Problem G

**Couple-Bachelor-Spinster Numbers**

**Input: **standard input

**Output: **standard output

**Time Limit:** 2 seconds

** **

Can any number be expressed
as a subtraction of two squares? The numbers, which can be expressed in such a
way, are called **square-couple** numbers. Your job is to find out

a)
If a number is **square
couple **number.

b)
If the number
is **square couple **then find that format.

c)
Find out how
many square couple numbers are there within a certain range (including the
terminal numbers).

** **

**Input**

Each set of input is given in a single line. Each input set may contain one or two signed 32 bit integer numbers. Input is terminated by end of file.

**Output**

If there is only a single number **N**
in a single line then print two non-negative integer numbers **a** and **b,**
such that **a*a-b*b = N**. If the number cannot be expressed in such a
format then print the line **“Bachelor Number.”** in a single line if such
number is even and print the line **“Spinster Number.”** if the number is
odd.

If there are two numbers **n1 **and
**n2 **in the input then print how many bachelor numbers are within **n1 **and
**n2 **(including **n1** and **n2**). Note that (**n1**≤**n2**
and (**n2**- **n1**)<=1000000).

** **

**Sample Input:**

12

3

**Sample
Output:**

4 2

2 1

“If all the sides of a cube
were identical, how could we tell which side is face up?”