Area of Mushroom

3
0 0 3
1 1 2
2 2 1
0

Case #1: 100

//109MS	292K
#include<stdio.h>
#include<math.h>
#include<algorithm>
using namespace std;
struct Point
{
    int x,y,k,id,vis,flag;
    Point(int x=0,int y=0):x(x),y(y) {} //构造函数
};
typedef Point Vector;
Point operator-(Point A,Point B)
{
    return Point(A.x-B.x,A.y-B.y);
}
int Cross(Point A,Point B)
{
    return A.x*B.y-A.y*B.x;
}
int cmp1(Point a,Point b)
{
    if(a.k==b.k)
    {
        if(a.x==b.x)return a.y<b.y;
        return a.x<b.x;
    }

    return a.k>b.k;
}
int cmp2(Point a,Point b)
{
    return a.id<b.id;
}

int ConvexHull(Point* p,int n,Point* ch)//求凸包
{
    int m=0;
    for(int i=0;i<n;i++)
    {
        while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--)
    {
        while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    if(n>1)m--;
    return m;
}

int main()
{
        int n,cas=1;
        while(scanf("%d",&n),n)
        {
            Point P[507],ch[507],v[507];
            int i;
            for(i=0; i<n; i++)
            {
                scanf("%d%d%d",&P[i].x,&P[i].y,&P[i].k);
                P[i].id=i;P[i].vis=P[i].flag=0;
            }
            sort(P,P+n,cmp1);
            v[0]=P[0];
            for(i=1;i<n;i++)
                if(P[i].k!=P[i-1].k)break;
                else
                {
                    v[i]=P[i];
                    if(P[i].x==P[i-1].x&&P[i].y==P[i-1].y)P[i].vis=v[i].vis=P[i-1].vis=v[i-1].vis=1;
                }
            int num=i;
            int m=ConvexHull(v,num,ch);
            if(P[0].k==0)num=0;
            for(i=0;i<num;i++)
                for(int j=0;j<m;j++)
                    if(Cross(ch[j]-ch[(j+1)%m],ch[j]-P[i])==0)
                    {
                        if(!P[i].vis)P[i].flag=1;
                        break;
                    }
            sort(P,P+n,cmp2);
            printf("Case #%d: ",cas++);
            for(int i=0;i<n;i++)
                printf("%d",P[i].flag);
            printf("\n");
        }
    return 0;
}