Domino and Tromino Tiling

You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes. Given an integer n, return the number of ways to tile an 2 x n board. Since the answer may be very large, return it 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.

Input Format

First Parameter: An integer n

Output Format

Return a single integer

Example 1

Input: n = 3
Output: 5
Explanation: The five different ways are show above.

Example 2

Input: n = 1
Output: 1

Constraints

• 1 <= n <= 1000
• Expected Time Complexity - O(n)
• Expected Space Complexity - O(n)