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.

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 $(x_2, y_2)$.

Print the minimum distance from the goatâ€™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 |
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6 0 0 2 7 6 |
2.0 |

Sample Input 3 | Sample Output 3 |
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3 -4 -3 -1 -1 2 |
5.0 |