Problem Statement

Taro and Jiro are talking to each other using radios.

The radios they use communicate directly with each other by radio waves,
and they can talk at distances of up to \(1km\).
In addition, the communication distance can be extended by placing \(1\) or more relay stations between them.

Communication between a radio and a relay station is possible only within \(1km\),
while communication between two relay stations is possible within \(10km\).
(These include exactly \(1km\) and exactly \(10km\), respectively.)

\(N\) relay stations stand on a 2-dimensional plane,
and their positions are represented by \(X_i,Y_i\ (1 \leq i \leq N)\).

Taro and Jiro can freely use all of these relay stations,
and they can move freely on the 2-dimensional plane carrying their radios. Under these conditions,
find the maximum straight-line (Euclidean) distance between Taro and Jiro
at which they can talk, either "directly" or "indirectly through relay stations".

Input

\(N\)
\(X_1\ Y_1\)
\(X_2\ Y_2\)
\(\dots\)
\(X_i\ Y_i\)
\(\dots\)
\(X_N\ Y_N\)

Line \(1\) contains an integer \(N\ (0 \leq N \leq 120000)\), the number of relay stations.
Each of the following \(N\) lines contains a pair of integers \(X_i,Y_i\ (-10000 \leq X_i,Y_i \leq 10000, 1 \leq i \leq N)\) separated by a space, representing the position of each relay station. (Unit: \([km]\))
No two relay stations exist at the same coordinates.
That is, if $i \neq j $, then $(X_i,Y_i) \neq (X_j,Y_j)$.

Output

Output the maximum straight-line distance at which Taro and Jiro can talk.
The answer is accepted if at least one of the absolute error or the relative error is at most \(10^{−6}\).
Print a newline at the end.

Sample

2
3 3
12 1

11.219544457

2
-5 -1
3 6

2

5
-8 7
-5 -1
3 5
9 -3
16 4

26.186773244