I. Neuvillette Circling
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are a traveler and one day you're traveling on the Tivat mainland. When you are at Fontaine, you find that there are $$$N$$$ treasures and there are paths between each pair of them. Each path has a Hilichurl who may appear at any point along the path. If you want to get the treasure, you must kill them. But Hilichurls are too strong to kill by yourself. So you call Neuvillette to kill them.

As we all know, Neuvillette can circle as a particular standing point and radius. Every Hilichurl standing on or within the circle will be killed.

Now, Neuvillette can choose any standing point. But he wants to minimize the radius, so that no matter where the Hilichurls are, he can select a starting point to eliminate at least $$$m$$$ Hilichurls.

Please tell Neuvillette the minimum radius he circling when $$$m=1,2,3,...,\frac{n(n-1)}{2}$$$.

Input

The first line contains an integer $$$n$$$ $$$(2\leq n\leq 100)$$$, representing the number of treasures.

The following $$$n$$$ lines, each contain two integers $$$x_{i}, y_{i}$$$ $$$(-10^3 \leq x_{i},y_{i}\leq 10^3,1\leq i\leq n)$$$, representing the coordinates of $$$i$$$-th treasures. It's guaranteed that there are no two treasures with the same coordinate or three treasures lying on one line.

Output

Output $$$\frac{n(n-1)}{2}$$$ lines with one integer. The output of $$$i$$$-th line represents the minimum radius Neuvillette circling to eliminate at least $$$i$$$ Hilichurls.

Your answer is considered correct if its absolute or relative difference to the correct answer is at most $$$10^{-6}$$$.

More formally, let $$$a$$$ be your answer and $$$b$$$ be the correct answer. Your output is considered correct if $$$\frac{\left|a-b\right|}{\max(1,b)} \le 10^{-6}$$$.

Example
Input
5
-6 -9
2 4
9 2
1 -1
-4 -5
Output
2.23606798
4.28602124
4.28602124
7.38241153
7.38241153
7.38241153
9.30053762
9.30053762
9.30053762
9.30053762
Note

This picture shows some circles you choose to eliminate Hilichurls.