Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Tetragon

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

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

Input

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).

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.

Examples

Input

3

1 1 2 2 3 3

0 1 1 0 2 2

9 3 7 9 9 8

Output

NO

YES

3.5 1.5 0.5 2.5 -0.5 -0.5 2.5 0.5

NO

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/25/2017 05:08:09 (c2).

Desktop version, switch to mobile version.

User lists

Name |
---|