#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
#include<cassert>
#define N 110
#define eps 1e-8
using namespace std;

int dlcmp(double x) {return x<-eps?-1:x>eps;}
double sqr(double x) {return x*x;}

struct Point
{
	double x,y;

	Point (){}
	Point (double a,double b):x(a),y(b){}

	void input() {scanf("%lf%lf",&x,&y);}

	Point operator + (const Point &p) const {return Point(x+p.x,y+p.y);}
	Point operator - (const Point &p) const {return Point(x-p.x,y-p.y);}

	double len() {return sqrt(sqr(x)+sqr(y));}
	Point trunc(double d) {d/=len(); return Point(x*d,y*d);}
};

double cross(Point a,Point b) {return a.x*b.y-b.x*a.y;}
double dot(Point a,Point b) {return a.x*b.x+a.y*b.y;}
double dis(Point a,Point b) {return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));}

Point pt[N];
vector<double>vec;
int n;

/*
// 0 in-in; 1 in-out; 2 out-in; 3 out-out
int check(Point s,Point e,Point a,Point o,Point b)
{
	Point v=e-s;

	if (dlcmp(vec,a-o)<=0&&dlcmp(vec,b-o)<=0)
		return 0;
	else if (dlcmp(vec,a-o)>0&&dlcmp(vec,b-o)>0)
		return 3;
	else if
*/

int segment_intersect(Point s1,Point e1,Point s2,Point e2)
{
	if (dlcmp(cross(e1-s1,s2-s1))*dlcmp(cross(e1-s1,e2-s1))<0&&
		dlcmp(cross(e2-s2,s1-s2))*dlcmp(cross(e2-s2,e1-s2))<0)
		return 1;
	else
		return 0;
}

Point interpoint_lines(Point s1,Point e1,Point s2,Point e2)
{
	Point v1,v2,res;

	v1=s1-e1; v2=s2-e2;

	double r=((s1.x-s2.x)*v2.y-(s1.y-s2.y)*v2.x)/(v1.x*v2.y-v2.x*v1.y);
	res.x=-r*v1.x+s1.x;
	res.y=-r*v1.y+s1.y;
	return res;
}
bool isChange(Point s,Point e,Point a,Point o,Point b)
{
	Point vec=e-s;

	if (dlcmp(cross(vec,a-s))*dlcmp(cross(vec,b-s))<0)
		return true;
	else
		return false;
}

void init()
{
	int i,cnt=0;

	cnt=2;
	for (i=2;i<n;i++)
	{
		while (cnt>1&&dlcmp(cross(pt[cnt-1]-pt[cnt-2],pt[i]-pt[cnt-1]))==0)
			cnt--;
		pt[cnt++]=pt[i];
	}
	n=cnt;
}

void solve(Point s,Point e,Point a,Point b,Point p,Point q)
{
	int dp,dq;

	dp=dlcmp(cross(e-s,p-s));
	dq=dlcmp(cross(e-s,q-s));
	if (dlcmp(dot(e-s,b-a))<0)
	{
		dp=-dp; dq=-dq;
	}


	if(dp>0&&dq>0)
	{
		vec.push_back(dis(s,a));
		vec.push_back(dis(s,b));
		//printf("put3 %.3f %.3f\n",a.x,a.y);
		//printf("put3 %.3f %.3f\n",b.x,b.y);
	}
	else if (dp>0&&dq<0)
	{
		vec.push_back(dis(s,a));
		//printf("put3 %.3f %.3f\n",a.x,a.y);
	}
	else if (dp<0&&dq>0)
	{
		vec.push_back(dis(s,b));
		//printf("put3 %.3f %.3f\n",b.x,b.y);
	}
}


int main()
{
	int i,j,k,m;
	double ans,tmp;
	Point s,e,a,b,o,aa,bb;

	int ys=0;

	while(scanf("%d",&n),n)
	{
		for (i=0;i<n;i++)
			pt[i].input();

		init();
		//printf("n %d\n",n);
		//for (i=0;i<n;i++)
			//printf("%.2f %.2f\n",pt[i].x,pt[i].y);

		ans=0;
		for (i=0;i<n;i++)
			for (j=0;j<n;j++)
			{
				if (i==j) continue;
				//printf("i%d j%d\n",i,j);
				s=pt[i]+(pt[i]-pt[j]).trunc(5000); e=pt[j]+(pt[j]-pt[i]).trunc(5000);

