You must have heard of Goldbach's conjecture, a well-known unsolved problem in number theory. It is stated that every even integer greater than 2 can be written as a sum of two prime numbers. Simple, yet extremely hard! No mathematician has been able to prove this conjecture for nearly 300 years. For example:

   4 = 2 + 2               14 = 3 + 11


6 = 3 + 3                  = 7 + 7

8 = 3 + 5               16 = 3 + 13

10 = 3 + 7                  = 5 + 11

 = 5 + 5               18 = 5 + 13


12 = 5 + 7                  = 7 + 11

                       ...

Let G(N) be the number of different ways to represent a number of the form 2N as a sum of two prime
numbers. As we have seen in the above examples:

            G(i) = 1, 1, 1, 2, 1, 2, 2, 2 for i = 2..9

With the definition of G(N), the Goldbach's conjecture can be stated as follows: G(N) > 0 for all
positive integers N > 1.

Given a number N, your task is to write a program to compute the following sum:

            F(N) = G(2) + G(3) + ... + G(N)