1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <cmath>
  5 #include <vector>
  6 #include <algorithm>
  7 using namespace std;
  8 
  9 const double eps=1e-8;
 10 const double Pi=acos(-1.0);
 11 struct Point
 12 {
 13     double x,y;
 14     Point(double x=0,double y=0):x(x),y(y) {}
 15 };
 16 typedef Point Vector;
 17 Vector operator +(Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
 18 Vector operator -(Vector A,Vector B){return Vector(A.x-B.x,A.y-B.y);}
 19 Vector operator *(Vector A,double p){return Vector(A.x*p,A.y*p);}
 20 Vector operator /(Vector A,double p){return Vector(A.x/p,A.y/p);}
 21 bool operator < (const Point &a,const Point &b)
 22 {
 23     return a.x<b.x||(a.x==b.x&&a.y<b.y);
 24 }
 25 int dcmp(double x)
 26 {
 27     if(fabs(x)<eps) return 0;
 28     else return x<0?-1:1;
 29 }
 30 bool operator == (const Point &a,const Point &b){
 31     return (dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0);
 32 }
 33 double Dot(Vector A,Vector B){return A.x*B.x+A.y*B.y;}//点积
 34 double Cross(Vector A,Vector B){ return A.x*B.y-A.y*B.x;}//叉积
 35 Point GetLineProjection(Point P,Point A,Point B)//P在直线AB上的投影点
 36 {
 37     Vector v=B-A;
 38     return A+v*(Dot(v,P-A)/Dot(v,v));
 39 }
 40 bool OnSegment(Point p,Point a1,Point a2)//点是否在直线上（不包括端点）
 41 {
 42     return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dot(a1-p,a2-p))<0;
 43 }
 44 Point getcenter(vector<Point> p)//多边形的重心
 45 {
 46     double area=0;
 47     Point c=Point(0,0);
 48     int i,n=p.size();
 49     for(i=1;i<n-1;i++)
 50     {
 51         double temp=Cross(p[i]-p[0],p[i+1]-p[0]);
 52         c.x+=temp*(p[i].x+p[i+1].x+p[0].x)/3.0;
 53         c.y+=temp*(p[i].y+p[i+1].y+p[0].y)/3.0;
 54         area+=temp;
 55     }
 56     c.x/=area;c.y/=area;
 57     return c;
 58 }
 59 vector<Point> ConvexHull(vector<Point>& p)//求凸包
 60 {
 61     sort(p.begin(), p.end());
 62     p.erase(unique(p.begin(), p.end()), p.end());
 63     int i,n = p.size();
 64     int m = 0;
 65     vector<Point> ch(n+1);
 66     for(i = 0; i < n; i++) {
 67         while(m > 1 && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--;
 68         ch[m++] = p[i];
 69     }
 70     int k = m;
 71     for(i = n-2; i >= 0; i--) {
 72         while(m > k && Cross(ch[m-1]-ch[m-2], p[i]-ch[m-2]) <= 0) m--;
 73         ch[m++] = p[i];
 74     }
 75     if(n > 1) m--;
 76     ch.resize(m);
 77     return ch;
 78 }
 79 
 80 void solve(vector<Point> p,Point center)
 81 {
 82     int ans=0,n=p.size();
 83     for(int i=0;i<n;i++)
 84     {
 85         Point t=GetLineProjection(center,p[i],p[(i+1)%n]);
 86         if(OnSegment(t,p[i],p[(i+1)%n])) ans++;
 87     }
 88     printf("%d\n",ans);
 89 }
 90 
 91 int main()
 92 {
 93     int i,t,n;
 94     double x,y;
 95     vector<Point> p;
 96     scanf("%d",&t);
 97     while(t--)
 98     {
 99         p.clear();
100         scanf("%d",&n);
101         for(i=0;i<n;i++)
102         {
103             scanf("%lf%lf",&x,&y);p.push_back(Point(x,y));
104         }
105         Point center=getcenter(p);
106         p=ConvexHull(p);
107         solve(p,center);
108     }
109     return 0;
110 }