Blocking the View

Anton is developing a 2D graphics engine for video games. It has to reach the market. To display objects correctly, he needs to determine whether one object blocks the view to another object when the player looks in a particular direction.

For the prototype, Anton treats objects as non-intersecting segments on the plane. Segment $a$ blocks the view to segment $b$ in the direction of vector $\vec{v}$ if there are points $A$ on $a$ and $B$ on $b$ such that the vectors $\overrightarrow{AB}$ and $\vec{v}$ are co-directed. In other words, there is a point on $a$ that, if it starts moving along the direction of $\vec{v}$, would hit segment $b$.

Anton is busy looking for investors, so he asks you to implement this part of the graphics engine.

The first line of input contains an integer $n$, the number of tests that follow ($1 \le n \le 50\,000$).

Each of the following $n$ lines contains 10 integers: $ax_1$, $ay_1$, $ax_2$, $ay_2$, $bx_1$, $by_1$, $bx_2$, $by_2$, $vx$, $vy$. These are the coordinates of the endpoints of the first segment, the coordinates of the endpoints of the second segment, and the coordinates of the view direction vector. The absolute value of every coordinate is at most $10^6$. Each segment has positive length, and the direction vector $\vec{v}$ is non-zero.

For each test, print "Yes" if the first segment blocks the view to the second segment in the given direction, otherwise print "No".