K. Kernel of the Disks
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a point $$$P$$$ and $$$n$$$ closed disks on the plane.

Disk $$$i$$$ is centered at $$$(x_i, y_i)$$$ and has radius $$$r_i$$$. It contains all points $$$(x, y)$$$ such that $$$$$$ (x - x_i)^2 + (y - y_i)^2 \le r_i^2. $$$$$$

It is guaranteed that the intersection of all $$$n$$$ disks is non-empty.

Find the minimum possible Euclidean distance from $$$P$$$ to a point that belongs to all disks.

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 500$$$).

The second line contains two integers $$$p_x$$$ and $$$p_y$$$ ($$$-1'000'000 \le p_x, p_y \le 1'000'000$$$), the coordinates of $$$P$$$.

Each of the next $$$n$$$ lines contains three integers $$$x_i$$$, $$$y_i$$$, $$$r_i$$$ ($$$-1'000'000 \le x_i, y_i \le 1'000'000$$$, $$$1 \le r_i \le 1'000'000$$$).

Output

Print one real number: the minimum distance from $$$P$$$ to the intersection of all disks.

Your answer will be considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.

Example
Input
3
-3 -4
1 0 1
0 1 1
0 0 10
Output
5.000000000000000
Note

The first two disks intersect in a lens whose boundary passes through $$$(0, 0)$$$ and $$$(1, 1)$$$. The third disk contains that whole lens.

The closest point in the common intersection to $$$P = (-3, -4)$$$ is $$$(0, 0)$$$, so the answer is $$$5$$$.