A bastion is the first type of fortress that relies solely on direct firepower and has no attack blind spots.
A simple non-degenerate polygon is a closed polygonal region composed of a sequence of $$$n$$$ ($$$n\ge 3$$$) vertices, satisfying the following conditions:
- The vertex sequence connects end to end, forming $$$n$$$ edges, constituting a compact closed set in the plane (including all boundary and interior points);
- The $$$n$$$ edges only meet at the vertices and do not intersect each other (adjacent edges have no other intersection points outside the common vertex);
- The $$$n$$$ vertices are distinct, not located inside any non-adjacent edges, and any three consecutive vertices are not collinear.
The bastion can be viewed as a simple non-degenerate polygon composed of $$$n$$$ points and $$$n$$$ edges. For two distinct points $$$P$$$ and $$$Q$$$ on the edges of the polygon, we define that point $$$P$$$ can directly fire at point $$$Q$$$ if and only if the line segment $$$PQ$$$ intersects the polygon only at points $$$P$$$ and $$$Q$$$. As shown in the figure below, points $$$A$$$ and $$$B$$$ cannot directly fire at point $$$X$$$, but point $$$C$$$ can. If there is a point $$$P$$$ on the edge of the polygon such that there is no other point $$$Q$$$ on the edge of the polygon for which point $$$Q$$$ can directly fire at $$$P$$$, then we call point $$$P$$$ a fire blind spot of the polygon.
We call a simple non-degenerate polygon a bastion if and only if it has at most a finite number of points that are fire blind spots. Given a simple non-degenerate polygon, please determine whether it is a bastion.
Formally, given a simple non-degenerate polygon, please determine whether there are only a finite number of points $$$P$$$ located on the edges of the polygon such that there is no other point $$$Q$$$ on the edges of the polygon for which the line segment $$$PQ$$$ intersects the polygon only at points $$$P$$$ and $$$Q$$$.
The input contains multiple test cases. The first line of the data contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) indicating the number of test cases. The following describes each test case.
The first line of each test case contains an integer $$$n$$$ ($$$3 \leq n \leq 10^5$$$), which is the number of edges of the polygon.
The next $$$n$$$ lines each contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^9 \leq x_i, y_i \leq 10^9$$$), describing a vertex of the polygon.
The input data guarantees that a simple non-degenerate polygon is formed. The vertices are given in counterclockwise order, that is, after traversing all the vertices in order, it rotates exactly $$$360^\circ$$$ counterclockwise. Connect edges in sequence according to the input order of the vertices (the $$$i$$$-th vertex is connected to the $$$(i + 1)$$$-th vertex, and the $$$n$$$-th vertex is connected back to the $$$1$$$-st vertex).
It is guaranteed that the sum of $$$n$$$ for all test cases does not exceed $$$2 \times 10^5$$$.
For each test case, output a single line containing a string. If the polygon is a bastion, output YES; otherwise, output NO. The answer is case insensitive.
2207 59 513 135 95 7-5 7-5 9-13 13-9 5-7 5-7 -5-9 -5-13 -13-5 -9-5 -75 -75 -913 -139 -57 -541 1-1 1-1 -11 -1
YES NO
