A7835 | Tetragon

You're given the centers of three equal sides of a strictly convex tetragon. Your task is to restore the initial tetragon.

The first input line contains one number $T$ — amount of tests ( $1<=T<=5·10^{4}$ ). Each of the following $T$ lines contains numbers $x_{1}$ , $y_{1}$ , $x_{2}$ , $y_{2}$ , $x_{3}$ , $y_{3}$ — coordinates of different points that are the centers of three equal sides (non-negative integer numbers, not exceeding 10).

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.