Flower

Time Limit: 8 Seconds
Memory Limit: 65536 KB
Special Judge

*Gao* and his girlfriend's relationship becomes better and better after
they flying balloon last week. Thus, *Gao* wants to play a simple but
evil game with his girlfriend at a late night.

The game is simple: there is a three-dimensional space, *Gao* chooses
`N` points to put flowers. For the point `i`, it has
`Fi` flowers. And his girlfriend has to move all these flowers to
**point 1** altogether. As everyone knows, his girlfriend is not
strong like *Gao*, so she can move flowers from one point to another if
and only if the Euclidean distance between two points are smaller or equal to
`R`. In another words, she perhaps has to move flowers to the
intermediate point for finally moving all flowers to the point one. In order
to stay with his girlfriend as much time as possible, he asks his girlfriend,
for the point `i`, that she can only move out no more than
`Li` flowers (including the points as an intermediate point).

Can you help his poor girlfriend to calculate the minimal `R`?

#### Input

There are multiple cases.

For each case, the first line contains an integer `N` (1 ≤
`N` ≤ 100), which means there are `N` points.

For the next `N` lines, each line contains five integers,
`Xi`, `Yi`, `Zi`, `Fi` and `Li`.
`Xi`, `Yi` and `Zi` are the coordinate of point
`i` (0 ≤ `Xi, Yi, Zi` ≤ 20000), `Fi` means
there are `Fi` flowers at the beginning. `Li` means this
point can be moved out no more than `Li` flowers.

#### Output

For each test case, it contains one real number indicating the minimal
`R`. The results should be rounded to seven decimal places. If there
is no solution for this case, please output -1. Output's absolute error less than 1e-6 will be accepted.

#### Sample Input

2
1 1 1 1 1
2 2 2 2 2

#### Sample Output

1.7320508

Author:

**REN, Qing**
Contest:

**ZOJ Monthly, March 2013**
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