CSES - Point in Polygon
• 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