The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Beta Round 51 |
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Finished |

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geometry

two pointers

*2500

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E. Very simple problem

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a convex polygon. Count, please, the number of triangles that contain a given point in the plane and their vertices are the vertices of the polygon. It is guaranteed, that the point doesn't lie on the sides and the diagonals of the polygon.

Input

The first line contains integer *n* — the number of vertices of the polygon (3 ≤ *n* ≤ 100000). The polygon description is following: *n* lines containing coordinates of the vertices in clockwise order (integer *x* and *y* not greater than 10^{9} by absolute value). It is guaranteed that the given polygon is nondegenerate and convex (no three points lie on the same line).

The next line contains integer *t* (1 ≤ *t* ≤ 20) — the number of points which you should count the answer for. It is followed by *t* lines with coordinates of the points (integer *x* and *y* not greater than 10^{9} by absolute value).

Output

The output should contain *t* integer numbers, each on a separate line, where *i*-th number is the answer for the *i*-th point.

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).

Examples

Input

4

5 0

0 0

0 5

5 5

1

1 3

Output

2

Input

3

0 0

0 5

5 0

2

1 1

10 10

Output

1

0

Input

5

7 6

6 3

4 1

1 2

2 4

4

3 3

2 3

5 5

4 2

Output

5

3

3

4

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