We have two types of tiles: a 2x1 domino shape, and an "L" tromino shape. These shapes may be rotated. XX <- domino XX <- "L" tromino X Given N, how many ways are there to tile a 2 x N board? Return your answer modulo 10^9 + 7. (In a tiling, every square must be covered by a tile. Two tilings are different if and only if there are two 4-directionally adjacent cells on the board such that exactly one of the tilings has both squares occupied by a tile.) Example: Input: 3 Output: 5 Explanation: The five different ways are listed below, different letters indicates different tiles: XYZ XXZ XYY XXY XYY XYZ YYZ XZZ XYY XXY Note: N will be in range [1, 1000].