{"problem":{"name":"Silver Woods","description":{"content":"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 ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc181_f"},"statements":[{"statement_type":"Markdown","content":"On the $xy$\\-plane, we have a passage surrounded by the two lines $y=-100$ and $y=100$.\nIn the part of this passage with $-100 < x < 100$, there are $N$ negligibly small nails. The coordinates of the $i$\\-th nail are $(x_i, y_i)$.\nTakahashi will choose a real number $r \\ (0 < r \\leq 100)$ and put a circle of radius $r$ so that its center is at $(-10^9, 0)$.\nThen, he will move the circle from $(-10^9, 0)$ to $(10^9, 0)$.\nHere, he continuously moves the circle so that the boundaries of the passage or the nails do not penetrate the interior of the circle.\nFind the maximum possible value of $r$ such that it is possible to move the circle to $(10^9, 0)$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 100$\n*   $|x_i|, |y_i| < 100$\n*   If $i \\neq j$, $(x_i, y_i) \\neq (x_j, y_j)$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$x_1$ $y_1$\n$\\vdots$\n$x_N$ $y_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc181_f","tags":[],"sample_group":[["2\n0 -40\n0 40","40\n\n![image](https://img.atcoder.jp/ghi/493d8b75d6dd331fcc0f3949f12262b3.jpg)\nAs shown in the figure, we can move the circle with $r=40$ from $(-10^9, 0)$ to $(10^9, 0)$ by moving it along $y=0$.\nWhen $x=0$, the circle exactly touches the two nails, which is fine since they do not penetrate the interior of the circle.\nAny value of $r$ greater than $40$ makes it impossible to move the circle to $(10^9, 0)$, so the maximum possible value is $r=40$."],["4\n0 -10\n99 10\n0 91\n99 -91","50.5"],["10\n-90 40\n20 -30\n0 -90\n10 -70\n80 70\n-90 30\n-20 -80\n10 90\n50 30\n60 -70","33.541019662496845446"],["10\n65 -90\n-34 -2\n62 99\n42 -13\n47 -84\n84 87\n16 -78\n56 35\n90 8\n90 19","35.003571246374276203"]],"created_at":"2026-03-03 11:01:14"}}