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Time limit1sMemory limit128 MB

Summary

Given up to 10 points, find the diameter of the smallest enclosing circle.

Level: Medium5 of 10
Topics: Geometry, Brute force, Math, Implementation
Solved: No attempts yet

Problem

Making chocolate chip cookies starts by mixing flour, salt, oil, baking soda, and chocolate chips into a dough, which is then rolled out flat into a single plane. Circles are cut from this flattened dough, placed on a cookie sheet, and baked in an oven.

Here we care only about cutting a single round cookie that contains every chocolate chip. Once the dough is rolled out, each chip appears as a single point on the plane, so we simply need a round cookie cutter large enough to enclose all of the chips. What is the diameter of the smallest round cookie that contains all of the chips?

Input

The first line contains a positive integer $n$ with $n \le 10$ . Each of the next $n$ lines gives the coordinates of one chocolate chip on the plane. Each coordinate is an integer in the range $[0, 1000]$ .

Output

Print a single real number: the diameter of the smallest round cookie that contains all of the chips, rounded to two decimal places.

Examples2

Example 1
Input
```
4
1 1
1 0
0 1
0 0
```
Expected output
```
1.41
```
Example 2
Input
```
3
1 1
10 0
0 0
```
Expected output
```
10.00
```