Straightening a bent wire

Steel maker P ran into trouble. Something went wrong on the line, and a wire that used to be straight now has right-angle bends all over it. The wire has to be pulled straight again.

Only one joint of the wire can be opened at a time, and the wire must not collide with itself while a joint is opening. Contact at a single point already counts as a collision. Opening a joint means the two edges meeting at that joint end up on one straight line. The joints are opened starting from one end of the wire, following the order in which they are connected, and that starting end is given in the input.

The figure below shows a wire lying in the plane, with its joints opened one after another from one end until the wire finally becomes a straight line.

Input is read from standard input. The first line holds the number of test cases $T$ ($1 \le T \le 20$).

The first line of each test case holds the number of joints of the wire, counting both endpoints. The next line holds the $x$ and $y$ coordinate of every joint in connected order starting from one end, separated by single spaces. Every coordinate is an integer with $0 \le x \le 1000$ and $0 \le y \le 1000$. The whole wire is at most $10000$ long, and there are at most $1000$ joints. Every edge of the wire is parallel to a coordinate axis.

The joints are opened in the order the coordinates are given. Coordinates are no longer restricted once a joint has been opened. In the starting state, with nothing opened yet, the wire has no collision, and it has no joint that is bent by anything other than a right angle.

Output is written to standard output. For each test case, print YES if opening the joints in the given coordinate order finally pulls the wire into a straight line, and NO otherwise, one answer per line.