Coach zxxxxzzz has two sons, one of them is radical. Today Coach zxxxxzzz takes his two son to Shenyang participate in the ICPC contest.

As you know, radical is a curious boy, besides, he is curious the things around him. Every time when he meet a problem, he will always ask his father for help. And this time when they arrive at Shenyang, the problem comes to him again. And coach zxxxxzzz is tired of answer his curious but silly son, so he asks you for help. For you are the local taxi driver, you will answer the question radical asked.

The problem is -- is this one the really hotel? You are in a car and erery buildings in your GPS is described to be a Convex polygon in the dimensional coordinate system. And the local hotel is very special --- for all of them are regular polygons. A regular polygon is a Convex polygon with the same angle and the same Side length. So little radical will see one building in the taxi GPS and ask you if it is a regular polygon. And now, you are also tired of answering the boring question and want to write a program to provide yourself a correct answer.

The input may describe more than once. And when radical ask the question, your taxi is regard as ( 0, 0 ) at the dimensional coordinate system. Meanwhile, radical will point at a Convex polygon with n( 1 <= n <= 1e5 ) point.Every time you will give n+1 lines, the first line has a integers n and the next n line will tell you the xi, yi( -1e9 <= xi, yi <= 1e9), which is the position of the point, and no two points will have a same position.

For each case, output "Yes" or "No" in one line. If the Convex polygon is a regular polygon outputs "Yes", else outputs "No".