1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <cmath>
  5 using namespace std;
  6 
  7 struct Point
  8 {
  9     double x,y;
 10 }h,p[3];
 11 
 12 double mins(double a,double b)
 13 {
 14     return a<b?a:b;
 15 }
 16 
 17 double dis(Point a, Point b)  ///两点之间的距离
 18 {
 19     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
 20 }
 21 
 22 double cale()
 23 {
 24     int a=0,b=1;
 25     double ret=dis(h,p[a])+dis(p[a],p[b])+dis(p[b],h);
 26     double ha,ab,bh;
 27     bool cx=0,cy=0;
 28     if(h.x*p[a].x<=0||h.x*p[b].x<=0||p[a].x*p[b].x<=0)
 29     cx=1;
 30     if(h.y*p[a].y<=0||h.y*p[b].y<=0||p[a].y*p[b].y<=0)
 31     cy=1;
 32     if(!cx&&!cy) ///三个点在同一个坐标系（看不懂后面的计算，需要自己画图理解）
 33     {
 34         Point t1,t2;
 35         t1.x=h.x;
 36         t1.y=-h.y;
 37         t2.x=-p[a].x;
 38         t2.y=p[a].y;
 39         ha=ret-dis(h,p[a])+dis(t1,t2);
 40 
 41         t1.x=p[b].x;
 42         t1.y=-p[b].y;
 43         t2.x=-p[a].x;
 44         t2.y=p[a].y;
 45         ab=ret-dis(p[a],p[b])+dis(t1,t2);
 46 
 47         t1.x=p[b].x;
 48         t1.y=-p[b].y;
 49         t2.x=-h.x;
 50         t2.y=h.y;
 51         bh=ret-dis(h,p[b])+dis(t1,t2);
 52 
 53         double ans=mins(ha,mins(ab,bh));
 54 
 55         t1.x=p[a].x;
 56         t1.y=-p[a].y;
 57         t2.x=-p[a].x;
 58         t2.y=p[a].y;
 59         ans=mins(ans,ret-dis(p[a],h)+dis(t1,h)-dis(p[a],p[b])+dis(t2,p[b]));
 60         ans=mins(ans,ret-dis(p[a],p[b])+dis(t1,p[b])-dis(p[a],h)+dis(t2,h));
 61 
 62         t1.x=h.x;
 63         t1.y=-h.y;
 64         t2.x=-h.x;
 65         t2.y=h.y;
 66         ans=mins(ans,ret-dis(p[a],h)+dis(t1,p[a])-dis(h,p[b])+dis(t2,p[b]));
 67         ans=mins(ans,ret-dis(h,p[b])+dis(t1,p[b])-dis(p[a],h)+dis(t2,p[a]));
 68 
 69         t1.x=p[b].x;
 70         t1.y=-p[b].y;
 71         t2.x=-p[b].x;
 72         t2.y=p[b].y;
 73         ans=mins(ans,ret-dis(p[a],p[b])+dis(t1,p[a])-dis(h,p[b])+dis(t2,h));
 74         ans=mins(ans,ret-dis(h,p[b])+dis(t1,h)-dis(p[a],p[b])+dis(t2,p[a]));
 75 
 76         ret=ans;
 77     }
 78     else if(cx==1&&!cy)
 79     {
 80         Point tmp;
 81         tmp.x=p[a].x;
 82         tmp.y=-p[a].y;
 83         ha=ret-dis(h,p[a])+dis(h,tmp);
 84         ab=ret-dis(p[a],p[b])+dis(tmp,p[b]);
 85 
 86         tmp.x=p[b].x;
 87         tmp.y=-p[b].y;
 88         bh=ret-dis(h,p[b])+dis(h,tmp);
 89 
 90         ret=mins(ha,mins(ab,bh));
 91     }
 92     else if(!cx&&cy==1)
 93     {
 94         Point tmp;
 95         tmp.x=-p[a].x;
 96         tmp.y=p[a].y;
 97         ha=ret-dis(h,p[a])+dis(h,tmp);
 98         ab=ret-dis(p[a],p[b])+dis(tmp,p[b]);
 99 
100         tmp.x=-p[b].x;
101         tmp.y=p[b].y;
102         bh=ret-dis(h,p[b])+dis(h,tmp);
103 
104         ret=mins(ha,mins(ab,bh));
105     }
106 
107     return ret;
108 }
109 
110 int main()
111 {
112     int T;
113     scanf("%d",&T);
114     while(T--)
115     {
116         scanf("%lf%lf%lf%lf%lf%lf",&p[0].x,&p[0].y,&p[1].x,&p[1].y,&h.x,&h.y);
117         printf("%.2lf\n",cale());
118     }
119     return 0;
120 }