#215793. [JAG 2024 Summer Camp #2] Half Plane Painting

You have a 2D plane that is initially entirely white. You can perform the following operation any number of times:

• Choose a line and the half-plane bounded by this line. Then, perform one of the following actions:
  • Paint the half-plane (excluding the boundary) black.
  • Paint the half-plane and the boundary white.

You are given the polygon with vertices, which is not necessarily convex. The vertices of are given in counterclockwise order as , , , , and the -th edge of connects vertex to vertex .

Determine whether it is possible to use the aforementioned operations to paint only the interior of polygon black, leaving everything else white.

The input is given in the following format:

• The vertices of polygon are given in counterclockwise order.
• The edges of polygon do not share any points other than the vertices.
• Each internal angle of polygon is not degrees.
• All input values are integers.

If it is possible to achieve the desired state with the operations, output Yes; otherwise, output No.

样例输入 1

4
10 -5
2 -5
-7 6
-7 -8

样例输出 1

Yes

样例输入 2

12
17 1
19 3
12 10
19 17
17 19
10 12
3 19
1 17
8 10
1 3
3 1
10 8

样例输出 2

No