You are given the coordinates of Freddy‘s stone, Fiona‘s stone and all other stones in the lake. Your job is to compute the frog distance between Freddy‘s and Fiona‘s stone.

Input

The input will contain one or more test cases. The first line of each test case will contain the number of stones n (2 <= n <= 200). The next n lines each contain two integers xi, yi (0 <= xi, yi <= 1000) representing the coordinates of stone #i. Stone #1 is Freddy‘s stone, stone #2 is Fiona‘s stone, the other n-2 stones are unoccupied. There‘s a blank line following each test case. Input is terminated by a value of zero (0) for n.

Output

For each test case, print a line saying "Scenario #x" and a line saying "Frog Distance = y" where x is replaced by the test case number (they are numbered from 1) and y is replaced by the appropriate real number, printed to three decimals. Put a blank line after each test case, even after the last one.

Sample Input

2
0 0
3 4

3
17 4
19 4
18 5

0

Sample Output

Scenario #1
Frog Distance = 5.000

Scenario #2

Frog Distance = 1.414

就是说公青蛙和母青蛙都在一棵树上时，求当前树上的最大边；最小生成树，最后用并查集思想过。

附ac代码：

   #include<stdio.h>
   #include<string.h>
   #include<algorithm>
   #include<math.h>
   using namespace std;
   int per[220000];
   struct node
   {
   	int start;
   	int end;
   	double dis;
   }t[200100];
   int cmp(node a,node b)
   {
   	return a.dis < b.dis ;
   }
   int find(int x)
   {
   	int r=x;
   	while(r!=per[r])
   	r=per[r];
   	return r;
   }
   int join(int x,int y)
   {
   	int fx=find(x);
   	int fy=find(y);
   	if(fx!=fy)
   	{
   		per[fx]=fy;
   		return 1;
   	 } 
   	 return 0;
   }
   int main()
   {
   	int i,n,j;
   	int flag=1;
   	double x[110000],y[110000];
   	while(scanf("%d",&n),n)
   	{
   		for(i=0;i<220000;i++)
   		per[i]=i;
   		for(i=1;i<=n;i++)
   		scanf("%lf%lf",&x[i],&y[i]);
   		int k=0;
   		for(i=1;i<=n;i++)
   		for(j=i+1;j<=n;j++)
   		{
   			t[k].start = i;
   			t[k].end = j;
   			t[k].dis =sqrt(((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]))*1.0);
   			k++;
   		}
   		sort(t,t+k,cmp);
   		double ans=0.0;
   		int a=0;
   		int b=0;
   		for(i=0;i<k;i++)
   		{
   			if(join(t[i].start,t[i].end))
   			{
   			/*if(ans<t[i].dis)
   			ans=t[i].dis;
   			if(x[t[i].start]==x[1]&&y[t[i].end]==y[1])
   			a=1;
   			if(x[t[i].start]==x[1]&&y[t[i].end]==y[1])
   			b=1;
   			if(a==1&&b==1)*/
			if(find(1)==find(2))//公青蛙和母青蛙，在同一颗树上， 
			{
			ans=t[i].dis;//按顺序加的边，当前边一定是所成树的最大边 
   			break;
   			}
   			}
   		}
   		printf("Scenario #%d\n",flag);
   		printf("Frog Distance = %.3f\n\n",ans);
   		flag++;
   	}
   	return 0;
   }