UVa OJ 1342

#include<cstdio>
#include<cmath>
#include<algorithm>
#include<iostream>
using namespace std;
struct Point{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
};
typedef Point Vector;
Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Point A,Point B){return Vector(A.x-B.x,A.y-B.y);}
Vector operator * (Vector A,double p){return Vector(A.x*p,A.y*p);}
Vector operator / (Vector A,double p){return Vector(A.x/p,A.y/p);}
bool operator <(const Point&a,const Point&b){
     return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
const double eps=1e-10;
int dcmp(double x){
    if(fabs(x)<eps) return 0;else return x<0?-1:1;
}
bool operator == (const Point&a,const Point&b){
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
double Dot(Vector A,Vector B){return A.x*B.x+A.y*B.y;}
double Length(Vector A){return sqrt(Dot(A,A));}
double Angle(Vector A,Vector B){return acos(Dot(A,B)/Length(A)/Length(B));}
double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}
double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}
Vector Rotate(Vector A,double rad){
   return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A){
   double L=Length(A);
   return Vector(-A.y/L,A.x/L);
}
Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){
   Vector u=P-Q;
   double t=Cross(w,u)/Cross(v,w);
   return P+v*t;
}
double DistanceToLine(Point P,Point A,Point B){
   Vector v1=B-A,v2=P-A;
   return fabs(Cross(v1,v2))/Length(v1);
}
double DistanceToSegment(Point P,Point A,Point B){
   if(A==B) return Length(P-A);
   Vector v1=B-A,v2=P-A,v3=P-B;
   if(dcmp(Dot(v1,v2))<0) return Length(v2);
   else if(dcmp(Dot(v1,v3))>0) return Length(v3);
   else return fabs(Cross(v1,v2))/Length(v1);
}
Point GetLineProjection(Point P,Point A,Point B){
   Vector v=B-A;
   return A+v*(Dot(v,P-A)/Dot(v,v));
}
bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){
   double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);
   double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
   return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
bool OnSegment(Point p,Point a1,Point a2){
   return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}
const int maxn=300+10;
Point P[maxn],V[maxn*maxn];
int main(){
    int n,kase=0;
    while(scanf("%d",&n)==1&&n){
        for(int i=0;i<n;i++){
           scanf("%lf%lf",&P[i].x,&P[i].y);
           V[i]=P[i];
        }
        n--;
        int c=n,e=n;
        for(int i=0;i<n;i++)
           for(int j=i+1;j<n;j++)
              if(SegmentProperIntersection(P[i],P[i+1],P[j],P[j+1]))
                 V[c++]=GetLineIntersection(P[i],P[i+1]-P[i],P[j],P[j+1]-P[j]);
        sort(V,V+c);
        c=unique(V,V+c)-V;
        for(int i=0;i<c;i++)
          for(int j=0;j<n;j++)
            if(OnSegment(V[i],P[j],P[j+1])) e++;
        printf("Case %d: There are %d pieces.\n",++kase,e+2-c);
    }
    return 0;
}