Have an infinite collection of pieces
1 × 1, 1 × 2 and 2 × 2,
and you must completely fill a 2 × *n* rectangle.
In how many ways can you do it?

For example, this is one of the many ways for *n* = 7:

unit=1.2cm
(9,4)

(1,1)(1,0)7 (1,1)(0,1)2 (8,3)(-1,0)7 (8,3)(0,-1)2

(2,1)(0,1)2 (2,2)(1,0)1 (3,1)(0,1)1 (3,2)(1,0)1 (4,2)(0,1)1 (4,2)(1,0)1 (5,1)(0,1)2 (7,1)(0,1)2 (7,2)(1,0)1

**Input**

Input consists of several cases,
each with an *n* between 1 and 10^{4}.

**Output**

For every case,
print the number of ways to fill a 2 × *n* rectangle.
Since this number can be very large,
make the computations modulo 10^{8} + 7.

**Observation**

It may be helpful to compute a quantity similar to the one asked for in the problem.

Public test cases

**Input**

1 2 3 4 10000

**Output**

2 8 26 90 52273134

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++ Java