Description

Given $n$ points on the Cartesian coordinate plane, find the distance between the two closest points and the distance between the two farthest points. Note that the distance is the straight-line (Euclidean) distance.

Input Format

The first line contains an integer $n$.
The next $n$ lines each contain two non-negative floating-point numbers, $x_i$ and $y_i$, representing the $x$-coordinate and $y$-coordinate of the $i$-th point.

Output Format

Output one line with two floating-point numbers: the shortest distance and the longest distance. An error of at most $0.01$ is considered correct.

4
0.0 0.0
0.0 1.0
1.0 0.0
1.0 1.0

1.00 1.41

Hint

• For $30\%$ of the testdata, $n \leq 2000$.
• For $70\%$ of the testdata, $n \leq 20000$.
• For $100\%$ of the testdata, $0 \lt n \leq 10^5$, and all numbers in the input are non-negative and do not exceed $10^9$ in value.

Translated by ChatGPT 5