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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

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