A Chocolate Manufacturer's Problem

My mama always said：Life is like a box of chocolate, you never know what you are going to get.
——From Forrest Gump


ACM is a chocolate manufacturer. Inspired by the famous quote above, recently, they are designing a new brand of chocolate named Life. Each piece of chocolate is a random simple polygon. After molding and shaping, every piece is put in a small box. Until you open the box, you will not know what you will get: a huge piece or only a tiny fraction. It is really like life and that is the reason it is named for.

However, here comes a problem. The manufacturer has to print the logo on each piece of chocolate. The logo is a circle with ‘ACM’ inside. Here is an example below. It is fortunate that the logo can be printed on the chocolate.

Now the manufacturer is asking you for help. Given the information about the chocolate shape and the radius of the logo, you need to judge whether or not there is enough space to print the logo.

The input contains no more than 20 cases, and each case is formatted as follows.
n
x₁ y₁
x₂ y₂
…
x_n y_n
r
The first line is the number of vertices of the polygon, n, which satisfies 3 ≤ n ≤ 50. Following n lines are the x- and y-coordinates of the n vertices. They are float numbers and satisfy 0 ≤ x_i ≤ 1000 and 0 ≤ y_i ≤ 1000 (i = 1, …, n). Line segments (x_i, y_i)–(x_{i+ 1} , y_{i + 1}) (i = 1, …, n) and the line segment (x_n, y_n)–(x₁, y₁) form the border of the polygon. After the description of the polygon, a float number r follows, meaning the radius of the logo( r <= 1000).
The input ends by a single zero.
You may assume that the polygon is simple, that is, its border never crosses or touches itself.

For each case, output “Yes” if the logo is able to be printed on the chocolate, otherwise output “No” instead.

3
0 0
0 1
1 0
0.28
3
0 0
0 1
1 0
0.3
0

Yes
No

Here is a picture illustrated the first case. It may be helpful for you to understand the problem.

2010 Asia Regional Hangzhou Site —— Online Contest