1 #include<stdio.h>
  2 #include<math.h>
  3 #include<algorithm>
  4 #include<iostream>
  5 using namespace std;
  6 struct Point {
  7     double x, y;
  8     Point(double x = 0, double y = 0) : x(x) , y(y) {}
  9 };
 10 typedef Point Vector;
 11 Vector operator + (Vector A, Vector B) {    return Vector(A.x + B.x, A.y + B.y);}
 12 Vector operator - (Point A, Point B)   {    return Vector(A.x - B.x, A.y - B.y);}
 13 Vector operator * (Vector A, double P) {    return Vector(A.x * P, A.y * P);}
 14 Vector operator / (Vector A, double P) {    return Vector(A.x / P, A.y / P);}
 15 bool operator < (const Point &a, const Point &b) {
 16     return a.x < b.x || (a.x == b.x && a.y < b.y);
 17 }
 18 const double eps = 1e-10;
 19 double fabs(double x) {
 20     return x > 0 ? x : -x;
 21 }
 22 int dcmp(double x) {
 23     if(fabs(x) < eps) return 0;
 24     else return x < 0 ? -1 : 1;
 25 }
 26 bool operator == (const Point &a, const Point &b) {
 27     return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
 28 }
 29 double Dot(Vector A ,Vector B) { return A.x * B.x + A.y * B.y;}//点积
 30 double Length(Vector A) { return sqrt(Dot(A, A));} //计算向量长度
 31 double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B));}// 计算向量夹角
 32 double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
 33 double Area2(Point A, Point B, Point C) { return Cross(B - A, C - A);}
 34 Vector Rotate(Vector A, double rad) {
 35     return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
 36 }
 37 Vector Normal(Vector A) {
 38     double L = Length(A);
 39     return Vector(-A.y / L, A.x / L);
 40 }
 41 Point GetlineIntersection(Point P, Vector v, Point Q, Vector w) {
 42     Vector u = P - Q;
 43     double t = Cross(w, u) / Cross(v, w);
 44     return P + v * t;
 45 }
 46 double DistanceToLine(Point P, Point A, Point B) {
 47     Vector v1 = B - A, v2 = P - A;
 48     return fabs(Cross(v1, v2) / Length(v1));
 49 }
 50 double DistanceToSegment(Point P, Point A, Point B) {
 51     if(A == B) return Length(P - A);
 52     Vector v1 = B - A, v2 = P - A, v3 = P - B;
 53     if(dcmp(Dot(v1, v2) < 0)) return Length(v2);
 54     else if(dcmp(Dot(v1, v2) < 0)) return Length(v3);
 55     else return fabs(Cross(v1,v2)) / Length(v1);
 56 }
 57 Point GetLineProjection(Point P, Point A, Point B) {
 58     Vector v = B - A;
 59     return A + v * (Dot(v, P - A)) / Dot(v, v);
 60 }
 61 bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
 62     double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1),
 63            c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
 64     return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
 65 }
 66 bool Onsegment(Point p, Point a1, Point a2) {
 67     return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
 68 }
 69 double ConvexPolygonArea(Point * p, int n) {
 70     double area = 0;
 71     for(int i = 1; i < n - 1; ++i)
 72         area += Cross(p[i] - p[0], p[i + 1] - p[0]);
 73     return fabs(area / 2);
 74 }
 75 const int maxn = 300 + 10;
 76 Point P[maxn], V[maxn * maxn];
 77 
 78 int main() {
 79     int n, kase = 0;
 80     while(scanf("%d", &n) == 1 && n) {
 81         for(int i = 0; i < n; ++i) {
 82             scanf("%lf%lf", &P[i].x, &P[i].y); V[i] = P[i];
 83         }
 84         n--;
 85         int c = n, e = n;
 86         for(int i = 0; i < n; ++i) {
 87             for(int j = i + 1; j < n; ++j) {
 88                 if(SegmentProperIntersection(P[i], P[i + 1], P[j], P[j + 1])) {
 89                     V[c++] = GetlineIntersection(P[i], P[i + 1] - P[i], P[j], P[j + 1] - P[j]);
 90                 }
 91             }
 92         }
 93         sort(V, V + c);
 94         c = unique(V, V + c) - V;
 95         for(int i = 0; i < c; ++i)
 96             for(int j = 0; j < n; ++j)
 97                 if(Onsegment(V[i], P[j], P[j + 1])) ++e;
 98         printf("Case %d: There are %d pieces.\n", ++kase, e + 2 - c);
 99     }
100     return 0;
101 }