Problem Statement

The vertices of a convex N-gon P in an xy-plane are given as $(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N)$ in the counterclockwise order. (Here, the positive direction of the x-axis is right, and the positive direction of the y-axis is up.)
Based on this polygon P, we consider $M convex N-gons P_1, P_2, \ldots, P_M$.
For $i = 1, 2, \ldots, M$, the polygon P_i is obtained by shifting P in the positive direction of the x-axis by u_i and in the positive direction of the y-axis by v_i. In other words, P_i is a convex N-gon whose vertices are $(x_1+u_i, y_1+v_i), (x_2+u_i, y_2+v_i), \ldots, (x_N+u_i, y_N+v_i)$.
For each of $Q points (a_1, b_1), (a_2, b_2), \ldots, (a_Q, b_Q)$,
determine if "the point is contained in all of the $M polygons P_1, P_2, \ldots, P_M$."
Here, we regard a point is also contained in a polygon if the point is on the polygon's boundary.

Input

Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
$\vdots$
x_N y_N
M
u_1 v_1
u_2 v_2
$\vdots$
u_M v_M
Q
a_1 b_1
a_2 b_2
$\vdots$
a_Q b_Q

Output

Print Q lines. For $i = 1, 2, \ldots, Q$, the i-th line should contain Yes if point (a_i, b_i) is contained in all of the $M polygons P_1, P_2, \ldots, P_M$; it should contain No otherwise.

Constraints

• $3 \leq N \leq 50$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq Q \leq 2 \times 10^5$
• -$10^8 \leq x_i, y_i \leq 10^8$
• -$10^8 \leq u_i, v_i \leq 10^8$
• -$10^8 \leq a_i, b_i \leq 10^8$
• All values in input are integers.
• $(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N) forms a convex N-gon$ in the counterclockwise order.
• Each interior angle of the polygon P is less than 180 degrees.

Sample Input 1

5
-2 -3
0 -2
1 0
0 2
-2 1
2
0 1
1 0
6
0 0
1 0
0 1
1 1
-1 -1
-1 -2

Sample Output 1

Yes
No
Yes
Yes
Yes
No

Polygon P is a pentagon (5-gon) whose vertices are (-2, -3), (0, -2), (1, 0), (0, 2), (-2, 1).

• Polygon P_1 is a pentagon (5-gon) obtained by shifting P in the positive direction of the x-axis by 0 and in the positive direction of the y-axis by 1, so its vertices are (-2, -2), (0, -1), (1, 1), (0, 3), (-2, 2).
• Polygon P_2 is a pentagon (5-gon) obtained by shifting P in the positive direction of the x-axis by 1 and in the positive direction of the y-axis by 0, so its vertices are (-1, -3), (1, -2), (2, 0), (1, 2), (-1, 1).

Thus, the following 6 lines should be printed.

• The 1-st line should be Yes because (a_1, b_1) = (0, 0) is contained in both P_1 and P_2.
• The 2-nd line should be No because (a_2, b_2) = (1, 0) is contained in P_2 but not in P_1.
• The 3-rd line should be Yes because (a_3, b_3) = (0, 1) is contained in both P_1 and P_2.
• The 4-th line should be Yes because (a_4, b_4) = (1, 1) is contained in both P_1 and P_2.
• The 5-th line should be Yes because (a_5, b_5) = (-1, -1) is contained in both P_1 and P_2.
• The 6-th line should be No because (a_6, b_6) = (-1, -2) is contained in P_2 but not in P_1.

Note that a point on the boundary of a polygon is also considered to be contained in the polygon.

Sample Input 2

10
45 100
-60 98
-95 62
-95 28
-78 -41
-54 -92
-8 -99
87 -94
98 23
87 91
5
-57 -40
-21 -67
25 39
-30 25
39 -20
16
4 5
-34 -8
-63 53
78 84
19 -16
64 9
-13 7
13 53
-20 4
2 -7
3 18
-12 10
-69 -93
2 9
27 64
-92 -100

Sample Output 2

Yes
Yes
No
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
No
Yes
No
No

见题面 Input 部分

见题面 Output 部分