Aerodynamic

题意翻译

- 给定一个由 $n$ 个点组成的**严格**（不存在三点共线）凸多边形。 - 你要将这个图形平移 $n$ 次，每次将一个顶点与原点 $(0,0)$ 重合。 - 请判断这 $n$ 个平移后的多边形除了与原点重合的点之外的点组成的多边形是否与原图形[相似](https://tinyurl.com/vp5m7vl)。 - 在读入中，保证输入的点按逆时针顺序排列，形成严格凸多边形。 - $3\le n\le 10^5$ - translate by @[ShineEternal](https://www.luogu.com.cn/user/45475)。

题目描述

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](https://tinyurl.com/vp5m7vl).

输入输出格式

输入格式

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.

输出格式

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).

输入输出样例

输入样例 #1

4
1 0
4 1
3 4
0 3

输出样例 #1

YES

输入样例 #2

3
100 86
50 0
150 0

输出样例 #2

nO

输入样例 #3

8
0 0
1 0
2 1
3 3
4 6
3 6
2 5
1 3

输出样例 #3

YES

说明

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