• محدودیت زمان: ۱ ثانیه
• محدودیت حافظه: ۲۵۶ مگابایت

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The contest area for the programming competition at Semnan University is a convex polygon with $n$ sides. You will be asked $q$ questions. In each question, the coordinates of a student are given, and you need to determine whether the student is inside the contest area or not.

input

The first line of input contains a positive integer $n$, representing the number of vertices of the polygon that defines the contest area in counter clockwise order.

The i-th line of the next $n$ lines contain two integers, $x_i$ and $y_i$, representing the coordinates of i-th vertex of the polygon in order.

The following line contains the integer $q$, indicating the number of students.

again In next $q$ lines, the i-th line contains two integers, $x_i$ and $y_i$, representing the coordinates of a student.

$$1 \leq n \leq 10^5$$ $$1 \leq q \leq 10^6$$ $$|x_i, y_i| \leq 10^9$$

output

For each student, print "IN" if they are within the contest area, or "OUT" if they are not.

example

sample input 1

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

sample output 1

IN
OUT