Problem Statement
You have been given a board where there are '2' rows and 'N' columns. You have an infinite supply of 2x1 tiles, and you can place a tile in the following ways:
1. Horizontally as 1x2 tile 2. Vertically as 2x1 tile
Count the number of ways to tile the given board using the available tiles.
Note :
The number of ways might be large so output your answer modulo 10^9 + 7.
Here is an example of tile and board for 'N' = 4 :
Input Format :
The first and only line of each test case contains an Integer 'N' which denotes the size of the board, i.e. '2' rows and 'N' columns.
Output Format :
For each test case, print the number of ways to tile the board modulo 10^9 + 7.
Note: You are not required to print the output explicitly, You just need to implement the function.
Constraints :
1 <= N <= 10^18 Where 'N' is the number of columns in the board.
There are three ways for a 2*3 board,:
1. Place all 3 tiles vertically.
2. Place first tile vertically and remaining 2 tiles horizontally.
3. Place first 2 tiles horizontally and remaining tiles vertically.