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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).
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Input: the integer, N (1<=N<=2^128)
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Input: the integer, N (1<=N<=2^1024)
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Output: the number of ways you can place red-colored books and blue-colored books onto the bookshelf. Since this number might be really big, output it mod 10^9+7.
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