C. Cube
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given eight points in three-dimensional space, please check if they can form a cube.

A cube is a regular hexahedron, bounded by six square faces, with three meeting at each vertex.

Input

The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 100$$$), denoting the number of test cases.

For each test case, each of the following eight lines containing three integers $$$x,y,z$$$ ($$$-100 \leq x,y,z \leq 100$$$), denoting the coordinates of the eight points, respectively.

Output

For each test case, output a single line "YES" if the points can form a cube, or "NO" if they don't.

Example
Input
3
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
-4 -6 -2
5 9 10
12 -11 11
-9 4 8
-2 -16 9
7 -1 21
-7 -6 19
10 -1 0
0 0 0
2 2 1
0 0 1
0 2 0
2 0 0
0 2 1
2 0 1
2 2 0
Output
NO
YES
NO