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.

Input

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.

Output

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 .

Note

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.