Yet Another Point Searching Problem

You are given $n$ points on the plane: $A\_1, A\_2, \cdots, A\_n$. Point $i$ has weight $w\_i$. Find such point $B$ that the maximum weighted distance $\max\limits\_{i=1}^{n}{w\_i \cdot |A\_{i}B|}$ is minimal possible.

The input consists of one or more test cases.

On the first line of each test case, there is an integer $n$: the number of points ($1 \le n \le 500\\,000$). Each of the next $n$ lines contains three integers: $x\_i$, $y\_i$ and $w\_i$. Each of these numbers does not exceed $10^7$ by absolute value. All weights are strictly positive.

The test cases follow one another without any gaps. The input is terminated by a line containing a single integer $0$. This line must not be considered a test case. The sum of all $n$ in the input does not exceed $500\\,000$. There are no more than $1000$ test cases in the input.

For each test case, print two real numbers: the coordinates of point $B$. Your answer will be considered correct if the absolute or relative error of the maximum weighted distance will be less than $10^{-9}$.