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

1. the coordinates of points $A$, $B$, $C$, and $D$ are integers;
2. $0 \le A_x, B_x, C_x, D_x \le X$ and $0 \le A_y, B_y, C_y, D_y \le Y$;
3. the length of segment $AB$ is at least $K$;
4. the length of segment $CD$ is at least $K$;
5. 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.

见题面 Input 部分

见题面 Output 部分

The answer for the first test case is shown below: