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One of the oldest and best-known unsolved problems in Mathematics is Goldbach's conjecture. It states that every even integer greater than 2 can be expressed as the sum of two primes. The expression of a given even number as a sum of two primes is called a Goldbach partition of that number. The following are examples of Goldbach partitions for some even numbers:
Your task is to write a program to check the number of Goldbach partitions for a given even number.
An even integer n (4 <= n <= 10000000) will be given in each input line. The end of input is indicated by a number 0.
For each line of input, print an integer in one line showing the number of Golbach partitions.
4 10 100 0
1 2 6