Problem Statement

On the xy-plane, we have a passage surrounded by the two lines y=-100 and y=100.
In the part of this passage with -100 < x < 100, there are N negligibly small nails. The coordinates of the i-th nail are (x_i, y_i).
Takahashi will choose a real number r \ $(0 < r \leq 100)$ and put a circle of radius r so that its center is at (-10^9, 0).
Then, he will move the circle from (-10^9, 0) to (10^9, 0).
Here, he continuously moves the circle so that the boundaries of the passage or the nails do not penetrate the interior of the circle.
Find the maximum possible value of r such that it is possible to move the circle to (10^9, 0).

Input

Input is given from Standard Input in the following format:
N
x_1 y_1
$\vdots$
x_N y_N

Output

Print the maximum possible value of r such that it is possible to move the circle to (10^9, 0).
Your output will be considered correct when its absolute or relative error from our answer is at most 10^{-4}.

Constraints

• All values in input are integers.
• $1 \leq N \leq 100$
• |x_i|, |y_i| < 100
• If $i \neq j, (x_i, y_i) \neq (x_j, y_j)$.

Sample Input 1

2
0 -40
0 40

Sample Output 1

40

As shown in the figure, we can move the circle with r=40 from (-10^9, 0) to (10^9, 0) by moving it along y=0.
When x=0, the circle exactly touches the two nails, which is fine since they do not penetrate the interior of the circle.
Any value of r greater than 40 makes it impossible to move the circle to (10^9, 0), so the maximum possible value is r=40.

Sample Input 2

4
0 -10
99 10
0 91
99 -91

Sample Output 2

50.5

Sample Input 3

10
-90 40
20 -30
0 -90
10 -70
80 70
-90 30
-20 -80
10 90
50 30
60 -70

Sample Output 3

33.541019662496845446

Sample Input 4

10
65 -90
-34 -2
62 99
42 -13
47 -84
84 87
16 -78
56 35
90 8
90 19

Sample Output 4

35.003571246374276203

见题面 Input 部分

见题面 Output 部分