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** `109 + 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 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`


def is_ideal_permutation(nums):
    for i, num in enumerate(nums):
        if abs(num - i) > 1:
            return False
    return True
