CSES - HIIT Open 2016 - Light and mirrors
• Time limit: 2.00 s
• Memory limit: 256 MB

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: