Your librarian has a 2-row bookshelf that can contain N books in each row. She wants to know the number of ways that she can fill the bookshelf with red-colored books and blue-colored books such that no 2 red-colored books are adjacent to each other (horizontally or vertically).
Input: the integer, N (1<=N<=2^1024)
Output: the number of ways you can place red-colored books and blue-colored books onto a N-column bookshelf. Since this number might be really big, output it mod 10^9+7.
Example: Input: 2
Your valid bookshelf layouts are:
BB
BB
BB
BR
BR
BB
RB
BB
BB
RB
RB
BR
BR
RB
Therefore, Output: 7