P9125 [USACO23FEB] Cow-libi S

注意：本题的时间限制为 4 秒，是默认限制的两倍。 有人在 Farmer John 的 $G(1 \leq G \leq 10^5)$ 个私人花园里偷吃了庄稼！通过他的专业法医知识，Farmer John 确定了每个花园被偷吃的具体时间。他还发现，这些事件的罪魁祸首是一头单独的奶牛。 为了回应这些犯罪行为，Farmer John 的 $N(1 \leq N \leq 10^5)$ 头奶牛每头都提供了一个不在作案现场的证明（即“不在场证明”），表明奶牛在特定时间出现在特定位置。请帮助 Farmer John 判断这些“不在场证明”中哪些能够证明奶牛的清白。 如果一头奶牛无法在她的“不在场证明”位置与所有被偷吃地点之间往返，则可以确定这头奶牛是清白的。奶牛的移动速度为每单位时间 $1$ 单位距离。本题中提到的距离均为欧几里得距离。

无

无

### Explanation for Sample 1 There were two grazings; the first at $(0,0)$ at time 100 and the second at $(50,0)$ at time $200$. The first cow's alibi does not prove her innocence. She has just enough time to arrive at the first grazing. The second cow's alibi does prove her innocence. She is nowhere near any of the grazings. Unfortunately for the third cow, being at the scene of the crime does not prove innocence. Finally, the fourth cow is innocent because it's impossible to make it from her alibi to the final grazing in time. ### SCORING - Inputs $2-4$: $1 \le G,N \le 10^3$. Also, for both the fields and alibis, $−10^6 \le x,y \le 10^6$ and $0 \le t \le 10^6$. - Inputs $5-11$: No additional constraints.