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Mine field

Time limit = 5 seconds

Petya have found himself standing in a minefield in a point A. He needs to go to a point B.

He 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#1
0 0
3 3
2
1 1
2 2
Output#1
1.41

Input#2
-10 0
0 0
4
1 1
1 -1
-1 1
-1 -1
Output#2
1.00

Author:
Voroztsov Artem
4 October 2003

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