Algorithms and Data Structures

Paint with colors

You’d like to paint a stripe with 3 colors - red, blue, and orange. You paint each unit with one color. To make it more eye-catching, you’ve decided to follow these rules:
  1. You cannot place the same colors next to each other
  1. The blue color should always be placed between the red and the orange or the orange and the red.
How many different stripes can you obtain if there are n units in the whole stripe?

Input

The input contains a single integer n (1 ≤ n ≤ ).

Output

The program should print the number of different stripes you can obtain. As the answer can be large, you are asked to print the answer modulo .

Examples

Input
Output
1
2
2
2
3
4

Explanation

  1. (red) (orange)
  1. (red, orange) (orange, red)
  1. (orange, red, orange) (red, blue, orange) (orange, blue, red) (red, orange, red)
 

Constraints

Time limit: 2.4 seconds

Memory limit: 512 MB

Output limit: 1 MB

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