Goat Rope

Interview

Time limit2sMemory limit512 MB

Summary

Given a point outside an axis-aligned rectangle, print the minimum distance from the point to the rectangle's boundary.

Level: Medium4 of 10
Topics: Geometry, Math, Implementation
Solved: No attempts yet

Problem

You have a fence post at the point $(x, y)$ in the plane, and a goat is tethered to it by a rope. You also have a house, which you model as an axis-aligned rectangle with diagonally opposite corners at the points $(x_1, y_1)$ and $(x_2, y_2)$ . You want to choose a rope length that guarantees the goat cannot reach the house. Find the minimum distance from the post to the house, so that you can be sure to use a shorter rope.

Input

The input consists of a single line containing six space-separated integers $x$ , $y$ , $x_1$ , $y_1$ , $x_2$ , and $y_2$ , each in the range $[-999, 999]$ .

It is guaranteed that $x_1 < x_2$ and $y_1 < y_2$ , and that $(x, y)$ lies strictly outside the axis-aligned rectangle with corners at $(x_1, y_1)$ and $(x_2, y_2)$ .

Output

Print the minimum distance from the goat's post to the house, with a relative or absolute error of at most $0.001$ .

Examples5

Example 1
Input
```
7 3 0 0 5 4
```
Expected output
```
2.0
```
Example 2
Input
```
6 0 0 2 7 6
```
Expected output
```
2.0
```
Example 3
Input
```
3 -4 -3 -1 -1 2
```
Expected output
```
5.0
```
Example 4
Input
```
7 4 0 0 5 4
```
Expected output
```
2.000
```
Example 5
Input
```
4 8 7 8 9 9
```
Expected output
```
3.000
```