- Time limit: 1.00 s
- Memory limit: 512 MB
You are given a polygon of n vertices and a list of m points. Your task is to determine for each point if it is inside, outside or on the boundary of the polygon.
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 ith 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
Example
Input:
4 3 1 1 4 2 3 5 1 4 2 3 3 1 1 3
Output:
INSIDE OUTSIDE BOUNDARY