题目描述

You are given a polygon $P$ with $N$ vertices, which is not necessarily convex. Initially, let $Q = P$. You can perform the following operation on $Q$ any number of times:

• Choose a line segment of positive length lying on the boundary of $Q$, and let $Q'$ be the figure obtained by reflecting $Q$ across the line containing this segment.
• If the interiors of $Q$ and $Q'$ intersect, the process ends immediately.
• Otherwise, update $Q$ to the union of $Q$ and $Q'$.

Determine whether the operation can be repeated indefinitely. In other words, determine whether it is possible to perform the operation at least $M$ times for every positive integer $M$.

:::align{center} :::

输入格式

The input consists of multiple test cases.

The first line contains an integer $T$ ($1 \leq T \leq 100$), representing the number of test cases.

$T$ test cases follow. Each test case is given in the following format.

$$\begin{aligned} & N \\ & x_{1} \ y_{1} \\ & \vdots \\ & x_{N} \ y_{N} \end{aligned}$$

For each test case, the first line contains an integer $N$ ($3 \leq N \leq 10\,000$), representing the number of vertices of the polygon.

Each of the following $N$ lines contains two integers $x_i$ and $y_i$, representing that the $i$-th vertex of polygon $P$ has coordinates $(x_i, y_i)$. These points satisfy the following conditions:

• $-10^{9} \leq x_{i}, y_{i} \leq 10^{9}$
• The vertices of polygon $P$ are given in counterclockwise order.
• $P$ is a simple polygon; in particular, no interior angle equals $180^{\circ}$.

输出格式

Output $T$ lines. For each test case, output "Yes" if it is possible to perform the operation infinitely many times, and "No" otherwise.

2
4
0 0
1 0
1 1
0 1
6
11 6
19 10
9 10
5 18
5 3
15 -2

Yes
No