Rotation Transformation

Julia loves simple motions very much, especially in three-dimensional space. Recently she found a matrix that corresponds to a rotation around an axis through the origin. The rotation is defined by a unit vector $v = \begin{pmatrix} v_x \\ v_y \\ v_z \end{pmatrix}$ and a rotation angle $\alpha$.

Look at the origin from the end of $v$. If the rotation is counter-clockwise, then $\alpha$ is positive. Otherwise, $\alpha$ is negative.

The rotation matrix moves a point $\begin{pmatrix} x \\ y \\ z \end{pmatrix}$ to $\begin{pmatrix} x' \\ y' \\ z' \end{pmatrix}$ as follows.

Julia does not know the values of $v$ and $\alpha$. She asks you to recover them so she can continue her simple motion.

You are given the matrix $A$. It is guaranteed that there is a rotation matrix $A'$ with $|A'_{ij} - A_{ij}| < 10^{-13}$ for all $i$ and $j$.

On the first line, print the angle $\alpha$ in degrees. On the second line, print the coordinates of the unit vector $v$. It is guaranteed that $1 \le |\alpha| \le 179$. Print every number as precisely as you can. Your answer is accepted if the difference between each $A_{ij}$ and the matrix built from your angle and unit vector does not exceed $10^{-6}$.