# April 16 Contest

# Inscribed Circle

The circle is **inscribed** in a polygon, if it has a point of contact with each side of the polygon.

Determine is it possible to inscribe a circle into a given convex polygon, and if the answer is positive, find the coordinates of its center and radius.

#### Input

The first line contains the number of vertices of the polygon **n** (**3** ≤ **n** ≤ **8**). The following **n** lines contain the coordinates of the vertices of the polygon in order circumvent anti-clockwise, each line contains two integers: `x`

and _{i}`y`

that do not exceed _{i}**1000** by absolute value.

#### Output

If an inscribed circle in polygon exist, print in the first line the word **YES**, otherwise print the word **NO**. If answer is yes, print in the second row the coordinates of the circle center and its radius. Print the answer with accuracy `10`

.^{-6}

4 0 0 1 0 1 1 0 1

YES 0.500000 0.500000 0.500000

4 0 0 1 0 1 2 0 2

NO