The border of Oopse is a polygon consisting of n straight segments. The vertices of the fence are in order (x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n).

The tax officer of Oopse needs to know for each m houses if they reside in Oopse or not. Unfortunately the officer is bad at reading maps and needs your help.

Input

The first line contains a single integer, n, the number of line segments describing the border of Oopse.

The next n lines each consist of two integers x_i and y_i: the position of i^{th} vertex is (x_i, y_i).

Then the input contains a single integer, m, the number of houses the tax officer needs to query.

The rest m lines each consist of two integers x_k and y_k: the position of k^{th} house is (x_k, y_k).

Output

For each house print a single line consisting either of "inside" (the house resides inside Oopse), "border" (the house resides on the border of Oopse) or "outside" (the house resides outside Oopse).

Limits

• 3 \le n \le 1000
• 1 \le m \le 100
• each coordinate is in the range -10^6 \ldots 10^6

Example

Input:

5
2 1
3 2
5 1
5 4
2 5
3
3 4
4 5
5 3

Output:

inside
outside
border