Problem Statement

To enjoy virtual space, it is essential to avoid collisions with objects in the real world.

Real Wanyu-kun is currently in a room on a sufficiently large two-dimensional plane. When he decides on three distinct coordinates $(X_A,Y_A),(X_B,Y_B),(X_C,Y_C)$, the circle of minimum radius containing those three points is defined as the play area.

There are currently $Q$ pieces of luggage in the room, placed at the coordinates $(X_i,Y_i)$ respectively.

Luggage inside the play area must be cleared away, so answer with Yes or No whether each piece needs to be cleared away.

For both the luggage and the coordinates defining the play area, points on the circumference are considered to be contained in the circle.

Input

$Q$
$X_A\ Y_A\ X_B\ Y_B\ X_C\ Y_C\ $
$X_1\ Y_1$
$X_2\ Y_2$
$\vdots$
$X_Q\ Y_Q$

• All inputs are integers
• $1\le Q \le 2\times 10^5$
• $|X_A|,|X_B|,|X_C|,|Y_A|,|Y_B|,|Y_C|,|X_i|,|Y_i|\le 10^4$
• $(X_A,Y_A),(X_B,Y_B),(X_C,Y_C)$ are all distinct

Output

For each of the $Q$ pieces of luggage, output Yes if it needs to be cleared away and No otherwise, separated by newlines.

Sample

Sample 1

Input

5
1 0 -1 0 0 2
0 1
0 2
0 3
2 2
0 -1

Output

Yes
Yes
No
No
No

The arrangement is shown in the figure below. $(X_A,Y_A),(X_B,Y_B),(X_C,Y_C)$ are the red points, the blue line is the play area, and the luggage locations are the green points.

$(0,1)$ is inside this circle, so output Yes.

$(0,2)$ is on the circumference, which also counts as inside this circle, so output Yes.

$(2,2)$ is not inside this circle, so output No.

Sample 2

Input

3
-1 0 0 0 1 0
0 1
0 -1
1 1

Output

Yes
Yes
No

Note that the play area is the circle of minimum radius containing the three points.

5
0 0 6 0 0 8
6 8
7 7
7 1
-1 7
-1 1

Yes
Yes
Yes
Yes
Yes