El Judge

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Time limit = 5 seconds

Petya have found himself standing in a minefield in a pointHe knows all mines positions but he would like his way (smooth curve) lies as far from mines as possible.

Please, help him. Write a program that finds maximal *R* for witch
the following condition is satisfied:
there is smooth curve from *A* to *B* witch stay away from all mines
more (or equal to) than distance *R.*

**Input**
Line 1: Coordinates of the point *A*.

Line 2: Coordinates of the point *B*.

Line 3: *M* — number of mines. 1 ≤ *M* ≤ 30.

Lines 4, *...*,M+3 : Coordinates of mines.

All coordinates are real numbers less than 100000 and greater than -100000

**Output**
Line 1: *R.* Two or more digits after point.

Input#10 0 3 3 2 1 1 2 2 |
Output#11.41 |

Input#2-10 0 0 0 4 1 1 1 -1 -1 1 -1 -1 |
Output#21.00 |

**Author:
Voroztsov Artem
**

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