Description

Original source: Ulm Local, problem statement available at: POJ 2262

Goldbach's Conjecture: Every even number greater than $4$ can be expressed as the sum of two odd prime numbers. For example:

$$\begin{align} 8&= 3 + 5\\ 20&= 3 + 17 = 7 + 13\\ 42&= 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23 \end{align} $$

Your task is to verify that numbers less than $10^6$ satisfy Goldbach's Conjecture.

Input Format

Multiple test cases, each containing an integer $n$.

Input ends with $0$.

Output Format

For each test case, output in the format $n = a + b$, where $a,b$ are odd primes. If there are multiple valid pairs of $a,b$, output the pair with the largest $b-a$ difference.
If no solution exists, output Goldbach's conjecture is wrong..

Sample 1

8
20
42
0

8 = 3 + 5
20 = 3 + 17
42 = 5 + 37

Data Range and Hint

For all data, $6\le n\le 10^6$.