Beru-taxi

题意翻译

**题意翻译** **题目描述** Vasiliy在点（a，b），他周围有n辆出租车，坐标在点（x，y），速度是v，假设Vasiliy已经知道了他最早能坐上哪辆出租车，请你求出他最早能坐上出租车的时间（出租车将直线朝Vasiliy行驶）。 **输入输出格式** **输入格式：** 第一行三个整数分别是Vasiliy的坐标a，b和出租车的数量n。 第二行到第n + 1行，每行有三个整数，分别是每辆出租车的坐标x，y和每辆出租车的速度v。 **输出格式：** 第一行一个浮点数，是Vasiliy最早能坐上出租车的时间，保留20位小数。

题目描述

Vasiliy lives at point $ (a,b) $ of the coordinate plane. He is hurrying up to work so he wants to get out of his house as soon as possible. New app suggested $ n $ available Beru-taxi nearby. The $ i $ -th taxi is located at point $ (x_{i},y_{i}) $ and moves with a speed $ v_{i} $ . Consider that each of $ n $ drivers will move directly to Vasiliy and with a maximum possible speed. Compute the minimum time when Vasiliy will get in any of Beru-taxi cars.

输入输出格式

输入格式

The first line of the input contains two integers $ a $ and $ b $ ( $ -100<=a,b<=100 $ ) — coordinates of Vasiliy's home. The second line contains a single integer $ n $ ( $ 1<=n<=1000 $ ) — the number of available Beru-taxi cars nearby. The $ i $ -th of the following $ n $ lines contains three integers $ x_{i} $ , $ y_{i} $ and $ v_{i} $ ( $ -100<=x_{i},y_{i}<=100 $ , $ 1<=v_{i}<=100 $ ) — the coordinates of the $ i $ -th car and its speed. It's allowed that several cars are located at the same point. Also, cars may be located at exactly the same point where Vasiliy lives.

输出格式

Print a single real value — the minimum time Vasiliy needs to get in any of the Beru-taxi cars. You answer will be considered correct if its absolute or relative error does not exceed $ 10^{-6} $ . Namely: let's assume that your answer is $ a $ , and the answer of the jury is $ b $ . The checker program will consider your answer correct, if .

输入输出样例

输入样例 #1

0 0
2
2 0 1
0 2 2

输出样例 #1

1.00000000000000000000

输入样例 #2

1 3
3
3 3 2
-2 3 6
-2 7 10

输出样例 #2

0.50000000000000000000

说明

In the first sample, first taxi will get to Vasiliy in time $ 2 $ , and second will do this in time $ 1 $ , therefore $ 1 $ is the answer. In the second sample, cars $ 2 $ and $ 3 $ will arrive simultaneously.