To accommodate his cows, Farmer Bob is planning to build a new pasture, which will be circular and centered at point . To ensure that the cows have enough food to eat, the pasture must contain at least patches of grass (each patch is either on the edge or completely inside the pasture). Luckily, Farmer Bob knows the location of patches of grass, each of which being located at point . Can you determine the smallest possible radius of the pasture that satisfies the constraints?
Constraints
For all subtasks:
Points Awarded | Additional Constraints |
---|---|
5 points | |
10 points | No further constraints |
Input Specification
The first line of input contains four integers , , and .
The next lines each contain two integers and , the coordinates of the patch of grass.
Output Specification
Output the smallest possible radius of the pasture. Your answer will be considered correct if it is within (8 decimal places) of the correct answer.
Sample Input
1 -1 6 6
2 5
-3 -3
3 0
3 0
-2 2
1 -1
Sample Output
6.08276253
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