+ محدودیت زمان: ۱ ثانیه + محدودیت حافظه: ۲۵۶ مگابایت ---------- 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 ```

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