31330번 - Yet Another Point Searching Problem 스페셜 저지다국어

문제

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.

입력

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ドル \le n \le 500,000円$). Each of the next $n$ lines contains three integers: $x_i,ドル $y_i$ and $w_i$. Each of these numbers does not exceed 10ドル^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ドル$. This line must not be considered a test case. The sum of all $n$ in the input does not exceed 500ドル,000円$. There are no more than 1000ドル$ test cases in the input.

출력

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ドル^{-9}$.

제한

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