Cocoa... That's Not It

Cocoa and Chino were looking for books in the library. Then Cocoa accidentally knocked over a bookshelf that held $2N+1$ books.

Luckily, each book has a number from 1 to $2N+1$ in order, so it was not hard to figure out the original order of the books on the shelf.

Cocoa and Chino agreed to split up the search. Cocoa found the $N+1$ books with odd numbers, that is, the books numbered $1, 3, \ldots, 2N+1$. Chino found the $N$ books with even numbers, that is, the books numbered $2, 4, \ldots, 2N$.

From now on, starting with Cocoa, they take turns placing the books they found, from the front. Let $A_i$ be the number of the book Cocoa places at the $i$-th position, and $B_i$ the number of the book Chino places at the $i$-th position. For every integer $1 \le i \le N$, book $A_i$ is placed in front of book $B_i$, and book $B_i$ is placed in front of book $A_{i+1}$.

Cocoa does not care much about placing books in order. So after placing a book, she picks any one of the remaining books as the next one to place.

Chino wants at least a minimal order to be kept. He checks the book Cocoa picked and places a book whose number lies between the numbers of the two books Cocoa places on either side of it.

That is, for every integer $1 \le i \le N$, either $A_i < B_i < A_{i+1}$ or $A_i > B_i > A_{i+1}$ must hold.

Write a program that tells Chino how to place the books in this way.