Problem Statement

Taro and Jiro are talking to each other using radios.

The radios the two are using communicate directly with each other by radio waves,
and allow them to talk at distances of up to \(1km\).
Apart from this, the communication distance can also be extended by placing \(1\) or more relay stations in between.

A radio and a relay station can communicate only within \(1km\),
whereas two relay stations can communicate within \(10km\).
(These include exactly \(1km\) and exactly \(10km\), respectively.)

There are \(N\) relay stations standing on a 2-dimensional plane,
and their positions are given 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 distance (Euclidean distance) between Taro and Jiro at which they can talk
either "directly" or "indirectly using 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 \(N\ (0 \leq N \leq 1000)\), the number of relay stations.
Each of the following \(N\) lines contains a pair of integers \(X_i,Y_i\ (-1000 \leq X_i,Y_i \leq 1000, 1 \leq i \leq N)\) 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.
Your 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

0

1