1 #include <iostream>
 2 #include <string>
 3 #include <cstdio>
 4 #include <cstring>
 5 #include <algorithm>
 6 #include <climits>
 7 #include <cmath>
 8 #include <vector>
 9 #include <queue>
10 #include <stack>
11 #include <set>
12 #include <map>
13 using namespace std;
14 typedef long long           LL ;
15 typedef unsigned long long ULL ;
16 const int    maxn = 1e2 + 10   ;
17 const int    inf  = 0x3f3f3f3f ;
18 const int    npos = -1         ;
19 const int    mod  = 1e9 + 7    ;
20 const int    mxx  = 100 + 5    ;
21 const double eps  = 1e-6       ;
22 const double PI   = acos(-1.0) ;
23 
24 struct node{
25     double x, y;
26     node(double a=0LL, double b=0LL){
27         x=a; y=b;
28     }
29 };
30 node vex[maxn], center;
31 node CircumCenter(node a, node b, node c){
32     double a1=b.x-a.x, b1=b.y-a.y, c1=(a1*a1+b1*b1)/2;
33     double a2=c.x-a.x, b2=c.y-a.y, c2=(a2*a2+b2*b2)/2;
34     double d=a1*b2-a2*b1;
35     return node(a.x+(c1*b2-c2*b1)/d,a.y+(a1*c2-a2*c1)/d);
36 }
37 double dis2(node a, node b){
38     return pow(a.x-b.x,2)+pow(a.y-b.y,2);
39 }
40 bool oneLine(node a, node b, node c){
41     return ((b.y-a.y)/(b.x-a.x))==((c.y-a.y)/(c.x-a.x));
42 }
43 int T, n, ans;
44 double R, D[maxn][maxn];
45 int main(){
46     // freopen("in.txt","r",stdin);
47     // freopen("out.txt","w",stdout);
48     while(~scanf("%d",&T)){
49         while(T--){
50             ans=1;
51             scanf("%d",&n);
52             for(int i=1;i<=n;i++)
53                 scanf("%lf %lf",&vex[i].x,&vex[i].y);
54             
55             if(oneLine(vex[1],vex[2],vex[3]))
56                 ans=0;
57             
58             if(ans){
59                 center=CircumCenter(vex[1],vex[2],vex[3]);
60                 R=dis2(center,vex[1]);
61                 for(int i=1;i<=n;i++)
62                     if(dis2(vex[i],center)!=R){
63                         ans=0; break;
64                     }
65             }
66 
67             if(ans){
68                 for(int i=1;i<=n;i++){
69                     D[i][i]=0.0;
70                     for(int j=i+1;j<=n;j++)
71                         D[i][j]=D[j][i]=dis2(vex[i],vex[j]);
72                     sort(D[i]+1,D[i]+1+n);
73                 }
74                 for(int i=2;i<=n;i++)
75                     if(!(D[i][2]==D[i][3] && D[i][2]==D[i-1][2])){
76                         ans=0; break;
77                     }
78             }
79             puts(ans?"YES":"NO");
80         }
81     }
82     return 0;
83 }