[Related](https://codegolf.stackexchange.com/questions/246025/average-ignorant-sets-of-integers).

Given a list of 3 or more positive integers, remove every number X for which there is another number Y in the list and the average of X and Y is also in the list. In other words, if X, Y, and the average of X and Y are all in the input, neither X nor Y should appear in the output.

Note: Pairs of numbers are not successively removed from the list, rather all at once. This avoids ambiguity. A pair of numbers whose average is in the list will be removed even if one or both of the numbers are already part of another such pair.

The average of two numbers is their sum divided by two.

Examples:

```
input => output
explanation

[1, 2, 3] => [2]
1 and 3 are removed because their average (2) is in the list.

[1, 2, 3, 4] => []
1 and 3 are removed because their average (2) is in the list,
2 and 4 are removed because their average (3) is in the list.

[1, 3, 4, 5] => [4]
1 and 5 are removed because their average (3) is in the list,
3 and 5 are removed because their average (4) is in the list.

[1, 5, 10, 20, 40] => [1, 5, 10, 20, 40]
No numbers are removed; No pair of numbers also has their average in the list.

[1, 5, 6, 10] => [1, 5, 6, 10]

[1, 2, 3, 4, 10, 52, 100, 200] => [10, 52, 200]

[1, 2, 3, 5, 8, 13, 21, 34] => []

```

You may assume numbers are given in ascending order with no duplicates.

[code-golf](/questions/tagged/code-golf "show questions tagged 'code-golf'") Shortest code wins.