26470번 - Most distant point from the stations 스페셜 저지다국어

문제

JAG-island is a rectangular island on the $xy$-plane. The 4 coastlines of JAG-island are parallel to the $x$-axis or the $y$-axis. The left-bottom and right-top corners of JAG-island are located at $(0,0)$ and $(W,H),ドル respectively.

There are $N$ stations in JAG-island. The $i$-th station is located in $(x_i, y_i)$. You are interested in the coordinates that maximize the (Euclidean) distance to the nearest station. Find the distance from such a coordinate to its nearest station. In other words, calculate the value of $$\max_{0 ≤ x ≤ W,0円 ≤ y ≤ H}\min_{i}\sqrt{\left(x-x_i\right)^2 + \left(y-y_i\right)^2}\text{.}$$

입력

$N$ $W$ $H$

$x_1$ $y_1$

$\vdots$

$x_N$ $y_N$

The first line of the input consists of three integers, the number $N$ (1ドル ≤ N ≤ 2,000円$) of stations, the width $W$ and the height $H$ (1ドル ≤ W, H ≤ 1,000円$) of JAG-island.

The $i$-th of the following $N$ lines has two integers $x_i$ and $y_i$ (0ドル ≤ x_i ≤ W,ドル 0ドル ≤ y_i ≤ H$), which represent the coordinate of the $i$-th station. The coordinates of stations are distinct, i.e. $(x_i, y_i) \ne (x_j, y_j)$ for any $i,ドル $j$ ($i \ne j$).

출력

Print the answer in a line. Absolute or relative errors less than 10ドル^{-6}$ are permissible.

제한

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