int main(){
int N, n_ind, t, combs, n_morto;
point input;
double p_killed;
cin >> t;
while(t--){
cin >> n_ind;
N = n_ind;
combs = (N*(N-1)*(N-2))/6;
positions.clear();
while(n_ind--){
cin >> input.x >> input.y;
positions.push_back(input);
}
n_morto = 0;
for(vp::iterator ii = positions.begin(); ii != positions.end(); ++ii){
for(vp::iterator jj = ii+1; jj != positions.end(); ++jj){
for(vp::iterator kk = jj+1; kk != positions.end(); ++kk){
n_morto += calc_morto(ii,jj,kk);
}
}
}
p_killed = ((double)n_morto)/(combs * ((positions.size()-3)));
cout << setprecision(8) << p_killed << "\n";
}
}
void dpri1()
{
int n = 10;
for(int i = 1;i<=n;++i)
{
int sign = (rand()%2)?1:-1;
int num = rand()%10;
int sign1 = (rand()%2)?1:-1;
int num1 = rand()%10;
test.pb(MP(sign*num,sign1*num1));
}
sort(test.begin(),test.end());
int u = unique(test.begin(),test.end())-test.begin();
for(int i = 0;i<u;++i)
{
pLL now = test[i];
while(test1.size() > 1 && det(test1[test1.size()-2],now,test1[test1.size()-1])<0)
test1.pop_back();
test1.pb(now);
}
ff(du,"list point(s):\n");
for(int i = 0;i<test.size();++i)
ff(du,"(%I64d,%I64d)",test[i].X,test[i].Y);
ff(du,"\nconvex hull point(s):\n");
for(int i = 0;i<test1.size();++i)
ff(du,"(%I64d,%I64d)",test1[i].X,test1[i].Y);
int _l = 0,_r = test1.size()-1;
pLL now = MP(-4,1);
while(_l<_r)
{
M;
if(mid == 0 || mid == test1.size()-1) break;
if((now*(test1[mid+1]-test1[mid])).X == 0 && (now*(test1[mid]-test1[mid-1])).X == 0) break;
if((now*(test1[mid+1]-test1[mid])).X > 0 && (now*(test1[mid]-test1[mid-1])).X < 0)
{_l = _r = mid;break;}
if((now*(test1[mid+1]-test1[mid])).X < 0) _l = mid+1;
else _r = mid-1;
}
ff(du,"\navailable point(s):\n");
for(int i = min(_l,_r);i<=max(_l,_r);++i)
ff(du,"(%I64d,%I64d)",test1[i].X,test1[i].Y);
}
int calc_morto(vp::iterator ia, vp::iterator ib, vp::iterator ic){
point a,b,c, p;
a = *ia;
b = *ib;
c = *ic;
// Ve se sao colineares
int A = abs(( ( ( a.x*b.y ) + ( a.y*c.x ) + ( b.x*c.y ) ) - ( (b.y*c.x) + (c.y*a.x) + (b.x*a.y) ) ));
if(A == 0) return 0;
// Encontrando retas
line ma, mb;
ma.m = ((double)(b.x-a.x))/((a.y-b.y));
mb.m = ((double)(c.x-b.x))/((b.y-c.y));
ma.q = ((a.y+b.y)-ma.m*(a.x+b.x));
mb.q = ((b.y+c.y)-mb.m*(b.x+c.x));
double Cx, Cy;
// Na verdade é dividido por 2, mas assim diminui uma operacao
Cx = (ma.m*(a.x+b.x)-mb.m*(b.x+c.x)+c.y-a.y)/(ma.m-mb.m);
Cy = ma.m*Cx+ma.q;
if(a.x == b.x)
Cy = (a.y+b.y);
else if(b.x == c.x)
Cy = (b.y+c.y);
if(a.y == b.y)
Cx = (a.x+b.x);
else if(b.y == c.y)
Cx = (b.x+c.x);
double R = ((Cx - a.x)*(Cx - a.x))+((Cy - a.y)*(Cy - a.y));
int kills = 0;
for(vp::iterator ii = positions.begin(); ii != positions.end(); ++ii){
if(ii != ia && ii != ib && ii != ic){
p = *ii;
// if(((Cx - p.x)*(Cx - p.x))+((Cy - p.y)*(Cy - p.y)) <= R) kills++;
// Original (tirei o 2 p compensar o 2 tirado dos Cx, Cy: if(((p.x*p.x)-(a.x*a.x)+(p.y*p.y)-(a.y*a.y)) <= 2*( (Cx*(p.x-a.x))+(Cy*(p.y-a.y)) )) kills++;
if(( (Cx*(p.x-a.x))+(Cy*(p.y-a.y)) ) >= ((p.x*p.x)-(a.x*a.x)+(p.y*p.y)-(a.y*a.y))) kills++; // teste maluco de int com double
}
}
return kills;
}
vp convex_hull(vp P) {
int n = P.size(), k = 0;
vp H(2*n);
sort(P.begin(), P.end());
for (int i = 0; i < n; i++) {
while (k >= 2 && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
H[k++] = P[i];
}
for (int i = n - 2, t = k + 1; i >= 0; i--) {
while (k >= t && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
H[k++] = P[i];
}
H.resize(k);
return H;
}
