FIB6

The Fibonacci sequence is defined by the following recursive formula:

$$\displaystyle F_0 = 0, F_1 = 1, F_{n+2} = F_{n+1} + F_n $$

The first terms of the sequence are: ~0~, ~1~, ~1~, ~2~, ~3~, ~5~, ~8~, ~13~, ~21~, ~34~, ~55~, ~89~, ~144~, ~233~, ~377~, ~610~, ~987~, ~1597~ and so on.

You are given a positive integer ~X~. You need to determine if ~X~ can be expressed as the sum of at most six Fibonacci numbers, not necessarily distinct. If there are multiple ways to achieve this, you should find a solution with the smallest possible number of addends.

Input

The input consists of a single line containing a single integer ~X~.

Output

The output should consist of a single line containing:

• Either the word "~impossible~", without the quotes, if ~X~ cannot be written as the sum of at most six Fibonacci numbers,
• Or an integer ~N~ between ~1~ and ~6~, inclusive, followed by ~N~ Fibonacci numbers separated by a single space, such that their sum is equal to ~X~ and ~N~ is minimized. If there are multiple correct solutions with the minimum number of addends, you can output any of them. All numbers in the line should be separated in pairs by a single space.

Constraints

~1 \le X \le 1.000.000.000~.
Execution time limit: 1 sec.
Memory limit: 16 MB.

Examples of Input - Output

1st

STDIN (fib6.in)

42

STDOUT (fib6.out)

2 8 34

2nd

STDIN (fib6.in)

166418946

STDOUT (fib6.out)

3 6765 832040 165580141

3d

STDIN (fib6.in)

649814661

STDOUT (fib6.out)

impossible