A10508 | Beru-taxi

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.

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.

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 .