Rotation Transformation

A simple motion over and over...

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t.A.T.u., <<A Simple Motion>>

Julia loves simple motions very much especially in three-dimensional space! Recently she found a matrix that corresponds with some rotation around an axis that goes through the origin. Rotation is defined by unit vector $v = \begin{pmatrix} v\_x \\\ v\_y \\\ v\_z \end{pmatrix}$ and rotation angle $\alpha$.

Suppose you look at the origin from the end of $v$ then if rotation is going counter-clockwise then $\alpha$ will be positive, negative overwise.

Rotation matrix moves point $\begin{pmatrix} x \\\ y \\\ z \end{pmatrix}$ to $\begin{pmatrix} x' \\\ y' \\\ z' \end{pmatrix}$ like this: $\begin{pmatrix} x' \\\ y' \\\ z' \end{pmatrix} = \begin{pmatrix} A\_{11} & A\_{12} & A\_{13} \\\ A\_{21} & A\_{22} & A\_{23} \\\ A\_{31} & A\_{32} & A\_{33} \\\ \end{pmatrix} \times \begin{pmatrix} x \\\ y \\\ z \end{pmatrix}.$

Unfortunately Julia doesn't know values of $v$ and $\alpha$, so she asked you to restore them and then she will continue her simple motion.

You are given matrix $A$. It is guaranteed that there is such rotation matrix $A'$ that $|A'\_{ij} - A\_{ij}| < 10^{-13}$.

First line should contain $\alpha$ in degrees. Second line should contain coordinates of unit vector $v$. It is guaranteed that $1 \le |\alpha| \le 179$. Output all number as precise as you can. Your answer will be considered correct if the difference between $A\_{ij}$ and the matrix constructed from your angle and unit vector will not exceed $10^{-6}$.