You are given a coordinate plane and three integers $$$X$$$, $$$Y$$$, and $$$K$$$. Find two line segments $$$AB$$$ and $$$CD$$$ such that

the coordinates of points $$$A$$$, $$$B$$$, $$$C$$$, and $$$D$$$ are integers;
$$$0 \le A_x, B_x, C_x, D_x \le X$$$ and $$$0 \le A_y, B_y, C_y, D_y \le Y$$$;
the length of segment $$$AB$$$ is at least $$$K$$$;
the length of segment $$$CD$$$ is at least $$$K$$$;
segments $$$AB$$$ and $$$CD$$$ are perpendicular: if you draw lines that contain $$$AB$$$ and $$$CD$$$, they will cross at a right angle.

Note that it's not necessary for segments to intersect. Segments are perpendicular as long as the lines they induce are perpendicular.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 5000$$$) — the number of test cases. Next, $$$t$$$ cases follow.

The first and only line of each test case contains three integers $$$X$$$, $$$Y$$$, and $$$K$$$ ($$$1 \le X, Y \le 1000$$$; $$$1 \le K \le 1414$$$).

Additional constraint on the input: the values of $$$X$$$, $$$Y$$$, and $$$K$$$ are chosen in such a way that the answer exists.

Output

For each test case, print two lines. The first line should contain $$$4$$$ integers $$$A_x$$$, $$$A_y$$$, $$$B_x$$$, and $$$B_y$$$ — the coordinates of the first segment.

The second line should also contain $$$4$$$ integers $$$C_x$$$, $$$C_y$$$, $$$D_x$$$, and $$$D_y$$$ — the coordinates of the second segment.

If there are multiple answers, print any of them.

Note

The answer for the first test case is shown below:

$\text{[math]}$ The answer for the second test case: $\text{[math]}$ The answer for the third test case: $\text{[math]}$ The answer for the fourth test case: $\text{[math]}$

Perpendicular Segments

Examples