- Time limit: 1.00 s
- Memory limit: 512 MB
The polygon consists of $n$ vertices $(x_1,y_1),(x_2,y_2),\dots,(x_n,y_n)$. The vertices $(x_i,y_i)$ and $(x_{i+1},y_{i+1})$ are adjacent for $i=1,2,\dots,n-1$, and the vertices $(x_1,y_1)$ and $(x_n,y_n)$ are also adjacent.
Input
The first input line has two integers $n$ and $m$: the number of vertices in the polygon and the number of points.
After this, there are $n$ lines that describe the polygon. The $i$th such line has two integers $x_i$ and $y_i$.
You may assume that the polygon is simple, i.e., it does not intersect itself.
Finally, there are $m$ lines that describe the points. Each line has two integers $x$ and $y$.
Output
For each point, print "INSIDE", "OUTSIDE" or "BOUNDARY".
Constraints
- $3 \le n,m \le 1000$
- $1 \le m \le 1000$
- $-10^9 \le x_i, y_i \le 10^9$
- $-10^9 \le x, y \le 10^9$
Input:
4 3
1 1
4 2
3 5
1 4
2 3
3 1
1 3
Output:
INSIDE
OUTSIDE
BOUNDARY