Seagulls over the sea
Soaring upwards, then diving down, They fly over the sea, touching the waves, And the fresh wind gives them strength In the vast blue skies from the heat…
(Lyudmila Simerenko "Seagulls over the Sea")
Seagulls over the sea... It's a delight to watch them when there aren't too many and they're not constantly flying overhead...
Seva loved observing the seagulls passing by at such times. One day, he was particularly fortunate: only 4 seagulls were flying over the sea, hunting for small fish, and the curious Seva immediately wondered: "Are all 4 seagulls currently in the same plane?"
He used ship instruments to determine the coordinates of the seagulls, but he wasn't very skilled in math. Help Seva with this task.
Input
The first line contains the number of test cases N (1 ≤ N ≤ 1000). Each of the next N lines provides the coordinates for the 4 seagulls: X_i Y_i Z_i (X_i, Y_i, Z_i ≤ |100|, 1 ≤ i ≤ 4). The seagulls can be considered as material points.
Since seagulls are not actually material points, in this problem, you should consider a seagull to belong to a plane if it is no more than 10^{-6} away from it.
Output
For each configuration of the seagulls, output a separate line with the message "Yes" (without quotes) if all 4 seagulls are in the same plane, and "No" otherwise.