This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define int long long
// #define double long double
#define endl '\n'
#define fastIO ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
#define setmin(x, y) x = min((x), (y))
#define setmax(x, y) x = max((x), (y))
#define sqr(x) ((x) * (x))
#define fi first
#define se second
#define all(x) x.begin(), x.end()
// mt19937 hdp(chrono::high_resolution_clock::now().time_since_epoch().count());
// int rand(int l, int r){return l + ((hdp() % (r - l + 1)) + r - l + 1) % (r - l + 1);}
const int NM = 2e5 + 5;
const int mod = 1e9 + 7;
struct mi
{
int v;
mi() : v(0){}
mi(int _v) : v(_v)
{
if (v >= mod)
v -= mod;
}
mi operator+(const mi& o)
{
return mi(v + o.v);
}
mi operator-(const mi& o)
{
return mi(v + mod - o.v);
}
mi operator*(const mi& o)
{
return mi(1ll * v * o.v % mod);
}
mi& operator+=(const mi &o)
{
v += o.v;
if (v >= mod)
v -= mod;
return *this;
}
mi& operator-=(const mi &o)
{
v += mod - o.v;
if (v >= mod)
v -= mod;
return *this;
}
mi& operator*=(const mi& o)
{
v = 1ll * v * o.v % mod;
return *this;
}
};
struct Pt
{
int x, y;
Pt(){}
Pt(int x, int y) : x(x), y(y){}
}pt[NM];
int cw(Pt a, Pt b, Pt c)
{
return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < 0;
}
vector<Pt> v[2];
mi ex[NM], ans;
int n;
void calc(int x)
{
v[0].clear(); v[1].clear();
for (int i = 1; i <= n; i++)
if (i != x)
v[pt[i].x > pt[x].x].push_back(pt[i]);
for (int i = 0; i < 2; i++)
sort(v[i].begin(), v[i].end(), [&](const Pt& a, const Pt& b) {return cw(pt[x], a, b);});
for (auto t : v[1])
v[0].push_back(t);
int m = v[0].size();
int j = 0, cnt = 0;
for (int i = 0; i < m; i++)
{
if (cnt == -1)
{
j = i;
cnt = 0;
}
while ((j + 1) % m != i && !cw(v[0][i], pt[x], v[0][(j + 1) % m]))
{
j = (j + 1) % m;
cnt++;
}
ans += ex[cnt];
cnt--;
}
}
void solve()
{
cin >> n;
ex[0].v = 1;
for (int i = 1; i <= n; i++)
ex[i] = ex[i - 1] * mi(2);
for (int i = 1; i <= n; i++)
cin >> pt[i].x >> pt[i].y;
for (int i = 1; i <= n; i++)
calc(i);
ans += mi(n);
cout << (mi(n) * ex[n] - ans).v;
}
signed main()
{
fastIO
if (fopen("in.txt", "r"))
{
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
}
int tc = 1;
// cin >> tc;
while (tc--)
solve();
}
Compilation message (stderr)
Main.cpp: In function 'int main()':
Main.cpp:129:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
129 | freopen("in.txt", "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
Main.cpp:130:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
130 | freopen("out.txt", "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
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