
y = _y;
}
void input()
{
cin >> x >> y;
}
};
const int MAXN = 2010;
int n;
pair < Point, ll > spot[MAXN];
void input()
{
cin >> n;
for (int i = 1; i <= n; i ++)
{
spot[i].first.input();
cin >> spot[i].second;
}
}
ll signed_area(Point A, Point B, Point C) /// returns signed area * 2
{
ll area = (B.x - A.x) * (A.y + B.y) +
(C.x - B.x) * (B.y + C.y) +
(A.x - C.x) * (C.y + A.y);
return area;
}
int orient(Point A, Point B, Point C)
{
ll area = signed_area(A, B, C);
if (area > 0)
return 1;
if (area < 0)
return -1;
assert(area != 0);
return 0;
}
void simulate()
{
ll result = 0;
for (int i = 1; i <= n; i ++)
for (int j = i + 1; j <= n; j ++)
{
vector < pair < ll, ll > > pos, neg;
for (int k = 1; k <= n; k ++)
{
if (k == i || k == j)
continue;
ll area = signed_area(spot[i].first,
spot[j].first,
spot[k].first);
/**if (i == 3 && j == 4)
{
cout << "pair with " << k << " area " << area << " value " << spot[k].second << endl;
}*/
assert(area != 0);
if (area > 0)
pos.push_back({area, spot[k].second});
else
neg.push_back({-area, spot[k].second});
}
sort(pos.begin(), pos.end());
sort(neg.begin(), neg.end());
ll best = 0, sum = 0;
ll ls = -1;
for (pair < ll, ll > cur : pos)
{
sum += cur.second;
assert(cur.first != ls);
ls = cur.first;
best = max(best, sum);
}
ls = -1;
sum = 0;
for (pair < ll, ll > cur : neg)
{
sum += cur.second;
assert(cur.first != ls);
ls = cur.first;
best = max(best, sum);
}
//cout << "HERE " << best << endl;
best = best + spot[i].second;
best = best + spot[j].second;
//cout << "new best " << best << endl;
//ll mx = min(spot[i].second, spot[j].second);
//cout << "mx " << mx << endl;
if (spot[i].second < 0)
best -= spot[i].second;
if (spot[j].second < 0)
best -= spot[j].second;
//cout << "pair " << i << " " << j << " " << best << endl;
result = max(result, best);
}
cout << result << endl;
}
void solve()
{
input();
simulate();
}
int main()
{
solve();
return 0;
}
/*
3
0 0 1
1 0 1
2 0 1
*/
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