Goldbach's Conjecture

Find every distinct way to write a given even number as a sum of two primes. A prime is an integer greater than 1 that is divisible only by 1 and by itself. The smallest primes are 2, 3, 5, 7, 11, and so on.

The German mathematician Goldbach (Christian Goldbach, 1690-1764) conjectured that every even number greater than 2 can be written as a sum of two primes. Nobody has proved the conjecture and nobody has found a counterexample. You may assume it holds for every number this problem asks about.

One even number can have several such representations. For example, 26 is 3 + 23, 7 + 19, and 13 + 13.

The first line has an integer $n$, the number of test cases. ($1 \le n \le 100$)

Each of the next $n$ lines has one even number $x$. ($4 \le x \le 32000$)

For each test case, first print one line in the form x has k representation(s), where $x$ is the given even number and $k$ is the number of distinct ways to write $x$ as a sum of two primes. Print representation(s) exactly like that even when $k$ is 1.

Then print each representation on its own line in the form a+b, in increasing order of the first addend $a$. The first addend must always be less than or equal to the second, so no representation appears twice.

Print a blank line between consecutive test cases.