Final Defense Line

In a country that has been frequently invaded by unidentified creatures, it has decided to protect important facilities with new defense weapons. This weapon can damage unidentified creatures by filling a polygonal area with a special gas. If the concentration of gas changes during the invasion of an unidentified creature, it will cause damage with the absolute value of the difference in concentration. No damage occurs when the gas concentration is moving in the same area. With current technology, the concentration of gas can only be kept constant, so a certain country decided to introduce multiple new defense weapons. The concentration of gas is the same for all weapons, and the concentrations of the parts contained in the territory of multiple weapons are added together. Based on the appearance point of unidentified creatures and the location of important facilities, please find the minimum value of damage that unidentified creatures will invade to important facilities. However, the invasion route of unidentified organisms shall not include the vertices of polygons and intersections with other polygons. Also, it does not invade along the sides of the polygon.

Constraints

• The coordinates included in the input are integers with an absolute value of 1,000 or less.
• The number of polygons is 1 or more and 5 or less
• The number of vertices of a polygon is 3 or more and 5 or less
• The number of data of appearance points and important facilities is 1 or more and 100 or less
• A polygon refers to a polygon formed by connecting given vertices in order, and there is no self-intersection.
• Spawn points and important facilities are never on the vertices and sides of a polygon

Input

The input is given in the following format.

Number of polygons Number of vertices of polygon x coordinate y coordinate x coordinate y coordinate ... Number of vertices of polygon x coordinate y coordinate x coordinate y coordinate ... Number of data on spawn points and important facilities X-coordinate of appearance position y-coordinate of appearance position x-coordinate of important facility y-coordinate of important facility X-coordinate of appearance position y-coordinate of appearance position x-coordinate of important facility y-coordinate of important facility ...

Output

Output the minimum value of damage that an unidentified creature invades to an important facility line by line for each group of spawn point and important facility.

Examples

Input

2 4 0 4 1 1 3 1 4 4 3 6 0 10 0 8 7 1 2 3 9 1

Output

2

Input

1 4 0 0 10 0 10 10 0 10 2 15 5 5 5 5 5 15 5

Output

1 1

Input

2 4 0 0 10 0 10 10 0 10 4 10 0 20 0 20 10 10 10 1 5 5 15 5

Output

0

Input

2 3 0 0 10 0 5 10 3 5 0 15 0 10 10 1 5 5 10 5

Output

2

Input

2 4 0 0 10 0 10 10 0 10 4 0 0 10 0 10 10 0 10 2 15 5 5 5 5 5 15 5

Output

2 2

inputFormat

input are integers with an absolute value of 1,000 or less.

• The number of polygons is 1 or more and 5 or less
• The number of vertices of a polygon is 3 or more and 5 or less
• The number of data of appearance points and important facilities is 1 or more and 100 or less
• A polygon refers to a polygon formed by connecting given vertices in order, and there is no self-intersection.
• Spawn points and important facilities are never on the vertices and sides of a polygon

Input

The input is given in the following format.

Number of polygons Number of vertices of polygon x coordinate y coordinate x coordinate y coordinate ... Number of vertices of polygon x coordinate y coordinate x coordinate y coordinate ... Number of data on spawn points and important facilities X-coordinate of appearance position y-coordinate of appearance position x-coordinate of important facility y-coordinate of important facility X-coordinate of appearance position y-coordinate of appearance position x-coordinate of important facility y-coordinate of important facility ...

outputFormat

Output

Output the minimum value of damage that an unidentified creature invades to an important facility line by line for each group of spawn point and important facility.

Examples

Input

2 4 0 4 1 1 3 1 4 4 3 6 0 10 0 8 7 1 2 3 9 1

Output

2

Input

1 4 0 0 10 0 10 10 0 10 2 15 5 5 5 5 5 15 5

Output

1 1

Input

2 4 0 0 10 0 10 10 0 10 4 10 0 20 0 20 10 10 10 1 5 5 15 5

Output

0

Input

2 3 0 0 10 0 5 10 3 5 0 15 0 10 10 1 5 5 10 5

Output

2

Input

2 4 0 0 10 0 10 10 0 10 4 0 0 10 0 10 10 0 10 2 15 5 5 5 5 5 15 5

Output

2 2

样例

2
4
0 4
1 1
3 1
4 4
3
6 0
10 0
8 7
1
2 3 9 1

2