Tetragon

Description:

Input:

The first input line contains one number T — amount of tests (1 ≤ T ≤ 5·10⁴). Each of the following T lines contains numbers x₁, y₁, x₂, y₂, x₃, y₃ — coordinates of different points that are the centers of three equal sides (non-negative integer numbers, not exceeding 10).

Output:

For each test output two lines. If the required tetragon exists, output in the first line YES, in the second line — four pairs of numbers — coordinates of the polygon's vertices in clockwise or counter-clockwise order. Don't forget, please, that the tetragon should be strictly convex, i.e. no 3 of its points lie on one line. Output numbers with 9 characters after a decimal point.

If the required tetragon doen't exist, output NO in the first line, and leave the second line empty.

Sample Input:

3
1 1 2 2 3 3
0 1 1 0 2 2
9 3 7 9 9 8

Sample Output:

NO

YES
3.5 1.5 0.5 2.5 -0.5 -0.5 2.5 0.5
NO