				vec.clear();
				for (k=0;k<n;k++)
				{
					a=pt[k]; b=pt[(k+1)%n];

					if (segment_intersect(s,e,a,b))
					{
						Point p=interpoint_lines(s,e,a,b);
						//printf("put1 %.3f %.3f\n",p.x,p.y);
						vec.push_back(dis(s,p));
					}
				}

				for (k=0;k<n;k++)
				{
					o=pt[k]; a=pt[(k-1+n)%n]; b=pt[(k+1)%n];

					if (dlcmp(cross(e-s,o-s))==0&&isChange(s,e,a,o,b))
					{
						//printf("put2 %.3f %.3f %.3f\n",o.x,o.y,dis(s,o));
						vec.push_back(dis(s,o));
					}
				}

				for (k=0;k<n;k++)
				{
					a=pt[k]; b=pt[(k+1)%n],aa=pt[(k-1+n)%n]; bb=pt[(k+2)%n];

					if (dlcmp(cross(e-s,a-s))==0&&dlcmp(cross(e-s,b-s))==0)
					{
						Point f1=e-s, f2=b-a;
						//printf("true k %d %.3f %.3f %.3f %.3f\n",k,f1.x,f1.y,f2.x,f2.y);
						solve(s,e,a,b,aa,bb);
					}
				}

				sort(vec.begin(),vec.end());
				m=vec.size(); assert(m%2==0);
				tmp=0;
				for (k=0;k<m;k+=2)
					tmp=max(tmp,vec[k+1]-vec[k]);

				ans=max(ans,tmp);
			}

		printf("Case %d: %.8f\n",++ys,ans);
	}

	return 0;
}
### Prompt

Generate a CPP solution to the following problem:

Mr. KM, the mayor of KM city, decided to build a new elementary school. The site for the school has an awkward polygonal shape, which caused several problems. The most serious problem was that there was not enough space for a short distance racetrack. Your task is to help Mr. KM to calculate the maximum possible length for the racetrack that can be built in the site. The track can be considered as a straight line segment whose width can be ignored. The boundary of the site has a simple polygonal shape without self-intersection, and the track can touch the boundary. Note that the boundary might not be convex.



Input

The input consists of multiple test cases, followed by a line containing "0". Each test case has the following format. The first line contains an integer N (3 \leq N \leq 100). Each of the following N lines contains two integers x_i and y_i (-1,000 \leq x_i, y_i \leq 1,000), which describe the coordinates of a vertex of the polygonal border of the site, in counterclockwise order.

Output

For each test case, print its case number and the maximum possible length of the track in a line. The answer should be given as a floating point number with an absolute error of at most 10^{-6}.

