CF1299B.Aerodynamic

Guy-Manuel and Thomas are going to build a polygon spaceship.

You're given a strictly convex (i. e. no three points are collinear) polygon $P$ which is defined by coordinates of its vertices. Define $P(x,y)$ as a polygon obtained by translating $P$ by vector $\overrightarrow {(x,y)}$. The picture below depicts an example of the translation:

Define $T$ as a set of points which is the union of all $P(x,y)$ such that the origin $(0,0)$ lies in $P(x,y)$ (both strictly inside and on the boundary). There is also an equivalent definition: a point $(x,y)$ lies in $T$ only if there are two points $A,B$ in $P$ such that $\overrightarrow {AB} = \overrightarrow {(x,y)}$. One can prove $T$ is a polygon too. For example, if $P$ is a regular triangle then $T$ is a regular hexagon. At the picture below $P$ is drawn in black and some $P(x,y)$ which contain the origin are drawn in colored:

The spaceship has the best aerodynamic performance if $P$ and $T$ are similar. Your task is to check whether the polygons $P$ and $T$ are similar.

Guy-Manuel 和 Thomas 将要建造一艘多边形宇宙飞船。

给定一个严格凸的（即任意三点不共线）多边形 $P$，其顶点坐标已知。定义 $P(x,y)$ 为将 $P$ 沿向量 $\overrightarrow{(x,y)}$ 平移后所得的多边形。下图展示了一个平移示例：

定义集合 $T$ 为所有满足原点 $(0,0)$ 位于 $P(x,y)$ 内（包括严格内部及边界上）的 $P(x,y)$ 的并集。另一种等价定义为：点 $(x,y)$ 属于 $T$ 当且仅当存在两点 $A,B \in P$，使得 $\overrightarrow{AB} = \overrightarrow{(x,y)}$。可以证明 $T$ 本身也是一个多边形。例如，若 $P$ 是一个正三角形，则 $T$ 是一个正六边形。下图中，黑色绘制的是 $P$，若干个包含原点的 $P(x,y)$ 以不同颜色绘制：

当 $P$ 与 $T$ 相似时，该宇宙飞船具有最佳空气动力学性能。你的任务是判断多边形 $P$ 与 $T$ 是否相似。

The first line of input will contain a single integer $n$ ($3 \le n \le 10^5$) — the number of points.

The $i$-th of the next $n$ lines contains two integers $x_i, y_i$ ($|x_i|, |y_i| \le 10^9$), denoting the coordinates of the $i$-th vertex.

It is guaranteed that these points are listed in counterclockwise order and these points form a strictly convex polygon.

输入的第一行包含一个整数 $n$（$3 \le n \le 10^5$）—— 表示点的数量。

接下来的 $n$ 行中，第 $i$ 行包含两个整数 $x_i, y_i$（$|x_i|, |y_i| \le 10^9$），表示第 $i$ 个顶点的坐标。

保证这些点按逆时针顺序给出，且构成一个严格凸多边形。

Output "YES" in a separate line, if $P$ and $T$ are similar. Otherwise, output "NO" in a separate line. You can print each letter in any case (upper or lower).

如果 $P$ 和 $T$ 相似，则在单独一行输出 "YES"；否则，在单独一行输出 "NO"。每个字母可使用大写或小写形式输出。

The following image shows the first sample: both $P$ and $T$ are squares. The second sample was shown in the statements.

下图展示了第一个样例：$P$ 和 $T$ 均为正方形。第二个样例已在题目描述中给出。