# Problem B: Random Walk

**Input**: `randomwalk.in`

**Output**: `randomwalk.out`

Random walks are used to model a wide range of phenomena, from
Brownian motion to gambling. For example, a gambler who bets on heads
or tails on a coin toss wins or loses his bet each turn. The amount
of money the gambler has throughout the game is a random walk.
Although the bets in each turn may be different, it is easy to see
that the gambler wins the maximum amount of money if he
wins every turn. Similarly, he loses the maximum amount if he loses
every turn.

We consider the following two-dimensional variation of the random
walk. We are given *n* two-dimensional nonzero vectors
*v*_{i} = (x_{i}, y_{i}), no two of
which are parallel. In step *i*, a coin is flipped. If it is
heads, we move *x*_{i} meters in the *x*
direction and *y*_{i} meters in the *y*
direction. If it is tails, we move *-x*_{i} and
*-y*_{i} meters in the *x* and *y*
directions.

We are interested in computing the maximum distance we can be away
from our starting point. This is easy in one-dimension, but it is
not so easy in the two-dimensional version.

## Input

The input consists of a number of test cases. Each test case starts
with a line containing the integer *n*, which is at most 100.
Each of the next *n* lines gives a pair of integers
*x*_{i} and *y*_{i} specifying
*v*_{i}. The coordinates are less than 1000 in
magnitude. The end of input is specified by *n* = 0.

## Output

For each test case, print on a line the maximum distance we can be
away from the starting point, in the format shown below. Output the
answer to 3 decimal places.

## Sample input

3
1 1
0 1
-1 1
2
4 0
1 1
7
1 3
-2 -7
7 8
-2 9
-7 -3
4 -3
-2 -2
0

## Output for sample input

Maximum distance = 3.000 meters.
Maximum distance = 5.099 meters.
Maximum distance = 37.336 meters.