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B - Longest Segment

Score : $200$ points

Problem Statement

There are $N$ points in a two-dimensional plane. The coordinates of the $i$-th point are $(x_i,y_i)$.

Find the maximum length of a segment connecting two of these points.

Constraints

• $2 \leq N \leq 100$
• $-1000 \leq x_i,y_i \leq 1000$
• $(x_i,y_i) \neq (x_j,y_j)\ (i \neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$x_2$ $y_2$

$\hspace{0.4cm} \vdots$

$x_N$ $y_N$

Output

Print the maximum length of a segment connecting two of the points.

Your answer will be considered correct when the absolute or relative error from the judge's answer is at most $10^{-6}$.

3
0 0
0 1
1 1

1.4142135624

For the $1$-st and $3$-rd points, the length of the segment connecting them is $\sqrt 2 = 1.41421356237\dots$, which is the maximum length.

5
315 271
-2 -621
-205 -511
-952 482
165 463

1455.7159750446