As we know, in 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture:
Every even number greater than 4 can be written as the sum of two odd prime numbers.
There are various decompose methods for a certain number. The maximal difference of these two prime numbers is called MDP. For example, 20 = 3+17 = 7+ 13, both of the equation satisfies the Goldbach rule. Here the maximal difference is 17 – 3 =14, so the MDP of 20 is 14.
Your task is to calculate all the MDP of even number between 6 and 2012 inclusive. Output these numbers and their MDP order by MDP in ascending sort order. If the MDP is same, order by their value.
Input
This problem has no input.
Output
You should output the even number and it’s MDP in one line (separated by a space) order by the condition above.
Sample Output
6 0……100 94……2012 1986……
Hint:Not all the numbers are listed in the sample. There are just some examples. The ellipsis expresses what you should calculate.