Problem Statement

There is a convex N-gon S in the two-dimensional coordinate plane where the positive x-axis points to the right and the positive y-axis points upward. The vertices of S have the coordinates $(X_1,Y_1),\ldots,(X_N,Y_N)$ in counter-clockwise order.
For each of Q points (A_i,B_i), answer the following question: is that point inside or outside or on the boundary of S?

Input

The input is given from Standard Input in the following format:
N
X_1 Y_1
$\vdots$
X_N Y_N
Q
A_1 B_1
$\vdots$
A_Q B_Q

Output

Print Q lines. The i-th line should contain IN if (A_i,B_i) is inside S (and not on the boundary), OUT if it is outside S (and not on the boundary), and ON if it is on the boundary of S.

Constraints

• $3 \leq N \leq 2\times 10^5$
• $1 \leq Q \leq 2\times 10^5$
• -$10^9 \leq X_i,Y_i,A_i,B_i \leq 10^9$
• S is a strictly convex N-gon. That is, its interior angles are all less than 180 degrees.
• $(X_1,Y_1),\ldots,(X_N,Y_N)$ are the vertices of S in counter-clockwise order.
• All values in the input are integers.

Sample Input 1

4
0 4
-2 2
-1 0
3 1
3
-1 3
0 2
2 0

Sample Output 1

ON
IN
OUT

The figure below shows S and the given three points. The first point is on the boundary of S, the second is inside S, and the third is outside S.

Sample Input 2

3
0 0
1 0
0 1
3
0 0
1 0
0 1

Sample Output 2

ON
ON
ON

见题面 Input 部分

见题面 Output 部分