Description

There are n points and m triangles in the plane. For each triangle, please compute the common area of the triangle and the polygon, which is the convex hull of the given n points:

Input

The first line of the input contains an integer number n, which is the number of the points. The follow n lines contain two integer numbers x_i and y_i, which describes the coordinate of each point. Then the next line contains an integer number m, which is the number of triangles, and there are 6 integer numbers ax_i, ay_i, bx_i, by_i, cx_i and cy_i in each of the follow m lines, which describe the coordinate of vertices in a triangle.

We guarantee that n and m do not exceed 100000. The absolute value of integers appear above is not larger than 20000000.

Output

For each triangle in input, output the common area of the triangle and the convex hull in a single line. The result should be rounded to nearest integer number.

5
0 0
0 2
2 0
2 2
1 1
2
3 3 3 4 4 3
2 0 2 4 0 2

0
2

Source

POJ Monthly--2006.06.25, Long Fan