Example

Input

4
0 0
10 0
10 10
0 10
3
0 0
1 0
0 1
0


Output

Case 1: 14.142135624
Case 2: 1.41421356

### Response

```cpp
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
#include<cassert>
#define N 110
#define eps 1e-8
using namespace std;

int dlcmp(double x) {return x<-eps?-1:x>eps;}
double sqr(double x) {return x*x;}

struct Point
{
	double x,y;

	Point (){}
	Point (double a,double b):x(a),y(b){}

	void input() {scanf("%lf%lf",&x,&y);}

	Point operator + (const Point &p) const {return Point(x+p.x,y+p.y);}
	Point operator - (const Point &p) const {return Point(x-p.x,y-p.y);}

	double len() {return sqrt(sqr(x)+sqr(y));}
	Point trunc(double d) {d/=len(); return Point(x*d,y*d);}
};

double cross(Point a,Point b) {return a.x*b.y-b.x*a.y;}
double dot(Point a,Point b) {return a.x*b.x+a.y*b.y;}
double dis(Point a,Point b) {return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));}

Point pt[N];
vector<double>vec;
int n;

/*
// 0 in-in; 1 in-out; 2 out-in; 3 out-out
int check(Point s,Point e,Point a,Point o,Point b)
{
	Point v=e-s;

	if (dlcmp(vec,a-o)<=0&&dlcmp(vec,b-o)<=0)
		return 0;
	else if (dlcmp(vec,a-o)>0&&dlcmp(vec,b-o)>0)
		return 3;
	else if
*/

int segment_intersect(Point s1,Point e1,Point s2,Point e2)
{
	if (dlcmp(cross(e1-s1,s2-s1))*dlcmp(cross(e1-s1,e2-s1))<0&&
		dlcmp(cross(e2-s2,s1-s2))*dlcmp(cross(e2-s2,e1-s2))<0)
		return 1;
	else
		return 0;
}

Point interpoint_lines(Point s1,Point e1,Point s2,Point e2)
{
	Point v1,v2,res;

	v1=s1-e1; v2=s2-e2;

	double r=((s1.x-s2.x)*v2.y-(s1.y-s2.y)*v2.x)/(v1.x*v2.y-v2.x*v1.y);
	res.x=-r*v1.x+s1.x;
	res.y=-r*v1.y+s1.y;
	return res;
}
bool isChange(Point s,Point e,Point a,Point o,Point b)
{
	Point vec=e-s;

	if (dlcmp(cross(vec,a-s))*dlcmp(cross(vec,b-s))<0)
		return true;
	else
		return false;
}

void init()
{
	int i,cnt=0;

	cnt=2;
	for (i=2;i<n;i++)
	{
		while (cnt>1&&dlcmp(cross(pt[cnt-1]-pt[cnt-2],pt[i]-pt[cnt-1]))==0)
			cnt--;
		pt[cnt++]=pt[i];
	}
	n=cnt;
}

void solve(Point s,Point e,Point a,Point b,Point p,Point q)
{
	int dp,dq;

	dp=dlcmp(cross(e-s,p-s));
	dq=dlcmp(cross(e-s,q-s));
	if (dlcmp(dot(e-s,b-a))<0)
	{
		dp=-dp; dq=-dq;
	}


	if(dp>0&&dq>0)
	{
		vec.push_back(dis(s,a));
		vec.push_back(dis(s,b));
		//printf("put3 %.3f %.3f\n",a.x,a.y);
		//printf("put3 %.3f %.3f\n",b.x,b.y);
	}
	else if (dp>0&&dq<0)
	{
		vec.push_back(dis(s,a));
		//printf("put3 %.3f %.3f\n",a.x,a.y);
	}
	else if (dp<0&&dq>0)
	{
		vec.push_back(dis(s,b));
		//printf("put3 %.3f %.3f\n",b.x,b.y);
	}
}


int main()
{
	int i,j,k,m;
	double ans,tmp;
	Point s,e,a,b,o,aa,bb;

	int ys=0;

	while(scanf("%d",&n),n)
	{
		for (i=0;i<n;i++)
			pt[i].input();

		init();
		//printf("n %d\n",n);
		//for (i=0;i<n;i++)
			//printf("%.2f %.2f\n",pt[i].x,pt[i].y);

		ans=0;
		for (i=0;i<n;i++)
			for (j=0;j<n;j++)
			{
				if (i==j) continue;
				//printf("i%d j%d\n",i,j);
				s=pt[i]+(pt[i]-pt[j]).trunc(5000); e=pt[j]+(pt[j]-pt[i]).trunc(5000);

				vec.clear();
				for (k=0;k<n;k++)
				{
					a=pt[k]; b=pt[(k+1)%n];

					if (segment_intersect(s,e,a,b))
					{
						Point p=interpoint_lines(s,e,a,b);
						//printf("put1 %.3f %.3f\n",p.x,p.y);
						vec.push_back(dis(s,p));
					}
				}

				for (k=0;k<n;k++)
				{
					o=pt[k]; a=pt[(k-1+n)%n]; b=pt[(k+1)%n];

					if (dlcmp(cross(e-s,o-s))==0&&isChange(s,e,a,o,b))
					{
						//printf("put2 %.3f %.3f %.3f\n",o.x,o.y,dis(s,o));
						vec.push_back(dis(s,o));
					}
				}

				for (k=0;k<n;k++)
				{
					a=pt[k]; b=pt[(k+1)%n],aa=pt[(k-1+n)%n]; bb=pt[(k+2)%n];

					if (dlcmp(cross(e-s,a-s))==0&&dlcmp(cross(e-s,b-s))==0)
					{
						Point f1=e-s, f2=b-a;
						//printf("true k %d %.3f %.3f %.3f %.3f\n",k,f1.x,f1.y,f2.x,f2.y);
						solve(s,e,a,b,aa,bb);
					}
				}

				sort(vec.begin(),vec.end());
				m=vec.size(); assert(m%2==0);
				tmp=0;
				for (k=0;k<m;k+=2)
					tmp=max(tmp,vec[k+1]-vec[k]);

				ans=max(ans,tmp);
			}

		printf("Case %d: %.8f\n",++ys,ans);
	}

	return 0;
}
```