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Tiling With Dominoes

Problem Description

Given an integer A you have to find the number of ways to fill a 3 x A board with 2 x 1 dominoes.

Return the answer modulo 109 + 7 .


  • See the sample explanation for better understanding.

  • Problem Constraints

    1 <= A <= 105

    Input Format

    First and only argument is an integer A.

    Output Format

    Return an integer denoting the number of ways to fill a 3 x A board with 2 x 1 dominoes with modulo 109 + 7.

    Example Input

    Input 1:


    Input 2:


    Example Output

    Output 1:


    Output 2:


    Example Explanation

    Explanation 1:

     Following are all the 3 possible ways to fill up a 3 x 2 board.

    Explanation 2:

     Not a even a single way exists to completely fill the grid of size 3 x 1.

    NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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