Description

Goldbach's conjecture reads as follows:

Whichever one is greater than Even numbers of 4 can be split into the sum of two odd prime numbers.

For an example:

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

Your task is to verify that a number less than $10^6$ satisfies the Goldbach conjecture.

Format

Input

The input contains multiple sets of data.

Each set of data occupies a row and contains an even number of $n(n \le 10^6)$. The input ends with $0$.

Output

For each set of data, the output is of the form n = a + b, where $a,b$ are odd primes. If there are multiple sets of $a,b$ that meet the conditions, the output is the largest group of $b−a$.

If there is no solution, the output Goldbach's conjecture is wrong.

Samples

8
20
42
0

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