Internal point

Given a strictly convex n-polygon and k points.

For each point you need to determine where she is - inside, on the border, or outside.

Input

Number n (3 ≤ n ≤ 10^5). Then given n points - the vertices of the polygon.

Number k (0 ≤ k ≤ 10^5). Then given k points - the queries.

All coordinates are integer, not exceeding 10^7 by absolute value.

Output

For each query print on a separate line INSIDE, BORDER or OUTSIDE.

Examples