## Problem B: Translation or rotation

A line segment is given in the plane by its endpoints
`a` = (`a`_{x},
`a`_{y}) and
`b` = (`b`_{x},
`b`_{y}), where `a` is not equal to `b`.
The segment has been moved either by a
counterclockwise rotation around some point or by a translation and
the final coordinates of its endpoints are known
`a'` = (`a'`_{x},
`a'`_{y}) and
`b'` = (`b'`_{x},
`b'`_{y}), where endpoint `a'` corresponds to the
original endpoint `a`, and `b'` to `b`.
Your task is to decide whether the segment
was rotated or translated and to report your findings.

Your program should read input from file named `moves.dat`.
Each line of this file contains 8 floating point numbers, separated by
spaces and giving the values of `a`_{x},
`a`_{y}, `a'`_{x},
`a'`_{y}, `b`_{x},
`b`_{y}, `b'`_{x},
`b'`_{y}. A line containing 8 zeros terminates the
input and should not be processed.

For each line of input produce one line of output in the format given
in the sample, where floating point numbers are printed to 3 digits of
the fractional part. The reported angle of rotation should be nonnegative
and smaller than 360. In your computations, two floating point numbers
differing by less than 10e^{-8} should be considered equal.
Note that when the segment has not changed its position then report
`No move.`

### Sample input

0 2 1 3 2 0 3 1
0 2 2 0 1 3 3 1
2.1 0 0 2.1 3 1 -1 3
2.1 0 2.9238080804 0.7366059011 0 2.1 -0.0347392304 0.9954452513
5 1 2 -2 10 1 2 -7
1 17 1 17 -14 -14 -14 -14
0 0 0 0 0 0 0 0

### Output for sample input

Translation by vector <1.000,1.000>.
Translation by vector <2.000,-2.000>.
Rotation around (0.000,0.000) by 90.000 degrees counterclockwise.
Rotation around (1.500,1.500) by 40.000 degrees counterclockwise.
Rotation around (2.000,1.000) by 270.000 degrees counterclockwise.
No move.

*P. Rudnicki*