There are a light source, a target point and five mirrors on a two-dimensional plane. Your task is to find out whether a ray that originates from the light source can reach the target point through exactly $0,1,\ldots,5$ reflections.
The light source sends rays to all directions. All mirrors are double-sided, i.e., a ray will reflect from both sides of the mirror.
Input
The first input line contains an integer $t$: the number of test cases. After this, the test cases are described as follows:
First there are two lines that specify the locations of the light source and the target point. Both lines contain two integers $x$ and $y$, meaning that the location of the point is $(x,y)$.
Finally, there are five lines that specify the locations of the mirrors. Each line contains four integers $x_1$, $y_1$, $x_2$ and $y_2$, meaning that a there is a mirror between points $(x_1,y_1)$ and $(x_2,y_2)$.
Output
For each test case, output a binary string $x_0x_1\ldots x_5$ where $x_i$ is $1$ if light reaches the target through $i$ reflections.
Constraints
- $1 \le t \le 10$
- all input coordinates are between $0 \ldots 10^9$
- the result does not change if the input coordinates are changed by at most one
- no three input points are collinear
- no mirrors intersect
Example
Input:
1
209000000 760000000
566000000 303000000
317000000 661000000 388000000 682000000
533000000 116000000 464000000 126000000
523000000 829000000 350000000 830000000
808000000 928000000 837000000 903000000
455000000 626000000 395000000 650000000
Output:
101010
The following figures show the setting in the example, and the areas that are reachable through $0,1,\ldots,5$ reflections: