Annie has a very long line of cards, numbered from 1 to $n$, such that every odd card is face-up and every even card is face-down. The only way she can modify the line is by taking any segment of consecutive cards that has an even number of face-up cards and reversing the order of the cards in this segment (note that none of the cards are flipped).
As a neat freak, she wants to get all the face-up cards to be next to each other. Tell her how to achieve this or show that it is impossible if:
- $n = 2014$
- $n = 2016$