Mid-Central USA Programming Contest 2018

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2018-11-03 17:30 UTC

Mid-Central USA Programming Contest 2018

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2018-11-03 22:30 UTC
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Problem F
Goat Rope

You have a fence post located at the point $(x, y)$ in the plane, to which a goat is tethered 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 pick a length of rope that guarantees the goat cannot reach the house.

Determine the minimum distance from the fence post to the house, so that you can make 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 $(x, y)$ is 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 no more than $0.001$.

Sample Input 1 Sample Output 1
7 3 0 0 5 4
2.0
Sample Input 2 Sample Output 2
6 0 0 2 7 6
2.0
Sample Input 3 Sample Output 3
3 -4 -3 -1 -1 2
5.0