34786번 - Fractal Painting 다국어

A fractal painting consists of an infinite number of line segments. The first segment, called A, connects points $(0, 0)$ and $(x_0, y_0)$.

The next two segments B and C connect $(x_0, y_0)$ to $(x_1, y_1)$ and $(x_0, y_0)$ to $(x_2, y_2)$, respectively.

The rest of the painting is defined recursively. We draw two segments D and E from $(x_1, y_1)$ so that the segments B, D, E are similar to the segments A, B, C. Here, similar segments mean that they can be matched point-to-point by performing translating, rotating, and scaling on the original segments.

Similarly, we draw segments F and G from $(x_2, y_2)$ so that the segments C, F, G are similar to the segments A, B, C.

This procedure continues indefinitely.

Find out whether it is possible to find a rectangle (of any size) that contains the entire fractal painting.

The first line of input contains a single integer $T$ $(1 \le T \le 10^4)$, representing the number of test cases. Each of the next $T$ lines describes a single test case. Each test case consists of a single line with six integers $x_0$, $y_0$, $x_1$, $y_1$, $x_2$, and $y_2$ in order. All coordinates are between $-10^4$ and $10^4$, inclusive. It is guaranteed that $(0, 0)$, $(x_0, y_0)$, $(x_1, y_1)$, and $(x_2, y_2)$ are all distinct points.

For every test case, output YES if the entire fractal painting can fit in some rectangular frame. Output NO if there is no such rectangle.